# What is the gravitational power that neutrinos created in the big bang exert on us?

I was thinking about the big bang, and I remembered that neutrinos not only travel at the speed of light, but they were also created in massive quantities very early in the universe (Hadron epoch).

Since the universe around that time was about the size of our solar system now, and neutrinos don't interact with matter very much, wouldn't those neutrinos be the 'edge' of the universe? I'll call this edge a 'neutrino shell'.

If I remember correctly, the Shell Theorem should apply here - except for one thing: if the speed of gravity is the speed of light, wouldn't matter feel some slight more gravitational power closer to the 'side' of the universe it started in?

That's because the other 'side' of the universe (assuming a sphere) is moving away from us faster than the speed of light - implying the force of gravity exerted by those neutrinos at some point disappeared.

And this would also mean that at some point the entirety of this 'neutrino shell' of the universe would be so far away from every piece of 'physical matter' in the universe, moving at speeds faster than the speed of light, that it would stop exerting gravity upon all matter?

And wouldn't that mean that after that time, the universe should stop expanding and start deflating (because galaxies inside the shell now have no 'external' gravity force exerted by the neutrino shell)?

I don't know if this makes sense or am I missing a fundamental piece of physics here?

• Commented Dec 15, 2015 at 1:32

## 1 Answer

The model we use to describe the universe, the FLRW metric, is based on the assumption that the universe is homogeneous i.e. it is everywhere the same. That means the neutrino density is constant everywhere and has been constant for as long as the neutrinos have existed. There is no shell of neutrinos at the edge of the universe.

Neutrinos are relativistic and as a result their energy density falls as $a^{-4}$, where $a$ is the expansion scale factor. By comparison the energy density of non-relativistic matter falls as $a^{-3}$ so the ratio of neutrino energy density to normal matter energy density falls as $\tfrac{1}{a}$. This means that for very small $a$, i.e. close to the Big Bang, the gravitational influence of neutrinos dominates over normal matter. However for large $a$ (small $\tfrac{1}{a}$) the gravitational influence of normal matter dominates over neutrinos.

I'm not sure when the switchover occurred, but neutrinos are currently gravitationally insignificant. Relativistic matter, including photons as well as neutrinos, ceased to dominate around 30,000 years after the Big Bang. Just as well really, as if neutrinos were still gravitationally significant they would have stopped matter clumping to form stars then galaxies and we wouldn't here to debate the point.

• It's more complicated for neutrinos. Although there is no doubt they were relativistic in the early universe, they are probably not now. Commented Dec 15, 2015 at 12:24
• One thing I don't understand about the big bang: how come you can say that the entire universe was the size of our solar system, yet that it doesn't have a center? I mean, it must, no? Even if the 'grid' as per the answer is infinite, we know, for instance, that 0 is at the center of the real line - because if we take a point and subtract that point to itself we get to 0. Commented Dec 15, 2015 at 15:54
• Also, isn't the assumption that the universe is infinite fairly strong? I mean, we have no idea. It may be practically infinite, since it expands at speeds that matter can't travel at, but it could be finite at every point in time. Commented Dec 15, 2015 at 16:02
• @EduardoSahione: The real line has no centre. You can pick any number you like, and the amount of the real line to the left and right of your chosen number will be the same. That's the wonder of infinity :-) An infinite universe has no centre for the same reason. Commented Dec 15, 2015 at 16:08
• @EduardoSahione: a flat homogenous universe must be either infinite or topologically closed. Infinite seems simpler to me than topologically closed, though your mileage may vary. I suppose you could argue that the universe is not homogenous, but then the FLRW metric no longer applies so all bets are off. Commented Dec 15, 2015 at 16:12