A Variation of Hubble constant in cosmological time

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The discussion centers on whether the Hubble constant decreases over cosmological timescales, with a consensus that it tends to infinity in the early universe due to the relationship H=V/D as distances approach zero. The Hubble parameter's behavior during different epochs is highlighted, particularly its validity during the radiation-dominated epoch but not during inflation. During inflation, the Hubble parameter may remain constant if the driving force behaves like a cosmological constant. Participants seek further resources for a deeper understanding of these concepts. The conversation emphasizes the evolving nature of the Hubble constant in cosmological contexts.
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Is the Hubble constant decreasing over cosmological timescales?
 
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Yes:
H evolution.png
 
Why did the Hubble constant tend to infinity in the early universe?
 
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.
 
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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?
 
spaghetti3451 said:
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.
 
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What would be the correct relation for the Hubble parameter in the inflationary epoch?
 
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.
 
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Would you share a review article which discusses this in more detail?
 
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