# If Hubble's parameter remained constant

• ULstudent91
In summary, the question asks how the cosmological scale factor a(t) changes between two times t0 and t if the Hubble's constant H0 remains constant. The person asking for help has attempted to use Hubble's law to integrate and find the answer, but has not been successful so far. They are looking for assistance with finding the correct solution.
ULstudent91
If Hubble’s constant H0 = da/a does not change in time between two times t0 and t, how does the cosmological scale factor a(t) vary between these times?

This is from a past exam paper, and being quite honest I don't even know where to start with it. Any help would be appreciated.

So far I think the scale factor is supposed to increase, if the hubble's constant is constant.
I have tried integrating Hubble's law d(dt)= H0dt between t0 and t but I'm not getting an answer I'm looking for.

Last edited:
ULstudent91 said:
I have tried integrating Hubble's law d(dt)= H0dt between t0 and t but I'm not getting an answer I'm looking for.

What do you get?

## What is Hubble's parameter?

Hubble's parameter, also known as the Hubble constant, is a measure of the rate at which the universe is expanding. It is denoted by the letter H and has units of kilometers per second per megaparsec (km/s/Mpc).

## Why is it important to study the constancy of Hubble's parameter?

Studying the constancy of Hubble's parameter can help us understand the evolution and fate of the universe. If the parameter remains constant, it suggests that the universe is expanding at a steady rate. However, if it changes over time, it could indicate the presence of unknown forces or phenomena that affect the expansion of the universe.

## What evidence do we have for the constancy of Hubble's parameter?

Several observations, including the redshift of galaxies and the cosmic microwave background radiation, support the idea that Hubble's parameter has remained relatively constant over the history of the universe. However, there is ongoing debate and research on the exact value of the parameter and whether it is truly constant.

## How do scientists measure the constancy of Hubble's parameter?

Scientists use a variety of methods to measure the Hubble constant, including analyzing the light from distant objects, such as supernovae and galaxies, and using mathematical models based on the theory of general relativity. These measurements are constantly being refined and updated as new data becomes available.

## What are the implications if Hubble's parameter is found to not be constant?

If Hubble's parameter is found to vary significantly over time, it could challenge our current understanding of the universe and potentially lead to new theories and discoveries. It could also have implications for our understanding of dark energy and the future expansion of the universe.

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