The Start of Dark Energy and the limits of the Universe

[bangstrom]

Your observer has no external source of measurement so how is she to tell if the blue lines are getting longer or if the red squares are getting smaller?

To follow up on the above question. Well, if the red cubes are to represent something real, they must be galaxy clusters. Now astronomers do not measure the redshift of the clusters directly, but rather the redshifts of the Ceiphed Variables stars and Type Ia Supernovae in them. Using these as 'standard candles' in the astronomical distance ladder, their distances can be determined and hence we can check out Hubble's law and determine Hubble's constant. Using Hubble's constant we can determine the distance to any distant type 1a supernova detected to a good accuracy.

I have written something on the distance ladder on my website page: http://www.einsteins-theory-of-relativity-4engineers.com/the-expanding-universe.html. For details, read the pdf linked from there.This was written in the late 1990's. Accuracies have improved considerably over the last 2 decades, but the principles remained the same.

Hence real life astronomy rules out the possibility of "red squares getting smaller of redder"...

In the red square model of shrinking matter, the light from 1a supernova becomes redder and the duration of their luminosity becomes longer because the rate of time was slower in the distant past than at present. The red cubes represent something real and that is the entire material world from atomic scales to galaxy clusters. As atoms grow smaller, their spin rates increase resulting in a global quickening of time as demonstrated by the example of the spinning ice skater. The shrinking red square model is one of a quickening rate of time while the lengthening blue bar model is one of expanding space. The Hubble constant based on the measurement of redshifting is equivalent in both models.

If space is expanding while time remains the same, that would make c a variable so time must necessarily quicken as space expands if c is to remain as a given constant in the model. Likewise in the model of shrinking red squares. If time quickens while space remains the same, this would also make c a variable.

These problems in both models can be dealt with mathematically by the use of comoving coordinates which allows us to consider either expanding space or quickening time as single elements of change. Either way, this makes both models appear artificial because the approach lacks symmetry.

A more symmetrical model would be a lattice model where space expands while time quickens in equal proportions. In this case, the blue bars would be growing longer while the red squares contract. This model, like many alternatives to the Standard BB would be a model in which there is no method for accurately determining the size or age of the universe other than by direct observation.

Another consideration can be drawn from Edwin Abbot’s classic book “Flatland” where he mentions the example of a sphere from beyond the 2D plane of Flatland crossing the Flatlander's 2D world and all they see is a circle with an expanding radius that comes from nowhere, expands, contracts, and disappears.

This is analogous to the case of a 4D sphere becoming apparent in our 3D world where we are within the 4D hypersphere but observing only a 3D expansion/contraction with no way of determining whether the change we observe is due to the expansion of space or the contraction of all material within a universe of constant radius- or any combination of the two. The take away from this is that we must not confuse cosmic expansion with the familiar expansion of an explosion in 3D space that throws ejecta into pre-existing space and expands by inertia. In expansion models, the universe expands by space itself expanding and this is a much different scenario and it is not inertia driven.

[BurtJordaan]

One thing that is certain: the determination of the cosmic age by near and far observation is presently way easier and more accurate than stellar/cluster age determination. It seems to me that the "Old Universe" idea is about as dead in the water as the "Young Earth" idea.

[Positor]

In the red square model of shrinking matter, the light from 1a supernova becomes redder and the duration of their luminosity becomes longer because the rate of time was slower in the distant past than at present.

Can someone please explain to a layman like me what it means to say that the 'rate of time' changes. How can time's 'speed' be measured, other than with reference to time itself? Are there two types of time, whereby a second of one type can be unequal to a second of the other type?

Also: are the expanding-space and 'quickening-time' explanations equivalent, or can one be objectively true and the other false? Is there a possible (or hypothetical) experiment which could decide the matter? Or can Ockham's Razor be used (i.e. one explanation would require many coincidences and/or unexplained phenomena, and the other would not)?

[BurtJordaan]

The WMAP satellite data did accord with Harrison’s prediction of a slower Hubble expansion and I expected Harrison to comment on it saying that they were observing the true rate of Hubble expansion rather than evidence for an accelerated expansion but, as far as I know, he was completely silent on the matter.

No, it did not. WMAP data gave an equivocal Ho of 69.8 km/s/Mpc, which is about 7 times larger than what Harrison postulated. The WMAP cosmic age was pinned at 13.766 billion years.

My guess is that Harrison stayed silent because he realized the error of his postulate. At WMAP's time the cosmic distance ladder was already a very refined piece of work and cosmological redshift was shown to be expansion driven.

And the LCDM model has nothing to do with Guth's inflation. All LCDM does is to work backwards from our present day observations to the time of the CMB radiation's release - and everything fits, even the age of clusters and stars. The small apparent discrepancies that do remain are most likely with star formation models, local inhomogeneity etc, not with LCDM.

Also, if you take WMAP/Planck data and you disallow dark energy (i.e. take a zero vacuum energy density), the age drops down to below 10 billion years, which would be a problem. But then, we do observe the accelerated expansion. We don't have to view it as dark energy, we can just plot all observed values backwards, near and far, and we end up with around 14 billion years before everything is clumped tightly together...

[Faradave]

~ Optional Aside ~

Can someone please explain to a layman like me what it means to say that the 'rate of time' changes.

I find it helpful to think in terms of relative "aging" rather than "time". The aging of the universe makes a good universal reference, if one accepts that: nothing in the universe is older than the universe. Thus, the "future" always implies the future of the universe.

