Does cosmology assumes that matter existed before the Big Bang?

Question

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 $\Delta \propto a^{-2}$"?

Answer 1

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.

Now, the end of inflation is effectively the hot big bang, as the inflaton decays to reheat the universe. So, in an operational sense at least, yes, there was matter and, specifically--perturbations--before the big bang.