A variable expansion speed theory of gravity

[Andrex]

Very good question Dave.

Let's talk, first of :
"The Lagrangian points move relative to the moving planets and are not a locked position. Matter passing through on route to some Gravity well (comets etc) are also moving. Everything is in motion. Collisions (accretion) is inevitable. "

I guess that the moving Langrangian points are responsible for the orbiting of planets since that's where they where "accreted". When all particles where part of a planet, the planets kept their orbit. Don't you think? Furthermore, "accretion" is primarily a consequence of "gravity" and not random "path crossing", since every particle matter is inside a "space-time deformation" (All have mass). The randomness of trajectory served to permit gravity to capture particles in its " space deformation". In a space deformation, every particle tends to "fall" at the center of gravity; so if you don't have a first Langrangian point to keep some particles from "falling" (to the Sun) and accrete, you will never get a planet formed. I think.

As for:
"why are all the major planets on the same plane of the Solar Ecliptic."

As a matter of fact, the plane you talk about stand between, at the most, 30 degrees each side of the "whatever" eclyptic you can find. Remember that to my point of vue, what is important is the geometric déformation of space (collapsing of the metric) which is gravity. This deformed geometric is a "ball (volume) of space" and its metric gained the possibility to diminish (collapse) when the gluon appeared in the universe. So maybe this limited part of a volume (each side of its "equator") is related to the fact that the gluon into which quarks appeared was a "surface" and not a "volume". I can't think of another reason; but the subject is surely mysterious to my mind. I'll probably get to it somme day. :-)

But from the top of my head, I remember that scientists while studying the spin of a photon, considered that spin as simply the rotation of a photon. So if I consider the rotation (spin) of a gluon (which is a boson just like the photon) and add the fact that the gluon is a "surface" instead of a "volume", I'm incline to accept that the rotation of the gluon has something to do with the flatness where talking about. Simply because that rotation will inevitably produce a centrifugal effect.

Thanks for the question.
André.

[Dave_Oblad]

Hi,

My personal speculation is that the Solar System was formed by the collision of two forming Stellar Bodies. The angle of attack would have spun them into a plane with the lesser stellar Mass forming the planets after the splash.

Regards,
Dave :^)

[Andrex]

Do you mean that the two former bodies where "spheres"?

But what formed all the other systems which also have a "plane" structure; planetary systems, galaxies etc...?

By the way; it's impossible that a "Sun" starts ignition (fusion) before some other planets start to "accrete" in a molecular cloud; because fusion needs so much particles to start that other particles have time enough to start accreting before the fusion of the center of the cloud (star).

As for the explanation of "Conservation of angular momentum" to explain the disk shape of systems, it doesn't apply because, as we have already seen previously, each particles or "bodies" is orbiting individually around the center of gravity. For example: the "space volume" of a galaxy doesn't rotate; the stars of that galaxy simply follow its own "path" (orbit) in regard to its own velocity. To have "Conservation of angular momentum" you need the rotation of a "compact" object where all particles "touch" each others; like Earth, basketball etc.

More info:

"The latest analysis of data from the Kepler planet-hunting spacecraft reveals that almost all stars have planets.
The researchers also asked whether certain sizes of planets are more or less common around certain types of stars. They found that for every planet size except gas giants, the type of star doesn’t matter. Neptunes are found just as frequently around red dwarfs as they are around sun-like stars. The same is true for smaller worlds. This contradicts previous findings."
Sources: Harvard Smithsonian CfA, AAS Press Conference

More info:

"The widely accepted modern variant of the nebular hypothesis is the solar nebular disk model (SNDM) or simply solar nebular model.
According to the nebular hypothesis, stars form in massive and dense clouds of molecular hydrogen—giant molecular clouds (GMC).

Star formation is a complex process, which always produces a gaseous protoplanetary disk around the young star. This may give birth to planets in certain circumstances, which are not well known. Thus the formation of planetary systems is thought to be a natural result of star formation (can't say anything against that; can't we?)
.
A Sun-like star usually takes approximately 1 million years to form, with the protoplanetary disk evolving into a planetary system over the next 10–100 million years."

This is where the explanation doesn’t fit: “Every nebula begins with a certain amount of angular momentum.”

Surprisingly, this whole “process” of planet “creation” was elaborated by Emmanuel Kant in 1755; and “corrections” have been added to the theory, to this day. But at the time, Kant didn’t know anything about Lagrangian points (1772) so, a new way of analysing the event was then available, but nobody used it.

But as I always say: I could be mistaken.

[Dave_Oblad]

Hi Andrex,

We have discovered that many other solar systems are Binary Stars. Long before Fusion begins you can have a gas giant, not unlike Jupiter. It would still have a Gravity well. Two such Gas Giants, if close enough could easily try to combine in a collision. Except for a straight on collision, any other passing, even if they don't touch, will create a vortex. If one giant is much smaller it will get shredded into a spiral on an axis dependent on the original approach vectors. The gas/dust in the spirals will eventually condense into bodies as proto planets.

Yes, I can also imagine a big ball/area of primordial gas/dust can have a net spin, which would collapse into a disk shape.. by conservation of angular momentum. Both concepts seem to me to be equally valid for explaining the solar ecliptic.

Regards,
Dave :^)

[Andrex]

Hi Dave

"a big ball/area of primordial gas/dust can have a net spin, which would collapse into a disk shape.. by conservation of angular momentum."

How could the "ball of gas/dust have "conservation of angular momentum" if every particles in the "ball" are individually following their orbit without any bond to each other. The "ball of space" containing the gas/dust doesn't rotate.

