Why Does t=1/H Represent the Age of the Universe?

[LSulayman]

Why does t=1/H (hubble constant) indicate that that is the age of the universe?

 

[Garth]

Why does t=1/H (hubble constant) indicate that that is the age of the universe?

It doesn't.

H^-1₀ is called Hubble Time and it is the first approximation to the time scale of the age of the universe.

Hubble time would be the age of the universe t₀ if the universe expanded at a constant rate (R(t)= ct), the so called Coasting Cosmology model.

If the universe is decelerating then it would have expanded more quickly in the past and the age of the universe would be less than Hubble Time.

If the universe is accelerating then it would have expanded more slowly in the past and the age of the universe would be more than Hubble Time.

In the standard cosmological LCDM model the universe is thought to have first decelerated, then accelerated explosively (Inflation), then decelerated, then accelerated (since a time where z ~ 1).

So what has been the result of this deceleration/acceleration process on the age of the universe?

The present best accepted values of cosmological parameters
(using the table at WMAP Cosmological Parameters)
H₀ = 70.4 km/sec/Mpsc
$$Omega_{\Lambda}$$ = 0.732
$$Omega_{matter}$$ = 0.268

Feeding these values into Ned Wright's Cosmology Calculator:

The age of the universe is = 13.81 Gyrs.

But with h₁₀₀ = 0.704,

Hubble Time = 13.89 Gyrs.

Strange that the age of the universe should be equal to Hubble Time to within an error of 0.6%, almost as if the universe had been expanding linearly, i.e. at the same rate, all the way along!

Garth

 

[Calimero]

Why does t=1/H (hubble constant) indicate that that is the age of the universe?

It is true in empty universe, without matter and cosmological constant. Then H=1/t, or inverse time.

 

[LSulayman]

But the fact that you are able to measure the age of the universe is evidence for a universe that is expanding, am I right?

 

[LSulayman]

Strange that the age of the universe should be equal to Hubble Time to within an error of 0.6%, almost as if the universe had been expanding linearly, i.e. at the same rate, all the way along!

I don't really understand what you mean with that last sentence.

 

[marcus]

But the fact that you are able to measure the age of the universe is evidence for a universe that is expanding, am I right?

There is a logical connection between expansion and what people mean by the age.

The age is a lower-bound estimate that derives from the standard expansion model.
By fitting the standard cosmology model to the data we can say that the current expansion has been going on for 13.7 billion years.

The universe could be much older, of course—something else may have been occurring before the observed expansion began.

So the 13.7 billion years is really the "age of expansion", not the age of the universe itself.

And it is derived by fitting a mathematical model to massive amounts of observational data.
The model, in turn, is based on the well-established theory of spacetime geometry and gravity: General Relativity (GR).

GR is a theory of how geometry behaves in response to matter. It has passed many tests with extreme precision. It suggests that a universe like ours should either be expanding or contracting. Distances should either be shrinking or growing—as it happens they are growing, in good agreement with the GR mathematical model.

The GR model only goes back 13.7 billion years and then it breaks down. It stops computing reasonable numbers. Some modified versions do go back further and show a universe that was contracting, then reached a very high concentration and began to expand—from then on behaving as predicted by the classic GR model. But the modifications have to be tested—they must prove able to make predictions of some phenomena more accurately than classic GR does. Until then we do not trust the new models, we can only say that it is possible the universe continues on back in time before the start of expansion 13.7 billion years ago.

 

[LSulayman]

So the 13.7 billion years is really the "age of expansion", not the age of the universe itself.

It's really fascinating how one sentence like that can explain so much to me.

 

[Garth]

Strange that the age of the universe should be equal to Hubble Time to within an error of 0.6%, almost as if the universe had been expanding linearly, i.e. at the same rate, all the way along!

Garth

I don't really understand what you mean with that last sentence.

It seems to be a strange coincidence.

With $\Omega =1$, if there were no DE then (Age of Universe)/ (H₀^-1) = 2/3, with DE it could be from 2/3 up to inifinity, depending on the amount of DE relative to matter; it just seems to me to be a coincidence that it should be ~unity.

Garth

 

[cepheid]

In the standard cosmological LCDM model the universe is thought to have first decelerated, then accelerated explosively (Inflation), then decelerated, then accelerated (since a time where z ~ 1).

So what has been the result of this deceleration/acceleration process on the age of the universe?

The present best accepted values of cosmological parameters
(using the table at WMAP Cosmological Parameters)
H₀ = 70.4 km/sec/Mpsc
$$\Omega_{\Lambda}$$ = 0.732
$$\Omega_{matter}$$ = 0.268

Feeding these values into Ned Wright's Cosmology Calculator:

The age of the universe is = 13.81 Gyrs.

But with h₁₀₀ = 0.704,

Hubble Time = 13.89 Gyrs.

Strange that the age of the universe should be equal to Hubble Time to within an error of 0.6%, almost as if the universe had been expanding linearly, i.e. at the same rate, all the way along!

Garth

Question: does Ned Wright's cosmology calculator just use the standard Friedman equations with cosmological constant, plug in the omegas given above, and numerically solve said DE to come up with the age of the universe and other things? If so, does that even really take into account the effects of the inflationary epoch? Because I've seen plots of the scale factor vs. cosmic time i.e. the solutions to said equations (with dark energy), and they look like this: first it is decelerating, then it is accelerating. There is only one inflection point (coincidentally quite close to now). So, this model (which is the one that has an age strikingly close to the Hubble time, albeit slighty less) doesn't seem to include inflation. Or does it?

EDIT: I just realized that the t = 0 of this standard Friedman model could be considered to be the start of everything that has happened post-inflation, in which case the age of your universe (obtained from the model) is only off by some 10^-36 seconds. In that case, I guess my question was pretty dumb. Sorry.

 

[PhilKravitz]

Strange that the age of the universe should be equal to Hubble Time to within an error of 0.6%, almost as if the universe had been expanding linearly, i.e. at the same rate, all the way along!
Garth

Maybe there was a slow part and later a fast part and we just happen to be near the point in time where the net of the two is zero.