# A Variation of Hubble constant in cosmological time

1. May 14, 2017

### spaghetti3451

Is the Hubble constant decreasing over cosmological timescales?

2. May 14, 2017

### Bandersnatch

Yes:

3. May 14, 2017

### spaghetti3451

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

4. May 14, 2017

### 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.

5. May 14, 2017

### 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?

6. May 15, 2017

### Orodruin

Staff Emeritus
No.

7. May 15, 2017

### spaghetti3451

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

8. May 15, 2017

### Orodruin

Staff Emeritus
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.

9. May 15, 2017

### spaghetti3451

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

10. May 15, 2017