WMAP proves spacetime HAS BEEN flat ??

[Widdekind]

People seem to say, that WMAP "proves" that our spacetime "is" flat; for, curved spacetime would lens and distort, our view, of the CMB.

 

But, CMB photons, observed by WMAP, have traveled across our cosmos, from the distant past, i.e. from "way over there, way back then"; to our modern earth, i.e. to "here, now". Thus, the flatness implied, by those un-lensed, un-distorted CMB photons, reflects their inbound, earth-bound, sightlines, from far far away, over the past ~10 Gyr. Er go, WMAP proves that our space-time HAS BEEN flat, along the light-like null-geodesics, along which those photons HAVE traveled, over the PAST billions of years, from the last-scattering-surface "then", to earth "now".

 

And, WMAP does not prove, that our space-time fabric IS flat, at PRESENT, in non-causally connected regions of space-time, at space-like separations from our earth, "here & now", to some distant regions of space, "there & now". Again, how could WMAP photons, from the CMB, which traveled through "there & then", imply anything whatsoever at all, directly, about "there & now", i.e. in space-like separated regions of space, "off of & above" our light-cone, about which WMAP photons "know nothing" directly ??

 

Borrowing a figure from another thread, WMAP observes photons, from our past-light-cone, from "there, then" to "here, now". So, how could WMAP photons directly imply anything whatsoever at all, about conditions in our space-time fabric, any "where-or-when" off of our past-light-cone, i.e. the null-geodesic lines-of-sight, along which those CMB photons traveled, e.g. points A or B, in the following figure ??

 

[Widdekind]

COBE + WMAP observations imply that our space-time fabric has been 'flat', all along the inbound CMB photon sight-lines, i.e. 'null geodesics', from the 'Last Scattering Surface' (LSS) "out-there-back-then", to earth "here-now", each 'event' (emission, detection) being at a 'light-like' separation from the other. However, CMB photons cannot carry non-local information, about elsewhere in space, "out-there-now", at 'space-like' separations from earth.

 

Therefore, CMB observations do not imply, that the matter-and-energy density, in our universe is 'critical', i.e. [math]\Omega_{M}(t_0) + \Omega_{\Lambda}(t_0) \neq 1[/math]; but, instead, that the matter-and-energy density, in our universe, has been critical, i.e. [math]\Omega_{M}(x,t) + \Omega_{\Lambda}(x,t) \approx 1 \; \forall x,t[/math] along in-bound CMB LOS, i.e. on our past light-cone.

 

The matter density was higher, i.e. closer to 'critical', in the past. Therefore, choosing a 'Dark Energy' (DE) density to achieve 'critical' closure density, at present epoch, would imply that the overall matter-and-energy density has been supra-critical, in the past:

 

[math]\Omega_{M}(t_0) + \Omega_{\Lambda}(t_0) \equiv 1[/math]

[math]\implies[/math]

[math]\Omega_{M}(x,t) + \Omega_{\Lambda}(x,t) \gg 1 [/math]

[math]\forall x,t[/math] on our past light-cone.

 

Please understand, that I'm asking a question -- have I made any errors, in this analysis ? What am I missing, i.e. how can CMB photons, from our past light-cone, directly reflect information, about space-like separated space-time, at present epoch ?? And, if CMB photons, from our past light-cone, directly reflect light-like separated space-time; and if those CMB photons imply that the space-time of our past-light cone has been 'flat'; then how could a constant-value Cosmological Constant account for that 'flatness' ? Would not 'DE' density have to evolve, in a matter-like way, in order to remain 'in lock-step', with matter density, "the whole way & entire time", from LSS "there-then", to earth "here-now", i.e. [math]\Omega_{M}(x,t) + \Omega_{\Lambda}(x,t) \approx 1 \; \forall x,t[/math] along in-bound CMB LOS ?

Edited November 25, 2011 by Widdekind

[guenter]

What am I missing, i.e. how can CMB photons, from our past light-cone, directly reflect information, about space-like separated space-time, at present epoch ??

Ω_M and Ω_lambda can vary with time. However their sum, the density parameter Ω = Ω_M + Ω_lambda = 1 over time. So, the universe had, has und will have euclidian geometry.

