# 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?

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.