"If one giant is much smaller it will get shredded into a spiral on an axis dependent on the original approach vectors."

Produced by the tidal wave effect that I explained with the wine glasses. I agree.

Interesting points.

André

[Andrex]

Today, I am very happy.

I just discovered a great man named: John Archibald Wheeler.

I thought that I was the only one that saw a possible explication of the universe by only the geometrical properties of space-time. Wheeler thought the same and developped the "geometrodynamics" theory. Is only problem was that, in his mind, the first instant of the universe was a "curved" space-time; which didn't permit the existence of fermions. If he had known that it was "flat" he would have found the explication of the appearence of space-time déformations in the universe and would have reach his goal; a "unified theory".

Over the years, Wheeler's graduate students included Katharine Way, Richard Feynman, David Hill, Bei-Lok Hu, Kip Thorne, Jacob Bekenstein, John R. Klauder, William Unruh, Robert M. Wald, Arthur Wightman, Charles Misner and Hugh Everett.

On April 13, 2008, Wheeler died of pneumonia at the age of 96 in Hightstown, New Jersey.

One of his quotes:

"It is my opinion that everything must be based on a simple idea. And it is my opinion that this idea, once we have finally discovered it, will be so compelling, so beautiful, that we will say to one another, yes, how could it have been any different.”

He was so right!

[Andrex]

Sorry but this post will be a long one. It's a compilation of notes I took from the 2015 results of Plancks data. Which is naturally relevant to my opinion described in this discussion.

Planck 2015

This Planck data release is both the first to include the data gathered over the full length of the mission and the first to contain polarization information.

Despite trying a wide range of extensions to the basic, 6-parameter ΛCDM model we find no significant evidence for a failure of the model. We continue to see tensions with some analyses of other astrophysical data sets. Planck Collaboration XIII (2016) shows that these tensions cannot be resolved with standard single parameter extensions of the base ΛCDM model. Resolving these discrepancies remains an area of active research.

XVIII. Background geometry and topology of the Universe

2. Previous results

It was concluded that a physically-motivated model was not favoured by the data.

For topology, we showed that a fundamental topological domain smaller than the Hubble volume is strongly disfavoured.

6. Discussion

Using both frequentist and Bayesian methods applied for the first time to polarization data, we find no evidence for a multi-connected topology with a scale less than roughly the distance to the last-scattering surface.

Although the evidence thus far corroborates the conventional wisdom that we live in the simplest FLRW Universe, this is likely to be only an approximation vastly beyond the Hubble scale.

3.1. Background parameterizations

The conventional approach, that we adopt also here, is to choose a minimally-coupled scalar field model also known as quintessence, which corresponds to the choice of a rest-frame sound speed (i.e., equal to the speed of light) and σ = 0 (no scalar anisotropic stress). In this case the relativistic sound speed suppresses the dark energy perturbations on sub-horizon scales, preventing it from contributing significantly to clustering.

3.2.1. Modified gravity and effective field theory

The first approach starts from a Lagrangian, derived from an effective field theory (EFT) expansion in the context of DE. Specifically, EFT describes the space of scalar field theories, with a Lagrangian written in unitary gauge that preserves isotropy and homogeneity at the background level, assumes the weak equivalence principle, and has only one extra dynamical field besides the matter fields conventionally considered in cosmology.

3.2.2. MG and phenomenological parameterizations

The second approach adopted in this paper to test MG is more phenomenological and starts from the consideration that cosmological observations probe quantities related to the metric perturbations, in addition to the expansion rate.

6. Conclusions

The quest for Dark Energy and Modified Gravity is far from over. Our focus has been on the scales where linear theory is applicable, since these are the most theoretically robust. Overall, the constraints that we find are consistent with the simplest scenario, ΛCDM, with constraints on DE models and MG models that are significantly improved with respect to past analyses.

Information on DE, complementary to (w0,wa), comes from asking whether there can be any DE at early times.

The background is then forced to be very close to ΛCDM, unless the tight constraints on early DE can somehow be evaded in a realistic model by “counter balancing effects”.

6.2. Early-Universe physics

We found no evidence for a tensor component or running of the scalar spectral index, no strong evidence for isocurvature perturbations or features in the primordial power spectrum and no evidence for non-Gaussianity cosmic strings or other topological defects. On large angular scales, the Planck data showed some evidence for “anomalies” seen previously in the WMAP data.

Thus, at present there is no convincing evidence of a primordial B-mode signal. At these low values of r, there is no longer any tension with Planck temperature constraints. (Personal: Cosmologists predict two types of B-modes, the first generated during cosmic inflation shortly after the big bang (gravitational waves), and the second generated by gravitational lensing at later times)

6.2.2. Scale dependence of primordial fluctuations

In summary, the Planck data are consistent with zero running of the scalar spectral index. However, as illustrated in Fig. 23, the Planck data still allow running at roughly the 10-2 level, i.e., an order of magnitude higher than expected in simple inflationary models.

6.2.3. Isocurvature perturbations

Finally, neutrino velocity potential and vorticity modes are other possible consistent perturbations to the photon-neutrino fluid after neutrino decoupling. However, they are essentially impossible to excite, since they consist of photon and neutrino fluids coherently moving in opposite directions on super-horizon scales (although the relative velocity would have been zero before neutrino decoupling).

6.2.4. Curvature

The simplifying assumptions of large-scale homogeneity and isotropy lead to the familiar Friedman-Lemaître-Robertson-Walker (FLRW) metric that appears to be an accurate description of our Universe.