[IM Egdall]

We are talking here about the OBSERVABLE universe here. This does not necessarily mean the entire universe, including what we can see and what we cannot see, is also "flat".

Edited November 30, 2011 by IM Egdall

[PorpoiseSeeker]

I suppose the best we can do is apply the cosmological principle (what's here is there) and speculate that what is outside our light cone must be like what we can see.

 

As Widdekind suggests, we can't prove anything we can't measure and observe.

 

In Lee Smolin's Three Roads to Quantum Gravity, he suggests that Topos theory offers mathematical tools to express partial or incomplete knowledge of the sort we seem to discuss here. The longer we wait, the more of the universe our light cone intercepts. Your light cone and mine can intercept different parts of the universe. But you and I can enter into an "honest" relationship (Smolin's words) and each learn more about the universe that we could know on our own. The tool (as far as I can tell) is called Adjointness (see Goldblatt, Topoi, around p430). It is a challenge to get one's head around being an observer of the universe from inside while being a component or product of that universe. The classical separation of observer and observed does not apply. Topos seems to provide tools that don't fall prey to self-reference paradoxes and incompleteness problems.

 

Is there a forum discussion for this topic?

[guenter]

Yes, nobody can exclude the possibility that the observable universe is a special place. However the standard FRW cosmology seems more likely.

[IM Egdall]

Yes, nobody can exclude the possibility that the observable universe is a special place. However the standard FRW cosmology seems more likely.

 

I think most cosmologists would say the reason why we see a "flat" observable universe is due to inflation -- the exponential expansion of the very early universe.

 

Per Wikipedia: http://en.wikipedia....ion_(cosmology)

 

"As a direct consequence of (inflation), all of the observable universe originated in a small causally connected region. Inflation answers the classic conundrum of the Big Bang cosmology: why does the universe appear flat, homogeneous and isotropic in accordance with the cosmological principle when one would expect, on the basis of the physics of the Big Bang, a highly curved, heterogeneous universe?"

 

Doesn't this imply that, even though our observable universe is flat, the entire universe is most probably not?

Edited December 2, 2011 by IM Egdall

[guenter]

Doesn't this imply that, even though our observable universe is flat, the entire universe is most probably not?

No, because according to the cosmological principle (FWR-cosmology), the local geometry is the same in arbitrary locations in the universe. Using PorpoiseSeeker's wording, if it is flat here, it's flat there.

 

But one should keep in mind, that the cosmological principle is an assumption.

[IM Egdall]

No, because according to the cosmological principle (FWR-cosmology), the local geometry is the same in arbitrary locations in the universe. Using PorpoiseSeeker's wording, if it is flat here, it's flat there.

 

But one should keep in mind, that the cosmological principle is an assumption.

 

 

I don't think physicists know this for sure. I think the entire universe is expected to not be flat. The curvature of the entire universe could be anywhere from -1 to +1. WHy does the obervable universe happen to have the exact value of 0? Inflation theory is supposed to answer this question.

 

 

 

Inflation makes our local observable universe flat. The analogy is: an ant looking across a football field thinks Earth is flat (this represents the observable universe). But a global view of the entire Earth shows it is curved. Inflation expanded the universe so much that it appears flat in the part we can observe, but the entire universe may not be.

 

So the cosmological priciple holds for the observable universe but probably does not for the entire universe.

Edited December 4, 2011 by IM Egdall

[guenter]

So the cosmological priciple holds for the observable universe but probably does not for the entire universe.

Look here :

 

The cosmological principle is usually stated formally as 'Viewed on a sufficiently large scale, the properties of the Universe are the same for all observers.' This amounts to the strongly philosophical statement that the part of the Universe which we can see is a fair sample, and that the same physical laws apply throughout.

and

as Andrew Liddle puts it, "the cosmological principle [means that] the universe looks the same whoever and wherever you are."

It would be meaningless to talk about a 3-torus-topology (signature of WMAP data) of the universe, if the cosmological principle wouldn't hold for any location on the torus, including our observable universe.

[michel123456]

and

as Andrew Liddle puts it, "the cosmological principle [means that] the universe looks the same whoever and wherever you are."

But not whenever.

[Widdekind]

Ω_M and Ω_lambda can vary with time. However their sum, the density parameter Ω = Ω_M + Ω_lambda = 1 over time. So, the universe had, has und will have euclidian geometry.

