Variation of Hubble constant in cosmological time

[spaghetti3451]

Is the Hubble constant decreasing over cosmological timescales?

 

[Bandersnatch]

Yes:

 

[spaghetti3451]

Why did the Hubble constant tend to infinity in the early universe?

 

[Bandersnatch]

Mostly for the same reason that f(x)=1/x goes to infinity as x goes to 0. Remember that H is the proportionality factor between recessional velocities and distances: H=V/D. As the distances between receding objects decrease to 0, H goes to infinity.
An additional effect comes from V being larger in the past, but that's secondary.

 

[spaghetti3451]

The relation

$$H = 1.67 \sqrt{g_{*}} \frac{T^{2}}{M_{P}}$$

is valid during the radiation-dominated epoch. Is it valid during the inflationary epoch?

 

[Orodruin]

The relation

$$H = 1.67 \sqrt{g_{*}} \frac{T^{2}}{M_{P}}$$

is valid during the radiation-dominated epoch. Is it valid during the inflationary epoch?

No.

 

[spaghetti3451]

What would be the correct relation for the Hubble parameter in the inflationary epoch?

 

[Orodruin]

That would depend on the equation of state for whatever is driving inflation. If what drives inflation behaves as a cosmological constant, then the Hubble parameter would be constant during inflation.

 

[spaghetti3451]

Would you share a review article which discusses this in more detail?

 

[Bandersnatch]

Would this be of any help?
https://ned.ipac.caltech.edu/level5/Watson/Watson5_3.html