Our Universe appears to be spatially flat to a 1σ accuracy of 0.25%. The red contours (on the graphic) tightly constrain the geometry of our Universe to be nearly flat.(Personal: which, in fact, means that no mesurements up to date has proven the universe being "curved")

6.3. Dark energy

The physical explanation for the observed accelerated expansion of the Universe is currently not known.

In standard ΛCDM the acceleration is provided by a cosmological constant, i.e., an additional fluid satisfying an equation of state w ≡ pDE/ρDE = −1. However, there are many possible alternatives, typically described either in terms of extra degrees of freedom associated with scalar fields or modifications of general relativity on cosmological scales

6.4.1. Constraints on the total mass of active neutrinos

Detection of neutrino oscillations has proved that neutrinos have mass. The Planck base ΛCDM model assumes a normal mass hierarchy with ∑ mν ≈ 0.06 eV.

Here we give constraints assuming three species of degenerate massive neutrinos. At the level of sensitivity of Planck this is an accurate approximation, but note that it does not quite match continuously on to the base ΛCDM model (which assumes two massless and one massive neutrino with ∑ mν = 0.06 eV).

Masses well below 1 eV have only a mild effect on the shape of the CMB power spectra, since they became non-relativistic after recombination.

Masses below about 0.4 eV can provide an acceptable fit to the direct H0 measurements, and adding the BAO data helps to break the acoustic scale degeneracy and tightens the constraint on ∑ mνsubstantially.

Although the posterior has less weight at zero, the lensing data are incompatible with very large neutrino masses

6.4.2. Constraints on Neff

Dark radiation density in the early Universe is usually parameterized by Neff, defined so that the total relativistic energy density in neutrinos and any other dark radiation is given in terms of the photon density.

The numerical factors in this equation are included so that Neff = 3 for three standard model neutrinos that were thermalized in the early Universe and decoupled well before electron-positron annihilation.

In this section we focus on additional energy density from massless particles. In addition to massless sterile neutrinos, a variety of other particles could contribute to Neff. We assume that the additional massless particles are produced well before recombination, and neither interact nor decay, so that their energy density scales with the expansion exactly like massless neutrinos. (Personal: Yet all neutrinos have been observed with left-handed chirality, and all antineutrinos right-handed. So a massless neutrino would be an antineutrino. The question, thus, remains: can neutrinos and antineutrinos be differentiated only by chirality?).

For Neff> 3, the Planck data favour higher values of the Hubble parameter than the Planck base ΛCDM value, which may be in better agreement with some direct measurements of H0.

As a result, these models increase the tensions between the CMB measurements and astrophysical measurements of σ8. It therefore seems unlikely that additional radiation alone can help to resolve tensions with large-scale structure data.

Observations of both the primordial helium and deuterium abundance are compatible with the predictions of standard BBN for the Planck base ΛCDM value of the baryon density.

As discussed in the previous sections, neither a higher neutrino mass nor additional radiation density alone can resolve all of the tensions between Planck and other astrophysical data. However, the presence of additional massive particles, such as massive sterile neutrinos, could potentially improve the situation by introducing enough freedom to allow higher values of the Hubble constant and lower values of σ8.

In the case of massless radiation density, the cosmological predictions are independent of the actual form of the distribution function, since all particles travel at the speed of light.

Although Planck is perfectly consistent with no massive sterile neutrinos, a significant region of parameter space with fractional ΔNeff is allowed, where σ8 is lower than in the base ΛCDM model. This is also the case for massless sterile neutrinos combined with massive active neutrinos.

6.4.4. Neutrino models and tension with external data

In summary, modifications to the neutrino sector alone cannot easily explain the discrepancies between Planck and other astrophysical data described in Sect. 5.5, including the inference of a low value of σ8 from rich cluster counts.

6.4.5. Testing perturbations in the neutrino background

The Planck data provide evidence for a cosmic neutrino background at a very high significance level.

6.5. Primordial nucleosynthesis

The Planck base ΛCDM predictions of Eq. (74) lie within 1σ of the Cooke et al. (2014) result. This is a remarkable success for the standard theory of BBN.

The region preferred by CMB observations lies at the intersection between the helium and deuterium abundance 68% CL preferred regions and is compatible with the standard value of Neff = 3.046. This confirms the beautiful agreement between CMB and BBN physics. Figure 36 also shows that the Planck polarization data help in reducing the degeneracy between ωb and Neff.

6.6. Dark matter annihilation

Note that to produce the observed dark matter density from thermal DM relics requires an annihilation cross-section of ⟨ σν ⟩ ≈ 3 × 10-26 cm3 s-1 (assuming s-wave annihilation) at the time of freeze-out (see, e.g., the review by Profumo 2013).

The dark grey dots indicate the best-fit dark matter models described in that paper. The favoured value of the cross-section is about two orders of magnitude higher than the thermal relic cross-section (≈3 × 10-26 cm3 s-1). Attempts to reconcile such a high cross-section with the relic abundance of DM include a Sommerfeld enhanced cross-section (that may saturate at ⟨ σν ⟩ ≈ 10-24 cm3 s-1) or non-thermal production of DM. ). Both of these possibilities are strongly disfavoured by the Planck data. ). Since the relative velocity of DM particles at recombination is many orders of magnitude smaller than in the Galactic halo, such a model cannot be constrained using CMB data.

6.7. Testing recombination physics with Planck

The cosmological recombination process determines how CMB photons decoupled from baryons around redshift z ≈ 103, when the Universe was about 400 000 years old.

