Shocks in the Early Universe

We point out a surprising consequence of the usually assumed initial conditions for cosmological perturbations. Namely, a spectrum of Gaussian, linear, adiabatic, scalar, growing mode perturbations not only creates acoustic oscillations of the kind observed on very large scales today, it also leads to the production of shocks in the radiation fluid of the very early Universe. Shocks cause departures from local thermal equilibrium as well as create vorticity and gravitational waves. For a scale-invariant spectrum and standard model physics, shocks form for temperatures $1\mathrm{GeV}<T<10^7\mathrm{GeV}$. For more general power spectra, such as have been invoked to form primordial black holes, shock formation and the consequent gravitational wave emission provide a signal detectable by current and planned gravitational wave experiments, allowing them to strongly constrain conditions present in the primordial Universe as early as ${10}^{-30}\sec$ after the big bang.

Figure 1

Simulation showing cosmological initial conditions (left) evolving into shocks (right). The magnitude of the gradient of the energy density is shown in grayscale. The initial spectrum is scale invariant and cut off at $1/128$ the box size, with rms amplitude $\epsilon =0.02$.

Figure 2

The growing mode perturbation, in a radiation-dominated universe, in conformal Newtonian gauge. The density perturbation ${\delta }_k(t)$ (black), the Newtonian potential $\mathrm{\Phi }$ (red), and the flat spacetime approximation to ${\delta }_k(t)$ (blue) are plotted against $k{c}_{s}t$.

Figure 3

Entropy, in units of its equilibrium value, versus the time $t$, in units of the sound-crossing time, for $512^3$ simulations of a perfect radiation fluid with cosmological initial conditions as in (1). The red dashed curve is a fit to the $\epsilon =0.05$ curve using (8) with $C=\frac{1}{4}$. For $\epsilon =0.1$, $t$ has been doubled and the entropy deficit rescaled by a quarter to verify good agreement with (8).