Allowing Einstein's exhaustively verified postulate of an finite, constant, universal and invariant speed limit, we find ∆x/∆t = c = c' = ∆x'/∆t'. In this expression, "time dilation" is better interpreted as "aging contraction", which varies identically with "length contraction", required to maintain the ratio c.

Wikipedia shows spacetime coordinates of a relatively moving frame (') with the scale of the temporal and spatial coordinates identically dilated. It then takes "longer" for a second to pass in the "moving" frame so: "moving clocks run slow".

This is verified, to the limits of accuracy, by observing the decay half lives (i.e. rates) of an unstable substance in relatively moving frames.

I'm personally most comfortable with a curved-space, radial-time model, which accommodates independent aging and non-aging paths to the future. The latter corresponds to speed c, consistent with Relativity's non-aging of light. It also explains c as the tangent speed limit, enforced by inherently unidirectional time.


In a curved-space, radial-time model (left), from any 4D event (p), a limited range of trajectories exist (center). Aging is maximal in the rest frame, decreasing with speed (v₁ & v₂) to complete non-aging at speed limit c (v_max). v_x is prohibited as a violation of unidirectional time. In the rest frame of speed v₁ (right), the cosmos is contracted in the direction of motion but the tangent speed limit persists. This expresses the invariance of c.

Note that unencumbered G and EM signals propagate at speed c. Thus, any body experiencing EM or G forces (i.e. accelerations by F = ma) will be 'pushed' toward a non-aging trajectory. This is true regardless of the spatial direction of the push (thus including decelerations) and can serve as the basis for the gravitational "time dilation" (i.e. aging contraction) of General Relativity.

[BurtJordaan]

I'm personally most comfortable with a curved-space, radial-time model, which accommodates independent aging and non-aging paths to the future.

Faradave, this is a nice picture in the realm of SR, but unfortunately gives a false picture in the cosmological realm. You can essentially stay with your depiction by just adding an extra dimension for time, forming a cone, so that you decouple time evolution and space evolution. The reason is that cosmic time ticks on linearly, while spatial expansion doesn't.

Here* is a plot of the whole history of the observable universe, including inflation and the future, plotted on log-log scales for obvious reasons. If you would rotate it around the Log(r/r_P) = 0 axis, where r_P is one Planck length, you will get your growing circle, with cosmic time running uniformly along the Log (t/t_P) axis. This can accommodate any instance of closed, open or flat space, inflation, big crunch, dark energy, big rip, whatever.

* Fig 25.4 of this pdf (from Relativity-4-Engineers) http://www.einsteins-theory-of-relativity-4engineers.com/support-files/cosmic-inflationy.pdf

[BurtJordaan]

How can time's 'speed' be measured, other than with reference to time itself? Are there two types of time, whereby a second of one type can be unequal to a second of the other type?

Time flows for everyone at 1 sec per (own) sec, wherever one may be. If we compare one of your seconds to one of my seconds, we may get something different from a 1:1 ratio, because we may be moving differently relative to Earth's center and we may be at different altitudes. After some testing, we may conclude that your time passes more rapidly than mine, or vice versa.

Also: are the expanding-space and 'quickening-time' explanations equivalent, or can one be objectively true and the other false?

Well 'quickening-time' is a false concept and has nothing to do with cosmic expansion, so it is not equivalent to expanding space. Also check what I wrote to Faradave.

[bangstrom]

Can someone please explain to a layman like me what it means to say that the 'rate of time' changes. How can time's 'speed' be measured, other than with reference to time itself? Are there two types of time, whereby a second of one type can be unequal to a second of the other type?

The “rate of time” is clock time. When time quickens, clocks run faster. This has nothing to do with the mechanics of the clock but it depends on the environment in which the clock is found. There is no universal time so time can vary from one location to another but locally time remains constant relative to c as measured in the local environment. The local environment is called an ‘inertial reference frame’ and in all reference frames c is taken as an absolute constant.

Since 1968, the length of a meter has been defined by convention as the distance light travels in 1/299,792,458th of a second and the duration of a second is defined as the time it takes light to travel 299,792,458 meters and c is a constant ratio of 299,792,458 meters per second. The units of time, distance and c are all mutually defined so, if clocks tick faster, the length of a meter must grow shorter if the value of c remains is to remain the same.

You have right idea to say that time is relative to time itself and you could say that units of length are relative to length itself but, more exactly, both time and distance are measured relative to c where c is equal to the the local distance over the local time so within all reference frames c=d/t. The not so obvious implication of this is that different reference frames can have different rates of c yet all observers measure c to be the same within their individual reference frames.

Also: are the expanding-space and 'quickening-time' explanations equivalent, or can one be objectively true and the other false? Is there a possible (or hypothetical) experiment which could decide the matter? Or can Ockham's Razor be used (i.e. one explanation would require many coincidences and/or unexplained phenomena, and the other would not)?

This is where it gets complicated. Changes in time are indistinguishable from changes in space because we have no universal reference for either one that could tell us which one or both are changing. Distant galaxies are said to be redshifted because space is expanding and light waves are being “stretched out” by their passage through expanding space. The color red lies on the long wave end of the light spectrum while blue and violet lie on the short wave end so redshifting is a move to longer waves and redder light.

Changes in time can also cause redshifting or blue shifting. If space is not expanding but time is quickening (clocks run faster) as the universe ages, then light from the distant past will appear redder compared to recent light sources because it was emitted from a point in time when time was slower and slower emission equates to longer waves.