For the base ΛCDM model, we find that the largest bias is on ns, at the level of 0.15σ (≈0.0006) for Planck TT,TE,EE+lowP+BAO. Although this is about 5 times larger than the difference in ns between CosmoRec and HyRec, this bias is nevertheless unimportant (really?) at the current level of precision.

7. Conclusions

a) The 2015 PlanckTT, TE, EE, and lensing spectra are consistent with each other under the assumption of the base ΛCDM cosmology. However, when comparing the TE and EE spectra computed for different frequency combinations, we find evidence for systematic effects caused by temperature-to-polarization leakage.

b) The PlanckTT, TE, and EE spectra are accurately described by a purely adiabatic spectrum of fluctuations with a spectral tilt ns = 0.968 ± 0.006, consistent with the predictions of single-field inflationary models. Combining Planck data with BAO, we find tight limits on the spatial curvature of the Universe, | ΩK | < 0.005, again consistent with the inflationary prediction of a spatially-flat Universe.

c) The Planck data show no evidence for tensor modes. Adding a tensor amplitude as a one-parameter extension to base ΛCDM, we derive a 95% upper limit of r0.002< 0.11. This is consistent with the B-mode polarization analysis reported in BKP, resolving the apparent discrepancy between the Planck constraints on r and the BICEP2 results reported by BICEP2 Collaboration (2014). In fact, by combining the Planck and BKP likelihoods, we find an even tighter constraint, r0.002< 0.09, strongly disfavouring inflationary models with a V(φ) ∝ φ2potential.

d) The Planck data show no evidence for any significant running of the spectral index. We also set strong limits on a possible departure from a purely adiabatic spectrum, either through an admixture of fully-correlated isocurvature modes or from cosmic defects.

e) The Planck best-fit base ΛCDM cosmology (we quote numbers for Planck TT+lowP+lensing here) is in good agreement with results from BAO surveys, and with the recent JLA sample of Type Ia SNe. The Hubble constant in this cosmology is H0 = (67.8 ± 0.9) km s-1Mpc-1, consistent with the direct measurement of H0 of Eq. (30) used as an H0 prior in this paper.

The amplitude of the present-day fluctuation spectrum, σ8, of the Planck base ΛCDM cosmology is higher than inferred from weak lensing measurements from the CFHTLenS survey and, possibly, from counts of rich clusters of galaxies.

The Planck base ΛCDM cosmology is also discordant with Lyα BAO measurements at z ≈ 2.35 At present, the reasons for these tensions are unclear.

f) The Planck data strongly disfavour fully thermalized sterile neutrinos with msterile ≈ 1 eV that have been proposed as a solution to reactor neutrino oscillation anomalies. FromPlanck, we find no evidence for new neutrino physics. Standard neutrinos with masses larger than those in the minimal mass hierarchy are still allowed.

g) The standard theory of big bang nucleosynthesis, with Neff = 3.046 and negligible leptonic asymmetry in the electron neutrino sector, is in excellent agreement with Planck data and observations of primordial light element abundances.

h) We have investigated the temperature and polarization signatures associated with annihilating dark matter and possible deviations from the standard recombination history. Again, we find no evidence for new physics from the Planck data.

i) The Planck results offer powerful evidence in favour of simple inflationary models, which provide an attractive mechanism for generating the slightly tilted spectrum of (nearly) Gaussian adiabatic perturbations that match our data to such high precision.

j) the Planck data show that the neutrino sector of the theory is consistent with the assumptions of the base ΛCDM model and that the dark energy is compatible with a cosmological constant. If there is new physics beyond base ΛCDM, then the corresponding observational signatures in the CMB are weak and difficult to detect.

10.3. Dark energy and modified gravity

Observations have long shown that only a small fraction of the total energy density in the Universe (around 5%) is in the form of baryonic matter, with the dark matter needed for structure formation accounting for about another 26%. In one scenario, the dominant component, generically referred to as dark energy (DE), brings the total close to the critical density and is responsible for the recent phase of accelerated expansion. In another scenario, the accelerated expansion arises, partly or fully, owing to a modification of gravity on cosmological scales.

As for Planck Collaboration XIII (2016), the results are consistent with the simplest scenario, ΛCDM, though all constraints on dark energy models… and modified gravity models…) are considerably improved with respect to past analyses. In particular, we improve significantly the constraint on the density of dark energy at early times, finding that it has to be below 2%... of the critical density (and an even tighter bound results if high-ℓ polarization is included).

10.5. Inflation

These results imply that V(φ) ∝ φ2 and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R2inflation. We search for several physically motivated deviations from a simple power-law spectrum of curvature perturbations, including those motivated by a reconstruction of the inflaton potential not relying on the slow-roll approximation. We find that such models are not preferred, either according to a Bayesian model comparison or according to a frequentist simulation-based analysis.

These results are consistent with the Planck 2013 analysis based on the nominal mission data and further constrain slow-roll single-field inflationary models as expected from the increased precision of Planck data using the full set of observations.

The addition of polarization data has significantly improved the limits on any isocurvature modes, which are now constrained at the percent level. Despite a detailed search, and study of several models, we see no statistically significant evidence for departures from a power law.

Single-field inflationary models with a standard kinetic term were also found to be compatible with the new tight upper bounds on the primordial non-Gaussianity parameters fNL No evidence of isocurvature perturbations as generated in multi-field inflationary models or by cosmic strings or topological defects was found.

