Why Doesn't the Comoving Hubble Length Always Increase?

[alialice]

How can inflation explain the particle horizon's problem?

 

[Mark M]

The horizon problem refers to the fact that the universe is the same temperature everywhere, yet it should have expanded far too fast for the temperature to balance out. Inflation solves this problem by allowing the universe to expand slowly at first and reach a specific temperature, and then undergo an enormous expansion.

 

[Naty1]

yes:

Inflation solves this problem by allowing the universe to expand slowly at first and reach a specific temperature via causal contact, and then undergo an enormous expansion.

alialice:
But I am not sure there is a 'particle horizon problem"

As a consequence of this inflationary expansion, all of the observable universe originated in a small causally connected region. Inflation answers why does the universe appear flat, homogeneous, and isotropic...
Is THAT the 'problem' to which you refer?

 

[alialice]

The horizon problem refers to the fact that the universe is the same temperature everywhere, yet it should have expanded far too fast for the temperature to balance out. Inflation solves this problem by allowing the universe to expand slowly at first and reach a specific temperature, and then undergo an enormous expansion.

Is THAT the 'problem' to which you refer?

The problem to which I refer is that answered by Mark M.
In the hot big bang theory, there is no time for photon to travel along the entire universe to explain the high degree of uniformity of CMB. Regions separated by more than 2 degrees would be causally separated at the period of decoupling. So it was postulated the theory of inflation as cited above.
My question is referred to the Hubble length:
(for reference see An introduction to cosmological inflation by Andrew R. Liddle, you can found it in arXiv)
It has been said that the Hubble length decreases during inflation (page 9).
I don't understand what is the meaning of this, probably I don't understand the meaning of Hubble length with respect to the scale factor a (page 5).
If can help me, thank you.

 

[Bobbywhy]

How can inflation explain the particle horizon's problem?

Classical relativistic cosmology is known to have the space-time singularity as an inevitable feature. The standard big bang models have very small particle horizons in the early stages which make it difficult to understand the observed homogeneity in the universe. The relatively narrow range of the observed matter density in the neighborhood of closure density requires highly fine tuning of the early universe. These represent the “particle horizon problem”.

 

[Bobbywhy]

yes:



alialice:
But I am not sure there is a 'particle horizon problem"

As a consequence of this inflationary expansion, all of the observable universe originated in a small causally connected region. Inflation answers why does the universe appear flat, homogeneous, and isotropic...
Is THAT the 'problem' to which you refer?

Classical relativistic cosmology is known to have the space-time singularity as an inevitable feature. The standard big bang models have very small particle horizons in the early stages which make it difficult to understand the observed homogeneity in the universe. The relatively narrow range of the observed matter density in the neighborhood of closure density requires highly fine tuning of the early universe. These represent the “particle horizon problem”.

 

[Chronos]

The particle horizon idea is very simple - it is merely the speed of light times the age of the universe. Confusion arises because the universe has been expanding since day one. The fact the rate of expansion has been accelerating over the past 5 or so billion years further complicates matters. Once you 'do the math', it becomes clearer.

 

[Naty1]

alia:

It has been said that the Hubble length decreases during inflation (page 9).

Hubble length [radius] is a concept I just know is lurking to fool me again.

I posted a related question recently based on a new paper:

...The quantum fluctuations generated during the inflationary phase — which act as seeds of structure formation in the universe— can be characterized by their physical wavelength. Consider a perturbation at some given wavelength scale which is stretched with the expansion of the universe as λ ∝ a(t). During the inflationary phase, the Hubble radius remains constant while the wavelength increases...,

My question:
So the first two sentences are ok...but can someone explain the underlying logic from which I can understand why the 'Hubble radius remains constant'...yet wavelength is stretched as the scale factor [a] evolves?

and the answer is post #10 here:

https://www.physicsforums.com/showthread.php?p=3984153#post3984153

There is some other discussion in that thread that may also be of interest to you.

 

[alialice]

My question:
So the first two sentences are ok...but can someone explain the underlying logic from which I can understand why the 'Hubble radius remains constant'...yet wavelength is stretched as the scale factor [a] evolves?

and the answer is post #10 here:

https://www.physicsforums.com/showthread.php?p=3984153#post3984153

There is some other discussion in that thread that may also be of interest to you.

Thank you.
I know that during the inflationary phase, H=Lambda/3, where Lambda is the cosmological constant, and the expansion is exponential. So H is constant.
But in Liddle it is said:

"During inflation
\frac{d\left( H^{-1} /a\right)}{dt}<0
The Hubble length, as measured in comoving coordinates, decreases during inflation. At any other time the comoving Hubble length increases. This is the key property of inflation; although typically the expansion of the Universe is very rapid, the crucial characteristic scale of the Universe is actually becoming smaller, when measured relative to that expansion."

How is this related to what we have observed above?

 

[George Jones]

I know that during the inflationary phase, H=Lambda/3, where Lambda is the cosmological constant, and the expansion is exponential. So H is constant.
But in Liddle it is said:

"During inflation
\frac{d\left( H^{-1} /a\right)}{dt}<0
The Hubble length, as measured in comoving coordinates, decreases during inflation.

H^{-1} /a is the comoving coordinate of the (proper) Hubble distance H^{-1}. If the Hubble distance is constant while the scale factor a increases, then the comoving coordinate of Hubble distance must decrease.

At any other time the comoving Hubble length increases. This is the key property of inflation;

While is true that

\frac{d\left( H^{-1} /a\right)}{dt}<0
is a "key property of inflation", it is no longer true that "At any other time the comoving Hubble length increases." Why not? Hint: Liddle's arXiv article is from 1999, which is not long after 1998.