It should be apparent that no matter what the age or state of the universe, a beam of light will always take one year to travel the distance of a light year. This means that, if space is expanding, our unit of length in ‘light years’ will lengthen perfectly in sync with the expansion of the universe so the radius can never expand when measured in light years. This observation applies all the way down to smaller units of measure based on the value of c. Measuring the speed of light over the distance of 10 meters is just a scaled down version of measuring the speed of light over the distance of a light year and the length of a meter also expands as space expands. The standard length of a meter is nothing more than the distance of a meter expressed in light seconds that can vary from one reference frame to the next.

Going much farther up the distance scale, the standard length of a megaparsec expressed in light years is 3261563.79673 and this distance, just as with the smaller light year and meter expands with the expansion of space.

The length of a light year expands as the universe expands so the calculated value for the radius, and by extension- the age, of the universe as measured in light years is a dimensional constant. The Hubble constant is a ratio of distance over time just as is the speed of light so the Hubble constant truly is a constant within all reference frames assuming the uncertain possibility that there are no outside forces acting to change it.

Here’s the rub. The WMAP data gave the universe an equivocal cosmic age of 13.766 billion years based on the Hubble rate of growth of 73.5 kilometers per second per megaparsec but the Hubble rate is a cosmological ratio of distance to time as is the constant c so the Hubble rate varies in sync with the expansion of the universe while remaining the same within each individual reference frame. The consequence of this is that the measured 13.766 billion year age of the universe will remain the same 10 billion years from now just as it was 10 billion years in the past.

The only meaningful cosmological measure for the residents of the universe is its density. This is the degree of crowdedness or space to matter ratio that makes the universe livable. The primal universe must have been intensely crowed beyond all imagination and it has been growing less crowded ever since. We can estimate the age and internal size of the cosmos based on how long it must have taken to evolve to our present state of density but measurements based on the assumption that galactic redshifts are giving us straight forward measurements of galactic recessional velocities are unrealistic.

[bangstrom]

You can essentially stay with your depiction by just adding an extra dimension for time, forming a cone, so that you decouple time evolution and space evolution. The reason is that cosmic time ticks on linearly, while spatial expansion doesn't.

If changes in time and spatial expansion are not in sync as a constant ratio, then c will not be a constant.
c=d/t where c is given as a constant and the only absolute.

Well 'quickening-time' is a false concept and has nothing to do with cosmic expansion, so it is not equivalent to expanding space.

In GR, time slows in a dense gravitational field and quickens as the field lessens. The expansion of space is also a decline in gravitational density as bits of matter move farther apart. The expansion of space is much like emergence from the depths of a gravity well where time quickens and space expands.

We know the cosmos is changing but changes in time are indistinguishable from changes in space in the absence of any external reference.

[BurtJordaan]

You can essentially stay with your depiction by just adding an extra dimension for time, forming a cone, so that you decouple time evolution and space evolution. The reason is that cosmic time ticks on linearly, while spatial expansion doesn't.

If changes in time and spatial expansion are not in sync as a constant ratio, then c will not be a constant.
c=d/t where c is given as a constant and the only absolute.

If you are talking about Schwartzschild coordinates around stars and planets, yes that's true. But here we are talking cosmological (co-moving) coordinates. Space itself is not a 'thing' that moves, but in these coordinates space expands and takes comoving things with it, without them having to move through space, so to speak. So Special Relativitic (SR) principles do not apply here.

Further, on the largest (cosmic) scale, the cosmic density of things are uniform and hence there are no gravitational potential differences, so General Relativistic (GR) gravitational time dilation does not apply either. There are tiny amounts (comparatively speaking) of redshift and blueshift as photons from a distant Supernova climbs out of its resident galaxy's gravitational well and then falls inwards into the Milky Way's well, but those are easily quantized and corrected for, if significant.

The idea that time ran slower (or faster) in the past and could explain the cosmic redshift has been considered for a very long time already, thoroughly refuted and rejected by the scientific community. The same thing is considered again in the search for quantum-gravity and quantum cosmology, but everything there is highly speculative and not compelling (yet) by a long shot...

[Faradave]

~ another sideline (or curve) ~

You can essentially stay with your depiction by just adding an extra dimension for time, forming a cone, so that you decouple time evolution and space evolution. The reason is that cosmic time ticks on linearly, while spatial expansion doesn't.

A curved-space, radial time model provides not just two but all four dimensions as fundamentally temporal, emanating unidirectionally outward from the Big Bang (BB). Such a temporal 4-field is comfortably similar to the fields classically emanating from electric or gravitational charges, but one dimension up. The BB then serves analogously as a temporal point charge.

We may not need to fully "decouple" spatial evolution from temporal evolution, considering Einstein worked so hard to unify spacetime. Instead we can invoke a non-linear relation. At the risk of oversimplifying, I model space as a cubic function of time. Space is an enclosing surface at any temporal radius. So, all of space is the 3-sphere enclosing the BB at any cosmic age. A 3-sphere expands with the cube of its radius (because it's what we perceive as a volume).


With the application of cosmological constants ∆a & ∆t, a cube function can approximate the profile of the expanding universe with acceleration a natural consequence.

[BurtJordaan]

You can essentially stay with your depiction by just adding an extra dimension for time, forming a cone, so that you decouple time evolution and space evolution. The reason is that cosmic time ticks on linearly, while spatial expansion doesn't.

We may not need to fully "decouple" spatial evolution from temporal evolution, considering Einstein worked so hard to unify spacetime. Instead we can invoke a non-linear relation. At the risk of oversimplifying, I model space as a cubic function of time. Space is an enclosing surface at any temporal radius. So, all of space is the 3-sphere enclosing the BB at any cosmic age. A 3-sphere expands with the cube of its radius (because it's what we perceive as a volume).