 

Can I question this conclusion? Please ponder the far future, i.e. [math]\Omega_M \rightarrow 0[/math]. Then, the only matter-energy density "left standing" is the [math]\Omega_{\Lambda} \approx 3/4[/math] term. If so, then, in the far future, [math]\Omega \approx \Omega_{\Lambda} \approx 3/4[/math], which is <1.

[guenter]

Can I question this conclusion? Please ponder the far future, i.e. [math]\Omega_M \rightarrow 0[/math]. Then, the only matter-energy density "left standing" is the [math]\Omega_{\Lambda} \approx 3/4[/math] term. If so, then, in the far future, [math]\Omega \approx \Omega_{\Lambda} \approx 3/4[/math], which is <1.

Ω = Ω_M + Ω_lambda = 1 over time, whereby Ω means the resp. energy density / critical density. Sorry, I can't write the correct symbols.

 

The microwave background revealed Ω = 1 (universe is flat) and Ω_M = 0.3 (roughly). So, an important contribution Ω? = 0.7 was missing. To detect this missing energy, later called dark energy, by analysing supernova Ia data independent of the CMB in the wright amount was a tremendous success.

 

From this it should be clear that the ratio Ω_M / Ω_lambda was very large in the past and will be very small in the future.

 

The curvature of the entire universe could be anywhere from -1 to +1.

In case you talk about chaotic inflation, meaning various universes, then you can expect a variation of geometry from universe to universe. However this is highly speculative and not standard cosmology.

[IM Egdall]

Am reading The Goldilocks Enigma by cosmologist Paul Davies. On page 275, he says "The limited accuracy of these (WMAP) observations cannot establish the universe is exactly flat. What they tell us is that if the universe is shaped like Einstein's hypersphere (positive curvature, not flat), then the radius of the hypersphere is exceedingly large, so that within the volume of space probed by our instruments (the observable universe), we cannot discern any curvature. Similar remarks apply to any negative curvature."

 

 

In other words, like ants on a gigantic balloon, we measure the region of the overall universe we can see as flat, but the overall universe may be positively (or negatively) curved.

 

I find physicists are very sloppy with their language and often use the word "universe' when they mean "observable universe." I claim the cosmological principle applies to the observable universe (due to inflation) and may not apply to the entire universe. I think Davies backs me up on this.

 

Please comment -- I welcome enlightenment.

[guenter]

Please comment -- I welcome enlightenment.

Let me try.

 

Wikipedia says: "The WMAP data are consistent with a flat geometry, with Ω = 1.02 +/- 0.02"

This is in agreement with Paul Davis. There is a very slight possibility, that the universe isn't flat, it could be a hypersphere. The majority of the cosmologists expect exact flatness however. They are arguing there should be a specific reason for that and that is inflation. It is very unlikely to arrive at Ω = 1.02 after blowing up the universe by a factor of 10^30. The Planck mission will increase the accuracy of Ω, then we know more.

 

So, Davis argues correctly with a lack of accuracy. He doesn't say the universe can be flat here and spherical or hyperbolic there. His message is, if it seems flat here then it still could be spherical. And of course, the larger the assumed radius, the lesser one can exclude spherical geometry, even in case Planck would yield Ω = 1.001 +/- 0.001.

 

If your claim that the cosmological principle applies only to the observable universe was correct, then why are cosmologists writing papers concerning the topology of the universe, the global structure of the universe as a whole? This wouldn't make any sense, if the cosmological principle wouldn't hold for the entire universe. But, it seems, I repeat myself. It is the Copernician idea, that the observable universe isn't special.

 

On the other hand, you can stay with your claim, why not. The standard cosmology is based on more or less plausible assumptions. In my opinion nobody can proof that you are not correct. Should you identify papers which support your claim, I would be interested.

[IM Egdall]

Let me try.

 

Wikipedia says: "The WMAP data are consistent with a flat geometry, with Ω = 1.02 +/- 0.02"

This is in agreement with Paul Davis. There is a very slight possibility, that the universe isn't flat, it could be a hypersphere. The majority of the cosmologists expect exact flatness however. They are arguing there should be a specific reason for that and that is inflation. It is very unlikely to arrive at Ω = 1.02 after blowing up the universe by a factor of 10^30. The Planck mission will increase the accuracy of Ω, then we know more.

