Horizon problem - why do we need inflation?

[Chalnoth]

Ok, looks like we have reached the constructive disagreement

But just 1 another question:

Do you agree that in the form how you wrote it:

C(\vec{r_1}, \vec{r_2}) = \sigma^2 \delta^3(\vec{r_2} - \vec{r_1})

There is no difference between that formula (except it is valid for t=0) and other formulas, responsible for Newtonian laws is our toy universe?

There's a huge difference: that formula requires a specific definition of coordinates, while any good physical law is independent of coordinate choice.

Why?
Homogeneity is symmetry which can be easily broken using randomness in CI or splitting in MWI. Then dark matter had 100000 years to magnify initial tiny fluctuations.

You have to have some sort of mechanism to generate the initial fluctuations, though. You can't simply say, "It's because of quantum mechanics."

This is one thing inflation does, by the way: it provides a mechanism for the generation of initial perturbations.

 

[Dmitry67]

1. Wow! Thank you! What a nice argument that I am right!
So this formula introduces another parameter, special frame where it is valid.
Our Universe has something like that (even it is not a 'frame', but in every point of the universe there is a special frame which is 'in rest to CMB'). So this is some kind of broken symmetry.

If initial conditions are not homogenous, then in some rest frames they are anisotropic

But even more, if density=const, then the actual value of const depends on the choice of a frame. The only exception - vaccum, where energy density is canceled by vacuum tension

So the ONLY lorentz-invariant initial conditions is the vacuum

Thank you again!

2. Initial perturbations are generated in any changing gravitational field. Even now (unruh radiation from the horizon)

 

[Chalnoth]

If initial conditions are not homogenous, then in some rest frames they are anisotropic

Not at all. These initial conditions aren't anisotropic either. They're approximately anisotropic, and approximately homogeneous, for some observers. Not for all, of course.

And for what observer, pray tell, would these initial conditions actually be anisotropic?

But even more, if density=const, then the actual value of const depends on the choice of a frame. The only exception - vaccum, where energy density is canceled by vacuum tension

So the ONLY lorentz-invariant initial conditions is the vacuum

Who cares if the initial conditions are Lorentz-invariant?

2. Initial perturbations are generated in any changing gravitational field. Even now (unruh radiation from the horizon)

And there would be no changing gravitational field if there were no perturbations. Your argument is circular.

 

[Chronos]

It is possible that unconnected regions of the universe could have the same properties without being causally connected. What seems highly improbable is they could be so remarkably similar in all directions.

 

[Dmitry67]

These initial conditions aren't anisotropic either. They're approximately anisotropic, and approximately homogeneous, for some observers. Not for all, of course.
And for what observer, pray tell, would these initial conditions actually be anisotropic?

For an observer moving thru that matter distributed 'randomly'
In the direction where she moves the Universe looks contracted due to Lorentz contraction.

Who cares if the initial conditions are Lorentz-invariant?

Occam.
Why are you introducing a preferred frame from the very beginning?
Why that particular fram is chosen?

And there would be no changing gravitational field if there were no perturbations. Your argument is circular.

Expansion itself does not require perturbations.

 

[Chalnoth]

For an observer moving thru that matter distributed 'randomly'
In the direction where she moves the Universe looks contracted due to Lorentz contraction.

Oops, sorry, that was a miswording on my part. I meant to ask for which observer would random initial conditions be isotropic, not anisotropic.

Occam.
Why are you introducing a preferred frame from the very beginning?
Why that particular fram is chosen?

Well, as I've said, I see no reason to introduce initial conditions at all. I suspect that for big bang events like our own, the preferred frame just happens to be set by the particular event that precipitates the new expanding region, a frame that is different for each such region.

Expansion itself does not require perturbations.

It does require non-zero vacuum energy, though, which you seem to have set to zero. Otherwise it requires some sort of matter, which means perturbations.

 

[Dmitry67]

What seems highly improbable is they could be so remarkably similar in all directions.

This is what I am trying to understand. Why?