I should have said "pictorially decouple" - I did not mean to throw Einstein out! ;-) In other words, it is a problem if you depict the expansion factor a(t) and time both in the radial direction. I like what you have done here:

But why don't you use the standard LCDM a(t) function? I doubt if your function will give anything close to what is observed.

[bangstrom]

If you are talking about Schwartzschild coordinates around stars and planets, yes that's true. But here we are talking cosmological (co-moving) coordinates. Space itself is not a 'thing' that moves, but in these coordinates space expands and takes comoving things with it, without them having to move through space, so to speak. So Special Relativitic (SR) principles do not apply here.

Co-moving coordinates are a mathematical device for modeling cosmological changes by placing one of two variables in the position of the individual reference frames where measurements do not change from frame to frame.

This simplifies the model but it represents a highly unlikely situation in the real world where space changes while time remains the same or alternatively where time changes while space remains the same. More likely, space and time vary simultaneously

SR principles don’t apply because SR only works in a Euclidean space where time is a constant but the universe is curved and mapped with a curved Riemann geometry where space and time vary and GR applies instead.

Further, on the largest (cosmic) scale, the cosmic density of things are uniform and hence there are no gravitational potential differences, so General Relativistic (GR) gravitational time dilation does not apply either. There are tiny amounts (comparatively speaking) of redshift and blueshift as photons from a distant Supernova climbs out of its resident galaxy's gravitational well and then falls inwards into the Milky Way's well, but those are easily quantized and corrected for, if significant.

I am ignoring the tiny local gravitational changes that light waves may encounter. The Big Bang singularity is the enormous gravity well from which the entire universe is climbing and the emergence from the well is singular in its direction from a condition an intense, highly curved gravitational field to one that is flat beyond all evidence of curvature.

The idea that time ran slower (or faster) in the past and could explain the cosmic redshift has been considered for a very long time already, thoroughly refuted and rejected by the scientific community. The same thing is considered again in the search for quantum-gravity and quantum cosmology, but everything there is highly speculative and not compelling (yet) by a long shot...

The only real refutation I know of is that changes in scale would change the chemical properties of atoms but global changes in scale due to changes in the rate of time should have no local effect since everything remains proportional. Present day atoms never react with the ghosts of unchanged atoms from the past so changes in scale are not a problem. The main refutation is that others, long ago, claimed it doesn’t work.

[BurtJordaan]

The Big Bang singularity is the enormous gravity well from which the entire universe is climbing and the emergence from the well is singular in its direction from a condition an intense, highly curved gravitational field to one that is flat beyond all evidence of curvature.

Bangstrom, sorry to say, but statements like these are borderline for being removed from this section, which is supposed to discuss the mainstream scientific view. It would more properly belong under Personal Theories, where people know not to take it too seriously. Here every controversial point made has to be answered and the time of the mainstream guys around here is limited. Especially since you are not known for accepting the canonical scientific view readily. ;-)

The BB did not happen at a point in space, but instead everywhere at a specific time in the past. It was not highly curved, but spatially flat and essentially of infinite spatial extent. Our observable universe was an infinitesimal part of this huge flat space of uniform energy density, apart from possibly quantum fluctuations that averaged out over the whole. So there was no gravitational field emanating from some point, but the whole cosmos was at the same gravitational potential.

I can understand that some readers may have difficulty coping with this principle, especially since things like the balloon analogy and radial time cosmic analogies (like Fardadave's) easily draw one into a false belief that there is a spatial center. The balloon analogy is only useful if one assumes that it did not begin as a point in the center, but that it was already of a size approaching infinity at the time of the BB and, as we have seen in the log-log plot, not increasing in size before the BB.

The BB event can then be viewed as a brief period of rapid further inflation of the entire balloon, so that its skin stretched further, absorbing an enormous amount of energy, coming from some quantum effect that we do not yet understand. Trough some other quantum effect, phase transition, or whatever, most of that energy suddenly got converted into uniformly spread elementary particles, photons and a uniform gravitational field, leaving some residual energy as further expansion of the balloon. This drove the particles further apart at a tremendous rate, like beads stuck onto the fast-stretching skin of the balloon.

The gravitational field immediately started to slow down the expansion of the balloon, ushering in the LCDM cosmic expansion that we observe today. At that time our observable universe was a just a circular patch on the skin of order one meter in diameter. Irrespective of where you pick a point on the entire surface, it would have this circular patch of observability around it. The rest is history...

[bangstrom]

I have been having an impossible time trying to enter my comments the usual way so I will try entering them as one lump in “quick reply” and see if it works.
I know I don’t draw a line between mainstream views and non but, specific to your last post, I don’t see anything that it not mainstream including your opening statement which implies that I find some of your views debatable as mainstream.
Here are my views for comparison.
It is not my view that, “The BB ever happened at a single point in space” and I am certain I never intended my comments to be interpreted as such. I did mention something about a point in space in reference to an example from Abbot’s book “Flatland” but this did not mean the universe started as a point and this is not how Abbot’s example should be interpreted either.
I understand the universe to be everywhere curved as described by Riemann geometry and it was much more strongly curved in its primal form than it is now. A “straight” line in Riemann geometry is never either straight, flat, or infinite. A straight line is part of a curved geodesic and, if extended far enough, will return to its origin. Your claim sounds like Euclidean geometry to me. Is that what you are saying?
‘Gravity’ is just another word for curved spacetime. This implies that the entire universe is composed of spacetime that is either more or less curved and the one trillion or so galaxies combined form a global and inescapable gravitational field.
Also, the entire history of the universe has been one of a relaxing of its spacetime curvature, in other words, it is a history of declining gravitational density.
I do not interpret Faradave’s writings as support for a “spacial center” or the balloon analogy either. That may be the most intuitive interpretation of the balloon analogy but I agree that it is false.
My understanding is that the primal universe contained as much energy and spacetime then as it does now.
I would say the one meter diameter patch of observable universe in the early BB would have looked like several billion light years if we could go back in time to take a look. Our scale of measurements can not be applied directly to the scale of the distant past.