The Planck 2013 results overall favoured the simplest inflationary models. However, we noted an amplitude deficit for multipoles ℓ ≲ 40 whose statistical significance relative to the six-parameter base Λ cold dark matter (ΛCDM) model is only about 2σ, as well as other anomalies on large angular scales.

10.6. Primordial non-Gaussianity

The global picture that emerges is one of consistency with the premises of ΛCDM cosmology, namely that the structure we observe today is the consequence of the passive evolution of adiabatic, Gaussian, nearly scale-invariant, primordial seed perturbations.

10.7. Isotropy and statistics

A large number of statistical tests indicate consistency with Gaussianity, while a power deficit at large angular scales is manifested in several ways.

10.8. The ISW effect (integrated Sachs-Wolfe effect)

Our analysis, using specially-constructed CMB temperature maps that are correlated and uncorrelated with E-modes, cannot rule out the ISW effect as the cause of these anomalies.

10.9. Cosmology from clusters

We confirm the 2013 results with the larger 2015 catalogue.

12. Summary and conclusions

Specifically, we can estimate the optical depth of reionization, τ, independently of other experiments. The value of τ is smaller than found in previous determination, implying later reionization.

There is no compelling evidence for any extensions to the 6-parameter model, or any need for new physics; five of the six parameters are now measured to better than 1% precision.
Using only Planck data, we find that the Universe is flat to 0.7% (1σ). Including BAO data, the constraint tightens to a remarkable 0.25%.

Models of inflation are more tightly constrained than ever before, with the simplest φn models being ruled out for n ≥ 2.

14. Conclusions

The Planck full mission temperature and polarization data are consistent with the spatially flat base ΛCDM model whose perturbations are Gaussian and adiabatic with a spectrum described by a simple power law, as predicted by the simplest inflationary models.

Among the models considered using this approach, the R2 inflationary model proposed by Starobinsky (1980) is the most favoured. Due to its high tensor-to-scalar ratio, the quadratic model is now strongly disfavoured and natural inflation is also disfavoured.

Finally we examined the connection between inflation and statistical isotropy. We found that a modulated curvaton model proposed to explain the observed large-scale dipolar power asymmetry cannot account for all of the asymmetry, and hence is not preferred over statistically isotropic base ΛCDM.

****************************************
The rest of the work should be done by Occam's razor.

[Dave_Oblad]

Hi Andrex,

My question is about how they define the curvature of the Universe.

If some Universe was a 3D sphere and 2D beings lived on that Surface and all information only traveled on that 2D Surface, then they would conclude no curvature to the surface, though we know its curved.

If such 2D beings could see far enough, then every straight line view in any direction would be a view of themselves, wrapped around the surface.

Or, I may be not understanding their definition of curvature.

Regards,
Dave :^)

[BurtJordaan]

Hi Dave,

Your 2D guys will notice the spatial curvature when they measure the sum of inside angles of largish triangles, wouldn't they?

Regards

[Andrex]

Exactly, BurtJordaan. Thanks!

Dave;
in "flat" space the sum of the angles of a (very very large) triangle is 180o; we're talking here of "cosmological" size; if that total is not 180o, then you're in "non flat space". Which means its "geometry" is not "flat".

Today, they use the CMB from Planck to "make" their triangle and they still come out without the "proof" that the universe is "curved". In fact, the more precise are the calculations, the closer the answer approaches to "flat space" status. They might be able to make a "bigger" triangle if ever scientists can have a "photo" of primordial neutrinos that appeared before CMB in the universe. Until then, they cannot go further back then CMB to make a "bigger" trangle.

Note that the universe could be a "sphere" anyway. The "flatness" of the universe doesn't relate to it's "shape". You can have a "flat" space universe inside a spherical universe. It's "flatness" concerns it's "inner geometry"; not its "exterior" shape. In other words, when you talk of the "flatness" of the universe, you're talking of it's "inner" geometry not, like many people think (even some scientists), its "overall shape".

To view this, imagine a "source" of light (in darkness) that starts to projects photons at light speed in all directions at the present moment. You'll get a "volume of light" that constantly "expands" at light speed with a constant radius around the "source"; which will produce a "ball" of light. So the trajectory of the light inside the "ball" will be in "straight" lines ; which means : "flat" geometry inside of the "light ball".
The difference with our universe is only that the "source" of light is "everywhere"; so the photons have "straight trajectories" whichever direction they're going ;because the universe doesn't have a "center". So light travels in straight trajectories whichever direction it takes (and so does objects in "flat space").

Lights trajectory, in "flat" space, is not deviated like it is, when going through a volume of "curved" space. I'll stop explaining here; because if I keep on, I'll be tempted to conclude that "gravity" is a local "effect", instead of a "universal" effect; which, naturally, I won't take the opportunity to say.

I hope this answers your question; and, mostly, I hope I'm right.
So, like with everything I say, you still have to check. :-)

[BurtJordaan]

Note that the universe could be a "sphere" anyway. The "flatness" of the universe doesn't relate to it's "shape". You can have a "flat" space universe inside a spherical universe.

Yes, but then you are talking topology vs. geometry. I think that a universe that is geometrically 100% flat cannot be a geometrical sphere. Topology is a tough subject that I do not know too much about.

[BurtJordaan]

Today, they use the CMB from Planck to "make" their triangle and they still come out without the "proof" that the universe is "curved". In fact, the more precise are the calculations, the closer the answer approaches to "flat space" status.

I fact, today the best observational evidence is that our observable universe is spatially flat to within 0.5% or so. This is not 'proof' of flatness or otherwise, just that it is very likely to be exactly spatially flat. It does not rule out a small spatial curvature (either way) though.

