# Does cosmology assumes that matter existed before the Big Bang?

In cosmology, studying the evolution of the matter perturbations for structure formation, one frequently mentions "horizon entry", meaning that a perturbation of (fixed) wavelength is super-horizon at first, but since the particle horizon evolves with time, it eventually becomes sub-horizon and causal connections are allowed.

Now, probably my misunderstanding is in the definition of "particle horizon", but what I have is that if one would have emitted a photon right at the big bang, the particle horizon $$R_H$$ is the distance that photon would have traveled, taken the expansion of the universe into account.

How can there be matter on a scale larger than the particle horizon at any set time? What does one mean when saying "before entering the horizon, the perturbation collapses at a rate $$\Delta \propto a^{-2}$$"?

• Are you asking about the horizon problem? Jun 9, 2020 at 11:37
• @PM2Ring no, I'm not. The horizon problem claims that the universe must have been all casually connected (inside the particle horizon) at the time of the CMB for it to be so homogenous. My question is how can there even be something outside of the said horizon, since for it to be there one must assume that it went there faster than light or that it was already there Jun 9, 2020 at 13:01
• If the universe is flat (as it appears to be), then it's infinite in size, and it has always been infinite for all time $t>0$ (the size at the $t=0$ instant of the Big Bang is an indeterminate form, $0×\infty$). See physics.stackexchange.com/q/136860/123208 So at the end of Big Bang nucleosynthesis, when the universe was about 20 minutes old, all of space was filled with matter, mostly hot hydrogen & helium. There were no empty regions that matter hadn't reached yet. Jun 9, 2020 at 15:08
• @PM 2Ring: the universe could be finite and bounded and still be flat if it has toroidal topology. Jun 9, 2020 at 18:17

Inflation. The expansion rate during inflation is such that $$\ddot{a}>0$$, and this has the bizarre result that physical length scales, $$\lambda \propto a(t)$$, grow faster than the horizon, given by the Hubble scale $$H^{-1} \approx {\rm const}$$. Quantum fluctuations born in the vacuum on sub horizon scales, $$\lambda \ll H^{-1}$$, get redshifted by the exponential inflationary expansion to super horizon scales, $$\lambda \gg H^{-1}$$. When inflation ends, the expansion proceeds at a decelerated rate and length scales grow slower than the horizon. For example, for radiation dominated expansion, we have $$\frac{d}{dt}(\lambda H) \propto -a^{-3}<0$$ and we say that these fluctuations fall back inside the horizon.