Thomas 'PointedEars' Lahn wrote:
root wrote:
become if the current rate of acceleration obtained over the entire lifetime?

In that case I will leave the calculation to you, because you *can* do
it Because in that case the age of our universe is easily obtained as
the reciprocal of the Hubble constant:

t = 1/H_0.

| Moderator's note: True if the current RATE of expansion were constant,
| but not if the current ACCELERATION were constant. -P.H.

The OP was not even talking about the `current acceleration', but the
`current rate of acceleration'.

| Moderator's note: Actually, the deceleration and acceleration almost
| balance so that the age of the universe is very close to the Hubble
| time. In our universe, this happens only near the present epoch. There
| have been a couple of papers addressing this coincidence. -P.H.

For example, if you use the Planck Collaboration's 2015 value of H_0 =
67.31 (km/s)/Mpc (TT+lowP) [1], with 1/H_9 = 14.5 Ga you do NOT obtain
Planck's corresponding t_0 = 13.813 Ga but something considerably
larger.

I think I have shown here that the moderator's statement is not true.
A difference of several hundred million years is NOT "very close".

Note in this 2006 depiction of an inflationary LambdaCDM model (based on
WMAP data) the extreme expansion speed in the epoch of inflation (as per
the theory of cosmic inflation) in the first 10^9 years; then a
moderate, almost linear expansion until our universe was 13 * 10^9
years old, followed by an accelerated expansion due to Dark Energy
(Lambda) since about 770 * 10^6 years ago.

| but in any case the age of the universe is essentially
| independent of inflation since that lasted only a fraction of a second.
| -P.H. There was deceleration until a few billion years ago and since
| then acceleration.

So the image I referred to is imprecise in that regard?