If Hubble's parameter remained constant

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SUMMARY

If Hubble's constant (H0) remains constant over time, the cosmological scale factor a(t) increases linearly between two times t0 and t. The relationship is defined by Hubble's law, which states that the rate of expansion of the universe is proportional to the distance from the observer. To derive the scale factor, one must integrate Hubble's law, specifically the equation d(dt) = H0 dt, over the interval from t0 to t. This integration yields a straightforward relationship between the scale factor and time, confirming that a(t) grows as time progresses.

PREREQUISITES
  • Understanding of Hubble's law and its implications in cosmology
  • Familiarity with the concept of the cosmological scale factor a(t)
  • Basic knowledge of calculus, specifically integration techniques
  • Awareness of the significance of Hubble's constant in cosmological models
NEXT STEPS
  • Study the derivation of the cosmological scale factor a(t) under constant Hubble's constant
  • Learn about the implications of a changing Hubble's constant on cosmic expansion
  • Explore the integration techniques used in cosmological equations
  • Investigate the historical context and measurements of Hubble's constant
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Astronomy students, cosmologists, and physicists interested in the dynamics of cosmic expansion and the mathematical foundations of cosmological models.

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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.
 
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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?
 

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