How old is the universe ? 11/16/22

Can we see the big bang?

When we say that the age of the universe is estimated at 13.7 billion years, does that mean that, we would see the big bang 13.7 billion years in our past?

Not withstanding with the fact that this would suppose very powerful means of observation, we will see that this is impossible.

Given the speed of light, which is a limit, the further we look at an event in space, the farther we see into our past, since the longer the light emitted by this event takes to reach us, then, far away in space, corresponding to 13.7 billion years of our past, would we see the big bang?

Alas no! The value of 13.7 billion years is that of the cosmological time, resulting from a foliation of spactime in the the Robertson-Walker metric, which not our current time, called proper time, which is that we are living in. .

In fact, for us, the big bang as described in the standard model of cosmology (big bang) is thrown off to infinity of our past, we cannot observe it.

More precisely , this time of 13.7 billion years corresponds to the time coordinate of a specific form of the equations which describe relativistic cosmology, including the Robertson-Walker metric which defines this time, called « cosmological time ».

This time which is not ours, is however linked to it by equations which precisely give a multiplicative factor which diverges towards infinity when we approach the big bang.

This possibility of existence of different times is a consequence of relativity where there is no universal time. Everyone can have their own time, different from everyone else’s. This is what happens in this case. So, be careful, when we talk about time, check which one it is.

The universe is ageless!

Indeed, Einstein’s equation defines a spacetime and not a space and a time. When we look towards the past, we receive signals (photons for instance), which have traveled on a geodesic of this spacetime.

This geodesic is a geometric object that belongs to spacetime and not to space and independently to time.

The concept of age of the universe implies a « creation » of the universe, which is an absolutely unnecessary assumption to describe relativistic dynamics.

We may, therefore, ignore this unnecessary hypothesis, which can only blur the knowledge of the nature of the phenomena to be studied.

This is what pointed out, among others, J. Peebles when he declared that he did not like the wording « Big Bang » which connotes an event somewhere, in a pre-existing space, at a given time in a pre-existing time.