Cosmological Density Perturbation vs Homogeneity: Questions Answered

[victorvmotti]

TL;DR Summary

In the early universe, with smaller scale factor and with density perturbations, is homogeneous density still valid? Isn't this a contradiction?

When arriving at the standard model of cosmology, i.e. the exapnding universe, we assume based on experirmental data that the cosmos is homogenous on large enough scales.

But when we go back in time, when the galaxies are beginning to form, we note that because of the growth of density perturbation, these gravitationally bound systems can emerge after cooling down due to expansion.

Isn't the density perturbation in the early universe a contradition with the present homogeneous density used to arrive at the exapnding model with an scale factor.

Is there a cut off time in the past that the scale factor used in the metric fails to be a valid theory?

 

[PeterDonis]

Isn't the density perturbation in the early universe a contradition with the present homogeneous density used to arrive at the exapnding model with an scale factor.

No. The density perturbations were very, very tiny in the early universe; the early universe was more uniform than our present universe. The perturbations have grown by many orders of magnitude due to gravitational clumping over billions of years.

Is there a cut off time in the past that the scale factor used in the metric fails to be a valid theory?

No.

 

[victorvmotti]

Also, answered by ChatGPT, fairly accurate!

The standard model of cosmology, known as the Lambda-CDM model, assumes that the universe is homogeneous and isotropic on large scales, and that the universe is undergoing a period of accelerated expansion. This model is supported by a wide range of observational data, including the cosmic microwave background radiation, large-scale structure, and the observed abundances of light elements.

In the early universe, density perturbations did exist, but these were small and smooth, leading to the formation of galaxies and other structures we observe today. The density perturbations do not contradict the overall homogeneity of the universe, but rather represent small deviations from it.

The standard model of cosmology is considered to be valid from the time of the last scattering surface (when the cosmic microwave background radiation was emitted) up until the present day. Beyond this, the validity of the standard model is currently uncertain, and there may be other factors at play that we do not yet fully understand. The scale factor of the expanding universe is considered to be a good approximation for this time range.

 

[PeterDonis]

The standard model of cosmology is considered to be valid from the time of the last scattering surface

No, it isn't, it's considered to be valid considerably further back than that. The baryon/photon ratio and Big Bang nucleosynthesis take place much earlier than last scattering and predictions about those observables are part of the standard model of cosmology.

This is a good example of why ChatGPT output is not reliable; yes, in this particular case most of the answer is reasonably correct, but you can't trust it to be correct; you have to already know what's correct to judge the output. Which makes asking ChatGPT for answers pointless.

 

[victorvmotti]

How long has been the knowledge on this specific point of validity available in the physics literature? Like since which year?

 

[PeterDonis]

this specific point of validity

What "point of validity"? The point about the standard model of cosmology being valid further back than the surface of last scattering? At least four and a half decades, since that's how long ago I read about Big Bang nucleosynthesis in Steven Weinberg's popular book The First Three Minutes. Note the book title and compare with the fact that the surface of last scattering for the CMB is several hundred thousand years after the Big Bang.

 

[victorvmotti]

ChatGPT must have found that validity range of time some where, now with your answer it is clear that its reference is way older than 40 years

 

[PeterDonis]

ChatGPT must have found that validity range of time some where

No, that's not how ChatGPT works. It isn't a search engine; it doesn't look through actual text on the web or anywhere else to find the things it outputs. It builds a model of word frequencies and correlations from its training data, and then spits out text that is generated by its model based on the input you give it. It does not check its output against anything, and the text it outputs does not have to have appeared anywhere in its training data.

 

[PeterDonis]

@victorvmotti further discussion of how ChatGPT works is off topic here. The only relevant fact for this thread is that ChatGPT is not a valid source for PF discussion in the science forums, and output from it should not be posted in those forums; all it does is clutter the discussion with noise.

 

[victorvmotti]

No, it isn't, it's considered to be valid considerably further back than that. The baryon/photon ratio and Big Bang nucleosynthesis take place much earlier than last scattering and predictions about those observables are part of the standard model of cosmology.

Still a little confused here that a cut off time is not needed. So suppose we go much further back than last scattering. With very high energies and fluctuations of the quantum field, we could have very high or powerful gravitational waves, right? That means fluctuations of spacetime itself will be high, propagating in all directions, so can we still make sense of a homogenous universe in these conditions? How to make sense of the notion of density that we define and have in the current universe with somewhat fixed background, when spacetime of very early universe is having such big fluctuations?

 

[PeterDonis]

Still a little confused here that a cut off time is not needed

I'm not sure what you mean by "a cut off time". If you mean that there is an earliest time at which we are confident in our model, yes, of course there is; it's just a lot earlier than the surface of last scattering for the CMB. Roughly speaking, it's the time at which the average temperature of the universe was of the same order of magnitude that we can reach with our most powerful current high-energy experiments, such as the LHC.

However, the meaning of that time is not that the general type of model we are using, with homogeneity and isotropy and a scale factor, ceases to be valid before that time; that's not the case. Inflation models, for example, have those same properties--the only difference is the equation of state of the stress-energy present. If you are looking for a "cutoff time" before which the entire concept of spacetime is believed not to be valid, that would be the time at which the universe was at the Planck density--at least that's what most physicists currently believe.

 

[vanhees71]

Hm, it's a bit hard to say from which epoch on in the table in

https://en.wikipedia.org/wiki/Chronology_of_the_universe

one can say we are "confident of our model". I'm conservative and think we can only be starting to be "confident of our model", when we can observe at least the state of the observable matter, which are as far as we can be confident of "made of" the particles of the standard model, i.e., leptons, quarks, W- und Z-Bosons, gluons, and Higgs bosons. I'd say with some good will we can say we have observed and also measured some properties of the "quark gluon plasma" in relativistic heavy ion collisions, i.e., I'd say we can be optimistic to have understood the universe from what Wikipedia calls "the quark epoch" on.

The electroweak epoch is already plagued by the question, what provides enough CP violation to explain the resulting/obseverd matter-over-antimatter dominance, but at least we have some idea about this phase transition. So maybe we can be a bit more optimistic and say we can be pretty confident on what happens close the end of "the electroweak epoch".

What happened before, is imho still quite speculative, although the hypothesis of inflation seems to be quite convincing, but I'd not say it's also not something one can be really "confident" about.

 

[victorvmotti]

If you are looking for a "cutoff time" before which the entire concept of spacetime is believed not to be valid, that would be the time at which the universe was at the Planck density--at least that's what most physicists currently believe.

Yes, that is what I was looking for. More precisely, do you mean by the entire concept of spacetime not be valid that a continuous smooth (differentiable) 4D manifold does not make sense and spacetime, or the metric field, has to be discrete?

 

[PeterDonis]

do you mean by the entire concept of spacetime not be valid that a continuous smooth (differentiable) 4D manifold does not make sense

Yes, that is what many physicists believe happens at energy scales above the Planck scale.

and spacetime, or the metric field, has to be discrete?

No, we don't know this, it's just one of many speculations about what might happen above the Planck scale.