[Andrex]

Yes, but then you are talking topology vs. geometry.

That's why I said:

Note that the universe could be a "sphere" anyway.

In cosmology, topology can be used to describe the overall shape of the universe. This area is known as spacetime topology.

In "metric geometry", a geodesic is a curve which is "everywhere locally" a distance minimizer (note: not "everywhere universally"). So the "geodesic" of the total universe would be "flat"; which means "not curved", while some of its local volumes would be "curved" by gravity.

I think that a universe that is geometrically 100% flat cannot be a geometrical sphere.

I really can't understand why. You'll have to explain; because at least, what you call: our observable universe is "spherical"; since Planck took its picture by rotating on itself, and the distances, in all directions, to CMB is the same, time wise and space wise.

[Andrex]

This is not 'proof' of flatness or otherwise

We're saying the same thing; but I look in the prospected "future" of the calculations while you look at what scientists use to think because they tought that "masses attracted themselves".

is spatially flat to within 0.5% or so

It's not space that is 0.5% spacially "flat"; it's the calculations. We don't know "how flat" is space. The progression of precision brings us toward a totally "flat space". Copying Plancks results above:

Combining Planck data with BAO, we find tight limits on the spatial curvature of the Universe, | ΩK | < 0.005, again consistent with the inflationary prediction of a spatially-flat Universe.

Which is not exactly 0.05%, by the way (it's a lot less).

It does not rule out a small spatial curvature (either way) though.

We agree; not YET.

And if ever it does come to be prooven exactly "flat", scientists will have problems with their notion of the "pressure of energy"; I guess (that's if they don't already have with that precision of | ΩK | < 0.005).

[vivian maxine]

Andrex, are you saying that there is no "original" source of light that all those photons emanate from? Would that mean we do not know from where these photons that give us light come/came?

Burt Jordaan, I have a feeling that you or somebody in the know has already answered this and I need to go back and find it. Just in case not - when anyone says "BIg Bang" I think of it flowing out in all directions which would result in sphere. Did someone say that isn't how the Big Bang worked? If you say yes, I'll search for it.

[BurtJordaan]

I think that a universe that is geometrically 100% flat cannot be a geometrical sphere.

I really can't understand why. You'll have to explain; because at least, what you call: our observable universe is "spherical"; since Planck took its picture by rotating on itself, and the distances, in all directions, to CMB is the same, time wise and space wise.

Yes, our observable horizon is roughly a sphere, but the space of a flat observable universe is not a curved geometry. It is like in the 2D analogy, if you draw a finite circle on a flat plane, it does not make the flat plane curved. In other words, on the large scale of a flat and homogeneous universe, parallel light beams do not converge or diverge - they stay parallel. So light cannot circumnavigate it.

[Andrex]

Hi Vivian

Andrex, are you saying that there is no "original" source of light that all those photons emanate from? Would that mean we do not know from where these photons that give us light come/came?

No. I used light as a model with a "fixed speed" that makes naturally a "balloon". Instead of photons, we can use "neutrinos"; but it's a little more complex. We know that gamma rays started with a wavelenght of (around) 10^-15 meter. So électromagnetic started then and that can be considered as the "factual" source of photons (photons before that wavelenght are "imaginatives"). Note that the "volume" of a gluon is 10^-15 meter; so there could be a relationship between a gluon and a gamma photon. Gluon "emitting" energy could "emit" 10^-15 m wavelenghts energy.

The photons that give you "light" is the photon your eyes can "capture"; so it's your eyes that produces the "light" you talk about; which is a particular wavelenght of électromagnetic.

[Andrex]

but the space of a flat observable universe is not a curved geometry.

I'm still looking for "who said that".

if you draw a finite circle on a flat plane, it does not make the flat plane curved.

Exactly! And if you blow a balloon, it doesn't make the distribution of the inside "air" curved.

on the large scale of a flat and homogeneous universe, parallel light beams do not converge or diverge - they stay parallel. So light cannot circumnavigate it.

The word "homogeneous" is irrelevant here, since the universe is not "homogeneous"; even the light coming from CMB is deviated successively while going through space deformations before getting to Planck satellite (which demands corrections).

In the space portion that is "flat", parallel light beams, obviously, stays parallel. So you cannot "see" the back of your head like you theorically could, in a "curved" space.
And since the majority of space "could be" flat, light beams "could" neither converge or diverge and could stay parallel, making it impossible to circumnavigate the universe.

[vivian maxine]

Hi Vivian

Andrex, are you saying that there is no "original" source of light that all those photons emanate from? Would that mean we do not know from where these photons that give us light come/came?

No. I used light as a model with a "fixed speed" to make a "balloon". Instead of photons, we can use "neutrinos"; but it's a little more complex. We know that gamma rays started with a wavelenght of (around) 10^-15 meter. So électromagnetic started then and that can be considered as the "factual" source of photons (photons before that wavelenght are "imaginatives").

The photons that give you "light" is the photon your eyes can "capture"; so it's your eyes that produces the "light" you talk about; which is a particular wavelenght of électromagnetic.

Hmm? I'd better stop there - for now - while I check out photons. Your last sentence leave me a quandary. Leave it to me for now. I know what I want to look for. Thanks.

[Andrex]

I know what I want to look for. Thanks.

I'm the one who should thank you for your question. If you have a different opinion, don't hesitate; I'm always interested. :-)

As for your other question, if I may:

when anyone says "BIg Bang" I think of it flowing out in all directions which would result in sphere. Did someone say that isn't how the Big Bang worked?

