$Question about Hubble's constant relating to the age of the universe.$

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$Question about Hubble's constant relating to the age of the universe.$

Hi, I've got a question about Hubble's constant that needs clarifying since I know my assumption is wrong, but it feels like the logic used is correct and I am not sure where I am going wrong.

If we consider two sets of galaxies, labeled as Set A and Set B. The galaxies within Set A are receding from us at a velocity of x, while those in Set B are moving away at a higher velocity of y, where y>x. Over time, due to the expansion of the universe, the recession velocity of galaxies in Set A increases until it matches the initial recession velocity of galaxies in Set B, denoted as y.

The question then arises when applying Hubble's Law, which relates the recession velocity of galaxies to their distance from us, thus allowing for the estimation of the universe's age. If we measure the distance and recession velocity of galaxies in Set A at the point their recession velocity equals y, and compare this to the distance and recession velocity of galaxies in Set B when their velocity was initially y, would we obtain the same estimate for the age of the universe? This query hinges on the principle that Hubble's Law provides a linear relationship between the recession velocity of galaxies and their distance from us, which in turn is used to infer the rate of expansion of the universe.

The crux of this inquiry is to understand whether the timing of observing these recession velocities impacts the estimated age of the universe, assuming identical velocities and distances are observed for both sets of galaxies. The linear nature of Hubble's Law suggests that the recession velocity directly correlates with distance, implying that identical velocities would correspond to identical distances, independent of when these observations occur. Consequently, this scenario posits that observing galaxies in Set A reaching a recession velocity of y at a later time should, in theory, yield a similar age estimate for the universe as observing galaxies in Set B with a recession velocity of y at an earlier time.

Thanks for reading.

Mathematical Physics

Mathgnome

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Based on Hubble's Law, if both sets of galaxies have the same recession velocity (y), their distances from us should be the same at that moment, regardless of when we observe them. The linear relationship implies that identical velocities correspond to identical distances.

Hubble's Law gives us a snapshot of the recession velocity and distance at a specific time. You're comparing Set A's current state (v = y, D1) with Set B's state at an earlier time (v = y, D2). However, both D1 and D2 correspond to the same expansion rate (Ho) at their respective times.

I think that Hubble's Law, while linear on large scales, doesn't necessarily imply a constant rate of expansion over time. It relates the recessional velocity of galaxies to their distance, but the rate of expansion can change over cosmic history due to various factors, one being the dark energy.

The overall expansion rate is a balance between the effects of gravity & dark energy. In earlier times, when galaxies were closer together, gravity dominated over dark energy; later, as the expansion proceeded, dark energy dominated.

I also think that observing galaxies in Set A reaching a recession velocity of y at a later time would indeed yield a similar age estimate for the universe as observing galaxies in Set B with a recession velocity of y at an earlier time if the expansion rate remained constant. However, if the expansion rate changed over time, which is suggested by current cosmological models, the ages estimated from these observations might differ. So, the timing of observing these recession velocities could impact the estimated age of the universe if the expansion rate varied over cosmic history.

Kav10

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$Question about Hubble's constant relating to the age of the universe.$

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