[BurtJordaan]

I know I don’t draw a line between mainstream views and non but, specific to your last post, I don’t see anything that it not mainstream including your opening statement which implies that I find some of your views debatable as mainstream.

If you can get the quote function to work, please indicate which of my views in this thread you find debatable as mainstream...

I understand the universe to be everywhere curved as described by Riemann geometry and it was much more strongly curved in its primal form than it is now.

No, it works the other way around. This from COSMOS - The SAO Encyclopedia of Astronomy >
Flatness Problem.

To phrase it more scientifically, the flatness problem arises because we appear to live in a Universe that has an observed a density parameter (Ω₀) very close to 1. In other words, the Universe is very close to the critical density. The ‘problem’ is that for the Universe to be so close to critical density after ~ 14 billion years of expansion and evolution, it must have been even closer at earlier times. For instance, it requires the density at the Planck time (within 10^-43 seconds of the Big Bang) to be within 1 part in 10⁵⁷ of the critical density. i.e. Ω₀ initially must have been almost exactly 1.

This is contra the balloon analogy and is a strong reason why I said the only way to use that analogy is to start with an "infinite" balloon and then blow it up further. It is also why I avoid it and rather use the infinite lattice analogy. The real cosmos has flat space, but curved spacetime, so it is not like Schwartzshild space.

Also, the entire history of the universe has been one of a relaxing of its spacetime curvature, in other words, it is a history of declining gravitational density.

Correct, but the cosmic large scale gravitational field is very-very close to uniform, isotropic and homogeneous. Also note that you said spacetime curvature, not spatial curvature, which, if any, is getting worse...

Our scale of measurements can not be applied directly to the scale of the distant past.

Depends on how distant. We directly observe the CMB radiation redshift and can easily deduce the size of our patch at 380 thousand years after inflation stopped - it works out to just over a million light years across. From there it is completely reasonable, knowing the expansion model, to extrapolate back to the time just after inflation, giving a mere meter across, give or take...

[bangstrom]

I see our differences mainly boil down to a difference in opinion about whether space is curved spacetime as described by Schwartzschild and Riemann or flat and whether space is finite or infinite in extent. I say curved and bounded- you say flat and infinite. To me “flat” space means Euclidean space or, in cosmology, flat means expanded to the point curvature is no longer apparent.
https://en.wikipedia.org/wiki/Curved_space

“Curved space often refers to a spatial geometry which is not "flat" where a flat space is described by Euclidean geometry. Curved spaces can generally be described by Riemannian geometry though some simple cases can be described in other ways. Curved spaces play an essential role in general relativity, where gravity is often visualized as curved space. The Friedmann-Lemaître-Robertson-Walker metric is a curved metric which forms the current foundation for the description of the expansion of space and shape of the universe. “

I also trust observation far more than models. No model can be complete in itself and having more than one equivalent model is better than just one because we can test the correctness of one model against the other.

The caution with models is that we should never confuse the map with the territory.

The model I trust the least is one that one that has been manipulated mathematically to simplify the model while it is inconceivable that the same manipulation could be a part of the natural world. This would include a model with co-moving coordinates.

In Riemann geometry a line can never be totally flat or infinite in extent. A line can be extended as far as as the curvature of spacetime will permit so a line is arbitrarily long but never infinite.

I find your “flatness problem” to be a perfect example of my concerns. Edward Harrison calculated that a universe 35 billion years old would fit all the parameters of the standard model without adjustments made to make the the model conform to observations. The observations he referred to were those other than the 15 billion year old estimate based on Hubble recessional redshifts. Redshifts are fine as long as they don't extend to distances where cosmological changes in spacetime become a problem.

The need for Guth’s inflation, dark matter and dark energy to make the model work within a 14 billion year old universe is letting the model and math overrule observations and this is what I find troubling. These adjustments to the model should be clues that the motion of an expanding universe is something separate from the kind of motion described in SR that can be measured by recessional redshifts.

I understand “gravity” to be another word for curved spacetime. How would you describe gravity?

[BurtJordaan]

I understand “gravity” to be another word for curved spacetime. How would you describe gravity?

The same, with the only difference that I understand local gravity as curved spacetime with curved space (the latter mandatory) and cosmological gravity as curved spacetime with on average flat space (the latter optional). Observations show space to be most likely flat, but the measurement accuracy allows for a tiny deviation to either side, i.e. small positive or negative overall spatial curvature. But spacetime is negatively curved on a cosmological scale, open with time going on forever.

Question to you. Why do you think the Edward Harrison model with Ho~10 and Omega=10 and 35 Gyr age has never been heard about lately? A simple Hubble-like measurement refutes it.

My personal philosophy on cosmic age: infinite, with many bounces, the last one being 14 Gyr ago. I say 'philosophy', because I do not understand the quantum effects involved. And unfortunately there appears to be no way of observing anything before the last bounce/bang, or whatever...

