I Inflation resolves the horizon problem

[Apashanka]

Can anyone please explain how inflation removes the horizon. problem of standard cosmology .
As much I know inflation is a period of accelerated expansion which can be approximated by ~exp(βt) which can be achieved if the energy density remains constt. throughout (e.g ≠ε(t)),which is the case for the vacuum energy (since P=-ρ)

 

[Orodruin]

It expands a causally connected region to envelop the entire current horizon.

 

[Apashanka]

It expands a causally connected region to envelop the entire current horizon.

Will you please explain it in details...
Thank you

 

[Ibix]

If I look to the left, the oldest light I can see has been traveling for 13.9bn years. If I look to the right, the oldest light I can see has been traveling for 13.9bn years. Yet the things I'm looking at appear to be at the same temperature. Why? It would only make sense if they were in causal contact and came into thermal equilibrium. But that would need at least 2×13.9bn years, so there isn't time.

Inflation solves the problem by having a rapid expansion phase that takes parts of the universe that were causally connected and disconnects them.

 

[Orodruin]

Exactly what part of that is unclear?

If you expect answers tailored to your level you cannot just assume that people know where that is. You need to describe your current understanding and what part you find unclear.

You cannot expect people to write you a textbook excerpt. There are several good resources online. Have you read about it and in that case what was not clear?

 

[Orodruin]

But that would need at least 2×13.9bn years

Quite a bit more due to expansion.

 

[Apashanka]

We take our universe now to be dominated by the dark energy followed by matter and radiation ,and our universe is now in an accelerating phase (since present value of q <0(-1.52)) and it has to be since dark energy provides exponential growth.
It is therefore after the time of dark energy matter equality ,inflationary (accelerated) phase starts which is ε(t)_m=ε(t)_d
ε_0m/a³=ε_0d
,a³=ε_0m/ε_0d=Ω_m0/Ω_d0=0.04/0.23
a(t)=.057
z=1/a-1=16.54
Can we say that at this redshift inflationary (accelerated phase/dark energy) phase starts??
Since for the matter and radiation dominated phase d²a(t)/dt²<0.

 

[Arman777]

We take our universe now to be dominated by the dark energy followed by matter and radiation ,and our universe is now in an accelerating phase (since present value of q <0(-1.52)) and it has to be since dark energy provides exponential growth.
It is therefore after the time of dark energy matter equality ,inflationary (accelerated) phase starts which is ε(t)_m=ε(t)_d
ε_0m/a³=ε_0d
,a³=ε_0m/ε_0d=Ω_m0/Ω_d0=0.04/0.23
a(t)=.057
z=1/a-1=16.54
Can we say that at this redshift inflationary (accelerated phase/dark energy) phase starts??
Since for the matter and radiation dominated phase d²a(t)/dt²<0.

Why did you take $\Omega_m=0.04$ and $\Omega_{\Lambda}=0.23$ ? Thats wrong. You should also take the dark matter account hence $\Omega_m=0.31$ and $\Omega_{\Lambda}=0.68$