I think that it's exactly how the BB worked. Except that even the "center" that could have existed at 10^-43 sec after time = zero, exploded and was propelled "everywhere". So today, wherever you're situated in the universe, you're always at its "center". Nevertheless, the "explosion" would produce a sphere.

[vivian maxine]

The sphere? That is what I think someone said but I could be wrong. I need to find that. I do, though, agree with how you describe it. But my notion has no scientific basis. It's only my impression of what big bang would do. I'll search for it but, right now, I am onto "spectrum" and the part of it that we humans can see.

You said: "The photons that give you "light" is the photon your eyes can "capture"; so it's your eyes that produces the "light" you talk about; which is a particular wavelength of électromagnetic."

If our eyes "capture" light from photons, then how can we say our eyes "produce" light? I would have thought the photons were producing the light that our eyes captured. I am perhaps over-simplifying?

[Dave_Oblad]

Hi Guys,

So back to 2D Flatlanders living on the surface of a sphere. I agree that one can form a triangle with three 90' angles mapped to a sphere. Say we start at the North Pole and go straight South to the Equator. Hang a 90' angle there and follow the Equator around for 25% of the circumference, then cut a 90' angle back to the North Pole. When we get there, we note that a fixed marker indication of our Original exit direction intersects our arrival at 90'. So we conclude that 3 angles that sum to 90' must be mapped to a sphere.

Fine.. But from a Flatlanders point of View, at the North Pole, the CMB might be the Equator and equal distance in all directions. Radiation from the Equator is coming to the Flatlanders in seemingly straight (but curved) lines from every direction. From this, how do the 2D Flatlanders conclude that they "don't" live on the surface of a sphere?

If that can't be answered.. then the real "US", living on the 3D surface of a Hyper-Sphere, also wouldn't be able to exclude the possibility that we live on the "curved" surface of a 4D sphere. It would appear flat, though it is actually curved.

As far as I know, Physics Treats our Quantum Reality as being 4D. Also note that the 3D surface of a Hyper-Sphere is Flat. Also note that Relativity (GR) treats reality as 4D (X,Y,Z,cT), with cT as Time.. how do we detect if Time has curvature or not?

Regards,
Dave :^)

[BurtJordaan]

Dave, the 4D hyper-sphere that we are talking about in relativity gives you a curved 3D surface, not a flat one. Remember, in cosmology the 4th dimension is not time, as apparently it is in FD's and your own 'models'. It is a fictitious 4th space-dimension in order to picture spatial curvature in 3D.^[1]

I suppose in the "round earth analogy", with light moving along the surface of "flatland", if you have 3 beacons arranged in a triangle, to which you can measure the distances from you and the angles from you, you can determine earth's surface curvature. Irrespective of where you are stationed on earth.

Jorrie

[1] Actually, one do not need to consider a 4th space dimension at all, one can just use semi-Riemannian Geometry and model the whole curvature issue in 3D.

[Dave_Oblad]

Hi Jorrie,

But from a Flatlanders point of View, at the North Pole, the CMB might be the Equator and equal distance in all directions. Radiation from the Equator is coming to the Flatlanders in seemingly straight (but curved) lines from every direction. From this, how do the 2D Flatlanders conclude that they "don't" live on the surface of a sphere?

There doesn't seem to be enough information to draw a conclusion about angles.

If we lived on a flat circle with us at the center.. we might know/guess the distance to the perimeter.

For any arbitrary angle at our center location and knowing the distance to the perimeter, we still don't have enough information to project the length of the base of said Triangle. We can assume the base to be an Arc, but it will still not differentiate a flat circle from a sphere.

Since everyplace is the center within our Universe and the CMB perimeter is always the same distance from anyplace, then all we have left to work with is Expansion over Time. I don't know if that helps.. but.. we still don't know if Space is Expanding by Addition or Stretching or both. We don't know if the Planck Length is the same size everywhere other than its relationship to Light Speed is a constant.

Feels like we are accepting an arbitrary model for the Universe being Flat and then concluding the Universe is Flat by that Model.

Forget the deviation of "Time" as a dimension for now.. unless you need Time to draw a conclusion on how we calculate the base angles for the CMB.

Regards,
Dave :^)

[Andrex]

Vivian

If our eyes "capture" light from photons, then how can we say our eyes "produce" light? I would have thought the photons were producing the light that our eyes captured. I am perhaps over-simplifying?

You're right; it's not our eyes that "produces" light; our eyes have the ability to capture only a small part of electromagnetism which we call "light". It's "special" only to our eyes; not to electromagnetism. Photons don't "produce" light either; photons are the "particle part" of light; the other part is "ondulation". Both are the causes of electromagnetism and of that portion we "see" as light.

Dave

So back to 2D Flatlanders living on the surface of a sphere.

Your 2D flatlanders are not living on the surface of a sphere; they're living "inside" the sphere; and inside that sphere, the "floor" (space) is "flat". Just like you're not living on the surface of the universal sphere; you're living "inside" that universal sphere. But I agree that if we talk of the North pole, then we're on the surface of a sphere. Both situation are far from being identical. You'll have to reconsider you analogy, I think.

Jorrie

the 4D hyper-sphere that we are talking about in relativity gives you a curved 3D surface, not a flat one.

Sorry my friend; what I'm talking about is our actual universe which seems to be "flat". If it fits with "relativity", so be it. If not`: too bad. What I mean is "relativity" is a "tool" to understand the universe; not a plan to build the universe accordingly. As you know, the universe is already "build". :-)

Actually, one do not need to consider a 4th space dimension at all

I agree. And even more so, if distance and time are the "same thing".