[Faradave]

~ continued aside ~

I like what you have done here … why don't you use the standard LCDM a(t) function?

Thanks, I'm still working toward that.

The BB did not happen at a point in space, but instead everywhere at a specific time in the past. … I can understand that some readers may have difficulty coping with this principle, especially since things like the balloon analogy and radial time cosmic analogies (like Fardadave's) easily draw one into a false belief that there is a spatial center.

Agreed, but I don't think that rules out a curved-space, radial-time model. Consider earth's south pole. For a particular latitude (-90°), it corresponds to every longitude (an infinite number of them from 0° to 360°).

A single geometric point, the south pole, corresponds to every longitudinal coordinate.

Interpolating back to a particular time (0 cosmic age), the singularity of the Big Bang (BB) would correspond to every spatial coordinate. This is not a spatial center but rather a spacetime center in 4D polar coordinates (red dot below). Space is technically "finite" at any given time but expands without bound.


Minkowski spacetime (left) reconfigured as curved-space, radial time (right). Red dot is Big Bang (BB). Blue dot is the 4D event (here, now). Time is unidirectional outward from BB. Green lines are bidirectional spatial simultaneities, shown in the rest frame of the BB (and cosmic background).

Observations show space to be most likely flat,

Again, I agree but with a caveat when light is the measure. Light doesn't travel through space. Tracing any path along a spatial simultaneity (flat or curved) would be instantaneous. Speed limit c is defined by an interval having inherently equal spatial and temporal components. Thus, light absorption always occurs in a simultaneity in the future of its emitter.

It's hard to imagine measurements employing the straight paths of V_max (i.e. speed c) yielding triangles (for example) with angles summing to anything other than 180°.

Straight interval lines (V_max) may obscure curved underlying space (t₁) to which it is tangent.

[bangstrom]

The same, with the only difference that I understand local gravity as curved spacetime with curved space (the latter mandatory) and cosmological gravity as curved spacetime with on average flat space (the latter optional).

What about curved time? I think space and time must change together.

Question to you. Why do you think the Edward Harrison model with Ho~10 and Omega=10 and 35 Gyr age has never been heard about lately? A simple Hubble-like measurement refutes it.

I have no idea what happened to Harrison’s model. He published one paper about it and, as far as I know, he never mentioned it again. I suspect his paper was ignored and never caught traction among his colleagues.

I have no confidence in the Hubble-like measurement. Hubble himself never accepted it either. Measuring distances against a background where both space and time are changing simultaneously introduces too many variables to make galactic redshifts a reliable tool.
Quantized redshifts suggest that expansion is not uniform but instead it advances with cycles of faster and slower expansion that can not explained as a Hubble expansion. The possibility is still under study.

My personal philosophy on cosmic age: infinite, with many bounces, the last one being 14 Gyr ago. I say 'philosophy', because I do not understand the quantum effects involved. And unfortunately there appears to be no way of observing anything before the last bounce/bang, or whatever...

I find the “many bounces “ scenario philosophically appealing but lacking evidence so I hesitate to go there. This is also known as the “string of pearls” model.

[BurtJordaan]

... but I don't think that rules out a curved-space, radial-time model.

The objection against it is that if you accept a linear cosmic time (like cosmologists do) you end up with a linear expansion law as well, which is surely frowned upon. That's why I originally said, split the time axis from the spatial axis in the diagram.

Interpolating back to a particular time (0 cosmic age), the singularity of the Big Bang (BB) would correspond to every spatial coordinate. This is not a spatial center but rather a spacetime center in 4D polar coordinates (red dot below). Space is technically "finite" at any given time but expands without bound.

Yea, this could be a representation of the observable universe, which surely is finite, but not of the whole universe, which must have the option of being open and infinite or perhaps closed and extremely large, approaching infinity. But I still object to a radial time coordinate - time must be perpendicular to the radial and to the spatial surface.

It's hard to imagine measurements employing the straight paths of Vmax (i.e. speed c) yielding triangles (for example) with angles summing to anything other than 180°.

Its not hard when we realize that on cosmological scale, space is essentially flat. In 4D space, apart from the tiny depressions and lensing caused by clusters and galaxies, light travels in straight lines. But because spacetime is not flat, in an expanding universe, parallel light rays diverge and in a collapsing universe, they converge.

[BurtJordaan]

What about curved time? I think space and time must change together.

Not curved time, flat space and curved spacetime. As I wrote to FD above:

... apart from the tiny depressions and lensing caused by clusters and galaxies, light travels in straight lines. But because spacetime is not flat, in an expanding universe, parallel light rays diverge and in a collapsing universe, they converge.

Quantized redshifts suggest that expansion is not uniform but instead it advances with cycles of faster and slower expansion that can not explained as a Hubble expansion.

No need for quantized redshift, standard cosmology with Hubble flow has exactly that. So far we had accelerating expansion, followed by decelerating expansion, a period of effectively coasting expansion and finally accelerating expansion again. All observed and explained by standard theory.

[Faradave]

~ optional ~

I still object to a radial time coordinate - time must be perpendicular to the radial and to the spatial surface.

Curved-space (blue simultaneities t₁ & future t₂) are here added to Sean Carroll's depiction of a radial-time (shown as a 2D slice of a temporal 4-field).

