[saspinski (OP)]

I was watching a video about astronomy and from the Hubble Law ( v = H0*r ), the age of the universe was said to be 1/H0. The estimated age changed in the last decades acccording to more and more precise measurements of H0.

At first it puzzled me, because v = H0*r is a differential equation, dr/dt = H0*r => r = Aexp(H0*t). But the age of the universe would be much greater, and not 1/H0.

After some time I realized that physics since Hubble time may have taken the galaxies as moving bodies free from external forces => constant velocities, and t = d/v. So, going backwards, in a time t = 1/H0 all the stuff was in a single place. And H0 as measured now, because it had to be greater and greater in the past.

When Hubble and others looked at so nice linear relation between a function and its derivative, an exponential universal expansion should be a natural hypotesis. But I never read that it was considered.

[evan_au]

Detection of the accelerating expansion of the universe required a red-shift survey of very distant galaxies that was not possible in Hubble's day. If you can only measure red-shift on fairly nearby galaxies, you will deduce a linear relationship.

Some cosmologists speculate that if the expansion of the the universe is speeding up (faster than Einstein's Cosmological Constant would imply), then we could end up with a "Big RiP". But this is a minority view.
https://en.wikipedia.org/wiki/Big_Rip

[evan_au]

Was an exponential universal expansion ever postulated?

Even those theories which suggest rapid acceleration in the future recognise that in the distant past, the universe was more compact and denser.

This means that the effect of gravity dominated, and there was a decelerating expansion.
However, there was a breakeven point in the expansion where the two forces balanced; this is estimated to be about 5 billion years ago. After this, the expansion accelerated.
See: https://en.wikipedia.org/wiki/Accelerating_expansion_of_the_universe

[alancalverd]

Worth noting that the "Hubble Law" (a) isn't established as a law at all, but is a rough approximation to a number of observations and (b) describes only the observable part of the universe. The apparent isotropic acceleration of distant objects requires an additional inflationary force within the observable universe but as yet unobserved, or an external "suction" from a source that cannot be observed directly.

[opportunity]

Videos are great.

If videos focus on what is actually happening, its hard to "convince" against otherwise ideas. Knowing what happened is "closure".

The point is videos make statements, and....we have to weigh that up.

A lot of our understanding of the universe thanks videos, yet where is the granular usefulness? Videos propose realities in the universe more "touched" than any greatest fantasy.

[saspinski (OP)]

1/H0 is still today taken as a good aproximation of the universe age. For H0 = 67 km/s/Mpc, = 6,8 *10^-14 km/year/km => 1/H0 = 14,7 billions of years, close to what is believed to be true.

I can understand that the idea since Hubble was supposing the same initial huge velocities for different bunches of matter. And those velocities being almost constant since then, increasing the relative distance between galaxies.

On the other hand, an exponential expansion would be more like a "small bang":  a small speed, gradually increasing with time. A galaxy at 1 billion of ly, if observed when it was at 500 millions of ly would have the same redshift of a galaxy today at 500 millions of ly.

Of course both approaches need corrections factors, but the later, as far as I know, was never mentioned as a core hypothesis.

[alancalverd]

a small speed, gradually increasing with time.

Why would the radial speed increase with time? Acceleration requires a force. Since that force would be separating all objects in the universe, why haven't we measured it?

[saspinski (OP)]

Why would the radial speed increase with time? Acceleration requires a force. Since that force would be separating all objects in the universe, why haven't we measured it?

Well, there is acceleration, it is observable according to the last findings. The way to account for it is tweaking the cosmological constant.

[Bill S]

Does "tweaking the cosmological constant" actually explain anything, or just shift the problem to somewhere where it can be sidelined?