[Dave_Oblad]

Hi Andrex,

Your 2D flatlanders are not living on the surface of a sphere; they're living "inside" the sphere; and inside that sphere, the "floor" (space) is "flat". Just like you're not living on the surface of the universal sphere; you're living "inside" that universal sphere.

You are forcing your Model to be the correct one by the assumption we live inside a 3D Universe and not living on the 3D surface of a Hyper-Sphere.

Thus you are eliminating my argument by your arbitrary choice of Models. Nothing wrong with My Model. For a 2D Flatlander living on the surface of a Sphere,.. how do they know it's a Sphere when all information available to them only travels on that surface?

Regards,
Dave :^)

[Andrex]

how do they know it's a Sphere when all information available to them only travels on that surface?

Because of the way the planck satellite made his "picture:



As you can see, the info didn't travel on the surface of space but through space; and I don't see any "corners" :-)

As for the triangle that sums 180o, we stand at one of its angles.

On the surface of a sphere, the sum is not 180o



This one, for example sums up to 270o

[Dave_Oblad]

Hi Andrex,

Your top Image can be simplified to the location of two feature points on the CMB. If you calculate the distance from us at the center to two points at the surface, you can remove the arc and end up with a perfect Triangle that will always add to 180'.

That doesn't prove or disprove the aspect that space is flat or not. You need more information.

The only way I can see is to reverse the concept and put the base of the triangle at the center and target a single point on the CMB. That way, you can use triangulation for the curvature (knowing two of the Angles).

But the problem with that is our greatest base length is the opposite sides of the earths orbit around the sun. With that limitation, we can't even even triangulate the distance to the nearest star. See? You need at least two parts of the Triangle to compute the 3rd angle. You can't do it only knowing 1 angle (home base).

You need more information!

From the North Pole to two points on the Earth at the Equator spaced at 25% of the Earths circumference where my local angle is 90', I will still calculate their angles to be 45' each when in fact, they are 90' each. Get it? You still need at least two angles to complete a proper triangle. You can't know the Angles at the Equator are 90' each unless you go there.

So again.. How do we know the values of the missing information?

As far as existing on the Surface of a Hyper-Sphere, 3D space will still look and measure flat (even when it's not). One needs to wrap their mind around 4D Geometry. (not easy)

Keep in mind that the standard inflationary model assumes every place in 3D space is the center, thus one can never reach the CMB no matter how fast you can travel (unless you can time travel..lol). See? In a 3D model of the Universe, someone has to be closer to the CMB horizon. But the CMB is in everyone's History at the same distance time wise. That's significant.

Regards,
Dave :^)

[Andrex]

Here is how I think it is done:



The distance between the satellite and CMB is 13, 7 billion light-years (which is a distance). The distance between both points on the CMB is given by the degrees chosen for the angle from the satellite; which is easy to transform in a distance mesure between the two points on CMB (mesure which becomes the base of the triangle). So you have one angle with a degree and one known length for the each sides of the triangle. You don't need more to find the degrees for the two angles missing. But like you say, what ever the measurements amount to, it will always give a triangle totalising 180o for the sum of its angles if we can't "see" the curvature of the light trajectory.

So, you have to check if the length of the base's triangle corresponds to the arc of the CMB behind it. To find the length of the arc, scientist know that the brightest microwave background fluctuations (or "spots") on the arc would be about one degree across if the universe is "flat". If the arc doesn't correspond to the base of the triangle, the light coming from CMB as a curved trajectory.
The "baseline of the triangle" is the patch of sky occupied by the largest fluctuations in the primordial plasma at the moment when the universe became transparent to light (CMB)

If the light coming from CMB as a curved trajectory, the sum of the degrees of the tree angles won't be 180o (The length of the arc is longer or shorter than what the length of the base of the triangle represents) .

Right now the precision to get to 180o is as little as I wrote previously. I agree, it doesn't tell us why the universe is so close to flatness, but the observation is mainly based on the "critical density". Which is completed by adding dark matter and dark energy. Two things that nobody ever observed. So what else can we say? I don't know.

As far as existing on the Surface of a Hyper-Sphere, 3D space will still look and measure flat (even when it's not).

Look again at the sphere with the triangle on it; the sum of the tree angles is 270o and that is what tells you that the surface represented by the triangle on your "flat" paper, is "curved". That is the same as a triangle figured on the Earth surface and represented on a "flat" sheet of paper. Just think of the trajectories of planes from one point to the other; they are not represented by straight lines on a sheet of paper; they are represented by "curved" lines.

Keep in mind that the standard inflationary model assumes every place in 3D space is the center,

Which means that you can do your triangle from anywhere in space and it will give you the same information regarding the overall "flatness". Mind you, you cannot place yourself closer or farther than 13,7 billions light-years from CMB. :-)

the CMB is in everyone's History at the same distance time wise

you should add...and distance wise.

[BurtJordaan]

Here is how I think it is done:

I don't think so. Imagine you sit at the center of local sphere and I am on the inside surface, where I choose 3 points so that they form a triangle. I connect the 3 points so that each line is great circle (geodesic). You can then use your optical instruments to measure the sum of internal angles of my triangle.

This is similar to how astronomers measure the overall spatial curvature of space using the CMB observations. My task was taken over by nature in the form of predictable ripples and oscillations that are present in the density of the CMB surface. Cosmologists use a lot of different datasets to find the most accurate curvature that fits all the observations so far.