Note that ∆T above is accomplished by both V₀ and geometrically-independent V_max. Thus, in terms of of future displacement, both may be considered "time" and calibrated in seconds. They differ in that V₀ is an aging path while V_max is non-aging for the "object" experiencing displacement. (I sometimes refer to these as "proper time" and "improper time".) Curved-space, radial-time thus provides ∆T "...perpendicular to the radial and the spatial surface."

On top of that, recall that curved-space, radial-time naturally explains a speed limit c which is finite, constant, universal and invariant. The tangent speed limit is enforced by radial, fundamentally unidirectional time. That ought to be compelling all by itself, as no conventional explanation exists.

"Why is the speed of light the same in all reference frames? I don’t know the answer to that question, and I don’t even know how to approach it. … the speed of light is unexplained." - Styer p.21

As if that's not enough, curved-space radial-time surprisingly provides, at any 4D location, coordinates which are wonderfully flat. V_max and V₀ correspond respectively to interval-time coordinates. Unless you're willing to toss out the spacelike interval equation:
(∆d)² = (∆x)² - (∆t)² (where ∆d is any spacetime interval),
I've merely rearranged it as: (∆x)² = (∆d)² + (∆t)²,
a Pythagorean relation which applies exclusively to Euclidean geometry.

[bangstrom]

What about curved time? I think space and time must change together.

Not curved time, flat space and curved spacetime. As I wrote to FD above:

I don't understand how one can separate changes in space from changes in either time or spacetime except on a graph.

Quantized redshifts suggest that expansion is not uniform but instead it advances with cycles of faster and slower expansion that can not explained as a Hubble expansion.

No need for quantized redshift, standard cosmology with Hubble flow has exactly that. So far we had accelerating expansion, followed by decelerating expansion, a period of effectively coasting expansion and finally accelerating expansion again. All observed and explained by standard theory.

Inflation and acceleration in the standard theory are not what I had in mind as quantized redshifts. Some observations indicate that expansion rates may have also varied periodically within the time between.
https://en.wikipedia.org/wiki/Redshift_quantization
Either way, there appears to more to the smooth coasting expansion than an inertially driven expansion used for calculating the Hubble rate and recessional velocities. This introduces an element of doubt to the calculations.

[BurtJordaan]

I don't understand how one can separate changes in space from changes in either time or spacetime except on a graph.

All I meant is that time ticks on and space can be static, expanding, contracting. They are coupled, but there is no linear connection between them.

Either way, there appears to more to the smooth coasting expansion than an inertially driven expansion used for calculating the Hubble rate and recessional velocities. This introduces an element of doubt to the calculations.

Yes, there are challenges to any model, but I think quantized redshifts, if it exists and is not just processing errors, is one of the least challenging. Fact is, the Hubble law works, can be observed and there is no valid argument against that. Theoretically, it is also the simplest of all possibilities - the LCDM model supports Hubble and fits observations.

[BurtJordaan]

Curved-space (blue simultaneities t₁ & future t₂) are here added to Sean Carroll's depiction of a radial-time (shown as a 2D slice of a temporal 4-field).

This is extremely vague, e.g. if time is radial, how can t1 and t2 be "simultaneities"? If the blue dashes represent space and spatial expansion, then this must mean linear spatial expansion against time, which flies in the face of both theory and observation.

[bangstrom]

All I meant is that time ticks on and space can be static, expanding, contracting. They are coupled, but there is no linear connection between them.

A given in the model is the assumption that c is an absolute against which we measure all changes in space and time. If time is a constant and space is a variable, that implies that c must also be a variable since c=s/t. You can’t have two absolutes in the same model. If space expands, the rate of time must quicken proportionally if c is to remain constant.

Fact is, the Hubble law works, can be observed and there is no valid argument against that. Theoretically, it is also the simplest of all possibilities - the LCDM model supports Hubble and fits observations.

The use of redshifts to measure recessional velocities is valid under local conditions where you can be certain that recessional velocity is the only cause of the redshifting. There are other possible causes for redshifting that come into play when applied to a changing universe over enormous amounts of distance and time. This is why Hubble never accepted his own law as valid.

The model does not legitimately fit observations. It only fits if you toss in the ad hock adjustments of inflation, dark matter, and dark energy and these are not minor adjustments since they must amount to 96% of the mass of the universe if they are real. Adding “dark” causes from beyond the defined laws of physics is in direct violation of Occam’s razor. Any model can conform to observations if you add enough fudge factors to make it fit.

[Faradave]

~ optional ~

As a sphere is all locations equidistant from a center, t₁ is a circumferential cross section of the spatial 3-sphere enclosing the Big Bang (BB) "now". t₂ is such a simultaneity in the future.

This is extremely vague, e.g. if time is radial, how can t1 and t2 be "simultaneities"?

This is a curved-space, radial-time model (though Carroll may not have intended that), meant to show two geometrically independent paths to the future V₀ & V_max (thus, both may be considered "temporal" in terms of future displacement ∆T). All locations at any given radial separation from the Big Bang (BB) represent a simultaneity (here shown in 2D cross section as circumferential arcs enclosing the BB). t₁ may be considered all space "now" while t₂ is all expanded space at a greater cosmic age (i.e. a "future" moment).

If the blue dashes represent space and spatial expansion, then this must mean linear spatial expansion against time, which flies in the face of both theory and observation.

I think you're seeing that correctly! A circumference of a sphere in any dimension varies linearly with radius. A 3-sphere is different from an ordinary 2-sphere in that a 3-sphere has three orthogonal equators intersecting at every location, while a 2-sphere has only two (e.g. earth's equator and its prime meridian).