 

So, Davis argues correctly with a lack of accuracy. He doesn't say the universe can be flat here and spherical or hyperbolic there. His message is, if it seems flat here then it still could be spherical. And of course, the larger the assumed radius, the lesser one can exclude spherical geometry, even in case Planck would yield Ω = 1.001 +/- 0.001.

 

If your claim that the cosmological principle applies only to the observable universe was correct, then why are cosmologists writing papers concerning the topology of the universe, the global structure of the universe as a whole? This wouldn't make any sense, if the cosmological principle wouldn't hold for the entire universe. But, it seems, I repeat myself. It is the Copernician idea, that the observable universe isn't special.

 

On the other hand, you can stay with your claim, why not. The standard cosmology is based on more or less plausible assumptions. In my opinion nobody can proof that you are not correct. Should you identify papers which support your claim, I would be interested.

 

 

Thank you for your response. I ask one thing. Please use the terms "observable universe" and "entire universe" so I can better understand your points.

 

I do agree with you that "if the universe seems flat here, then it still could be spherical." I think this is saying the observable universe seems flat, but the entire universe could be spherical.

 

And I don't think the possibility that the entire universe is spherical or negatively curved is slight. Doesn't general relativity say it is very likely curved in some way. After all, having a net curvature of zero seems an extraordinary coincidence. In fact, the big question before inflation theory was why our observable universe appears flat. Inflation explained why the observable universe is flat -- because it has been expanded exponentially. But again, the entire universe would still retain some curvature even after inflation. Wouldn't it?

 

What I am trying to say about the cosmological principle is that if the entire universe is not flat, then this principle applies only to the observable universe. And yes, I agree that anywhere in the entire universe, the observable part obeys the cosmological principle. But not necessarily the universe as a whole. Does this make sense to you?

Edited December 6, 2011 by IM Egdall

[guenter]

I do agree with you that "if the universe seems flat here, then it still could be spherical." I think this is saying the observable universe seems flat, but the entire universe could be spherical.

Supposed Ω = 1.02 exactly (what we don't know), then it seems (almost flat) here in our observable universe and also in other arbitrary places thereout, because the value is close to 1. But infact it would be spherical, yes.

 

Sorry, I am in a hurry and will come back to your post later.

[guenter]

And I don't think the possibility that the entire universe is spherical or negatively curved is slight. Doesn't general relativity say it is very likely curved in some way. After all, having a net curvature of zero seems an extraordinary coincidence. In fact, the big question before inflation theory was why our observable universe appears flat.

According to General Theory of Relativity the sign of the curvature parameter k depends on the ratio total energy density / critical density = Ω. The curvature determined by this means the local curvature, which is important to know. And since the cosmological principle is the foundation of the FRW-model it follows that the local curvature is constant, means it is the same on each place in the entire universe.

To avoid a possible misunderstanding: Imagine the torus e.g., which is one of the 5 possible topologies in case k = 0 (flat). The torus as a whole looks round, however is flat locally everywhere. It is thus advisable not to mix up geometry with topology.

GRT says nothing about the topology, but there is a chance to detect it via the CMB.

 

Inflation explained why the observable universe is flat -- because it has been expanded exponentially. But again, the entire universe would still retain some curvature even after inflation. Wouldn't it?

Why are most of the cosmologists convinced that the universe is locally flat (see above), inspite of the uncertainty of Ω? If Ω would have been even very slighty >1 before inflation, then the entire universe would have collapsed within seconds and in the case of Ω <1 (even slightly) it would have expanded so fast that no galaxies could have been formed, because it is a slow process. This one has to believe as a result of the einsteinian equations. The conclusion is that the early universe (entire) was by a factor of 10^-15 closer to Ω = 1 than today (cosmologist G. Hasinger).

 

What I am trying to say about the cosmological principle is that if the entire universe is not flat, then this principle applies only to the observable universe. And yes, I agree that anywhere in the entire universe, the observable part obeys the cosmological principle. But not necessarily the universe as a whole. Does this make sense to you?

Sorry, I don't understand this point. Perhaps the above clarifies it.

Edited December 8, 2011 by guenter