There are 2 options: initial conditions are simple and there are no parameters;
Initial conditions are complicated and there are many parameters;

Why between these options you chose the state with more information and complexity? For me it is less likely state.

 

[Dmitry67]

Oops, sorry, that was a miswording on my part. I meant to ask for which observer would random initial conditions be isotropic, not anisotropic.

isotropic of course for an observer looking the the Universe from the frame you used to define these initial conditions.

It does require non-zero vacuum energy, though, which you seem to have set to zero. Otherwise it requires some sort of matter, which means perturbations.

At least vacuum energy does not manifest directly (non-gravitationally) because its energy canceled by vacuum tension, and it is lorentz-invariant.

So I did not set it to zero. My requirement is just lorentz-invariance and minimum information (as less as possible free parameters)

 

[Chalnoth]

At least vacuum energy does not manifest directly (non-gravitationally) because its energy canceled by vacuum tension, and it is lorentz-invariant.

So I did not set it to zero. My requirement is just lorentz-invariance and minimum information (as less as possible free parameters)

In which case you don't have an expanding universe either, because the expansion breaks the Lorentz invariance.

 

[Haelfix]

Look, there is no way around it. If you want just the standard big bang to explain the horizon problem you are forced, by hand, to pick extremely special highly fine tuned values. That requires knowledge of every single perturbation that may enter the picture, at almost every scale and at every point in space.

It is a fact that any random set of initial conditions will assuredly not produce this result, and those that do are measure zero. Further, the observations cannot be explained by any simple choice of initial conditions, like say perfectly homogenous density profiles.

The analogy would be the following. Imagine that 10 years ago, when extra solar planets started to be discovered, the observation was that everywhere we found them, they looked identical to the earth. Same mass, same temperature, same chemical composition. Obviously, there is no reason that should be the case, so people would look for a hidden mechanism, perhaps something they overlooked about planet formation and not simply fall back upon initial conditions.

 

[Dmitry67]

The analogy would be the following. Imagine that 10 years ago, when extra solar planets started to be discovered, the observation was that everywhere we found them, they looked identical to the earth. Same mass, same temperature, same chemical composition. Obviously, there is no reason that should be the case, so people would look for a hidden mechanism, perhaps something they overlooked about planet formation and not simply fall back upon initial conditions.

I see what your problem is.

I agree, it would be very strange to find out that all these planets are identical! I agree with you. Because these planets had a HISTORY, an amount of PROPER TIME, and knowning that QM looks random (from observers perspective) it is very unlikely that different systems (even starting from the same conditions) end in the same final state.

Note this common-sense logic is not applicable to the initial conditions, because these systemes, these different regions did not experience any proper time before they are compared! Check my bold. There WAS NO REASON because there was no time before it!

Their state is axiomatically evolved, determined by some function. So it is logical to expect something simple (density=0) and it is unlikely to see something complicated, like, BM particles positioned in a form of unicorns.

 

[BillSaltLake]

One of the worst enemies of clear thinking is the illusion that we think we know more than we actually know. Without an actual model to compare to, we can't know whether one part in 100,000 is "high" or "low" in the single-example universe. It accomplishes nothing to say that you have a feeling that the observed number is too low.

Looking back in time, the Universe was smoother and smoother. Perhaps the information density (in some non-rigorous sense) approached zero at t=0. We don't yet know. If this was the case, then GR might predict perfect uniformity now (which is of course wrong).

One analysis that could predict a quotable number for fluctuations (at t > 0) is gaussian statistics. A sample with 10¹²⁰ photons (such as the observable Universe) might have an initial fractional deviation of one part in 10⁶⁰. I think this is sufficient (if this deviation were present at say the Planck time) to cause either collapse or runaway expansion by now. Smaller samples representing 1/10 or 1/100 of the Universe would have larger fractional deviations.

This 10⁶⁰ analysis is probably wrong because the gaussian count fluctuation applies to a system where the countable elements are in contact, and they were probably not in this case. However, if it were a valid analysis, it would yield a number that suggests inflation is necessary.