Without additional influences, two distant galactic clusters sitting on arc t₁ would experience linear expansional recession. (My cube function above referred to the expanding volume of the cosmos.) To accommodate such influences, the spacing of tics along any temporal radius would vary - thus your "scale factor" (or bangstrom's varied "pace of time") is introduced. I'm happy to discuss those influences if there is any interest but it gives rise to awkward expressions such as "During inflation, the cosmos aged much faster than it does now."

[BurtJordaan]

A given in the model is the assumption that c is an absolute against which we measure all changes in space and time.

Hmm, not quite. Time is based on fundamental processes and we use use the speed of light to define a metric for space. In fact it is only the two-way speed of light that is an invariant c - the one-way speed is a how we define space for convenience. There are other equally valid definitions of space with, but it makes the math much, much more complicated and is hence inconvenient.

Furthermore, the 'convenience definition' only holds for inertial frames of reference and there are many more valid reference frames, like accelerating frames, curved spacetime frames, cosmological frames, non-symmetrical frames... In cosmology we normally use either proper distance coordinates or comoving coordinates, in neither of which the speed of light is a constant. The speed of light is constant in all intermediate inertial frames, but the frames themselves are moving away from each other in terms of proper distance.

The use of redshifts to measure recessional velocities is valid under local conditions where you can be certain that recessional velocity is the only cause of the redshifting. There are other possible causes for redshifting that come into play when applied to a changing universe over enormous amounts of distance and time. This is why Hubble never accepted his own law as valid.

I'm rather sure that he would have once the Hubble telescope revealed that his 'law' held to the farthest reaches of the observable universe. By comparison, he had very tiny patch to look at.

Recession speed is simply the growth in proper distance between observer and source per observer's proper time interval. At cosmological distances, this cannot be interpreted as a Doppler redshift, as for local inertial frames. It tells us by what factor the distance between the source and observer has grown in the time it took light to travel that distance, i.e. by how much space has expanded in that time.

The model does not legitimately fit observations. It only fits if you toss in the ad hock adjustments of inflation, dark matter, and dark energy and these are not minor adjustments since they must amount to 96% of the mass of the universe if they are real.

Inflation is a different animal than the LCDM model (preceding LCDM), but the latter is the only one that can fit the observation fairly comfortably. Do you know about any other model that can come even close and survive scrutiny?

BTW, dark energy is not really so 'dark' anymore. It can be very simply explained by a residual spacetime curvature (not space curvature, which is very close to zero) left over from the BB, whatever that may have been - inflation, bounce, weird quantum event, etc. Theorists like to keep their options open for other models, but none has been convincing so far.

Further, dark matter does not need Einstein, LCDM or inflation - simple galaxy rotation curves and things like galactic collision observations provided enough evidence for something dark going on. And matter that does not radiate is as simple as Occam can go.

[bangstrom]

Time is based on fundamental processes and we use use the speed of light to define a metric for space. In fact it is only the two-way speed of light that is an invariant c - the one-way speed is a how we define space for convenience. There are other equally valid definitions of space with, but it makes the math much, much more complicated and is hence inconvenient.

We use time to define space and space to define time or consider them as one spacetime. Equivalent but alternate cosmological models using the same math and observed values agree that universal changes involve too many variables to provide a reliable method for calculating the density value of the universe and the standard model has no fewer variables than the alternatives. A reliable method for determining the size and age of the universe is what we need.

The Hubble values are convenient and give us a reasonably good estimate in the model but they are only as good as the assumptions supporting their use.

The speed of light is constant in all intermediate inertial frames, but the frames themselves are moving away from each other in terms of proper distance.

This statement contains assumptions that may not be valid. One is the assumption that the speed of light is constant over cosmological times and the other is that the universe is expanding. Other agents of change could explain the same observations. Changes in Newton’s G, or changes in the rate of time are two possibilities that have been explored with plausible conclusions. Another possibility is that the universe remains constant in size while all matter within is growing smaller.

Do you know about any other model that can come even close and survive scrutiny?

All the alternative models I am familiar with and consider valid agree that universal changes involve too many variables to be useful in determining the size and age of the universe so the standard model is an outlier in this respect. Cosmological change could be due to changes in space or changes in time or any combination of the two but we have no way of knowing if one dominates the other or if the changes are exactly proportional. The use of c as an absolute assumes that the changes are exactly proportional which is necessary for the standard model but it may not be the reality.

BTW, dark energy is not really so 'dark' anymore. It can be very simply explained by a residual spacetime curvature (not space curvature, which is very close to zero) left over from the BB, whatever that may have been - inflation, bounce, weird quantum event, etc. Theorists like to keep their options open for other models, but none has been convincing so far.

The evidence for dark matter is based on the observation that galaxies rotate more like solid objects than objects held together by gravity. An early explanation for dark matter is that galaxies are made up of stars and stars are composed largely of plasma. Clouds of plasma rotate much like solid objects.

The electromagnetic force among charged bodies is many times greater than the force of gravity and this is the understanding behind the Electric Universe model. Luminous objects resembling tiny galaxies have been created by passing high voltage electricity through a vacuum in glass spheres. The effect looks exactly like a galaxy in a bottle.

Further, dark matter does not need Einstein, LCDM or inflation - simple galaxy rotation curves and things like galactic collision observations provided enough evidence for something dark going on. And matter that does not radiate is as simple as Occam can go.

Occam’s razor defines “simpler” as the explanation having the fewest number of assumptions. Saying something exists because it does not radiate and therefore can’t be directly observed is not the simplicity Occam had in mind.