Is it be correct to say that we live in a young (only 14 billion years old) universe?

Is it be correct to say that we live in a young (only 14 billion years old) universe?

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From what I have read, it seems that our universe is expected to function more or less as it does now for some $10^{12}$ years, possibly more. If that is correct, our universe's current age of $14$ billion years seems like this place we live in is still a baby, or at most a child.

I realize we are a long way from being sure about making such a broad characterization. Nevertheless, does it generally accord with current astronomical and cosmological thinking to say that our universe is still young?

Calling something young or old is normally done in reference to some special age. For things that have limited lifespans it is usually the average life expectancy (old people are people who are close to or beyond the life expectancy). For things that can potentially remain arbitrarily long we compare to some typical timescale of their evolution, in particular the longest dynamical timescale (one might call a piece of a decaying radioactive element "old" when it has been around more than a few half-lives).

Since the current $Lambda$CDM consensus model of the universe has an unlimited long future we need to find a good reference timescale.

We are living in the stelliferous era, when stars form and shine. This lasts from some hundred million years after the big bang until $10^{12}$ to $10^{14}$ years in the future. Many people implicitly assume a biocentric perspective thinking that life is only possible during this era and that the end of stars would be the end of the universe, at least the end of anything interesting. By this standard we are in the early part of the stelliferous, so it is a young universe.

However, as discussed in (Adams & Laughlin 1997) there is a lot more happening in later eras. My own research indicates that the degenerate era $sim 10^{14}$ to $sim 10^{33}$ years might be quite habitable for technological life. Even if one disregards life, in terms of change of structures and matter composition there are significant future changes: a separation of gravitationally bound objects in $sim 10^{11}$ years, merger processes evolving galactic contents into denser forms, the dissolution of galaxies in $sim 10^{20}$ years, proton decay removing baryonic matter in $sim 10^{33}$ years or more, black hole decay in $sim 10^{60}$ to $10^{100}$ years… basically all of these timescales make our present moment early and the universe young.

To claim the universe is old one needs to have a reference timescale that is fairly short. But even the particle physicist saying that what truly matters is the formation of stable particles and hence we should use baryogenesis during the big bang as the timescale has to admit that the stelliferous era involves a lot of particle conversion, and the degenerate era will involve a lot of conversion of protons and electrons into neutrons inside neutron stars (not to mention proton decay). I think it is hard to argue for any early timescale in any principled way. So we are living in a young, evolving universe.

An alternative way of looking at it is that we live in a dying universe. It may have a long, drawn out end, but the peak of star forming activity happened about 10 billion years ago, both in our own Galaxy (see Is there a stellar database that indicates how long ago stars in our Galaxy formed?) and in the universe as a whole (see Will new stars stop forming at some point of time? ) and most quasar activity petered out about 5 billion years ago (e.g. see Why are all quasars so far away? ).

On the other hand, it is true that the number of (low-mass, very low luminosity) stars in the universe is still increasing (e.g. When will the number of stars be a maximum?), thanks to their very long lifetimes. So although the fireworks are over, the bonfire is still smouldering (to use a UK metaphor that will have others baffled!).

I guess it all depends on whether you are a glass half-full or half-empty kind of person.

Another thing to consider from a philosophical point of view is the Carter catastrophe. The basic idea here is that it is unlikely for us to be alive at a special time just after the beginning of the human race, and that this indicates we are shortly to be doomed. This is normally framed in terms of humans and our survival on this planet, but I suppose could also be applied to the universe as a whole. The arguments that the universe could last trillions of years are based on concordance cosmology with the parameters for dark matter and dark energy fixed. The problem is we don't know what dark energy is or whether it varies in time or exactly what the relationship is between dark energy density and the (negative) pressure it exerts. There are big rip scenarios that may see the end of the universe within a mere 100 billion years!