Defrosting in an Emergent Galileon Cosmology

TL;DR

The paper addresses how an NEC-violating Emergent Galileon condensate (Galileon Genesis) transitions to a radiation-dominated expansion via a defrosting/preheating mechanism. It shows that coupling a matter scalar to the Galileon through the effective metric $\mathfrak{g}^{f}_{\mu\nu}=e^{2\pi}g_{\mu\nu}$ yields a scale-invariant spectrum for matter fluctuations and, when expansion is accounted for, suffices to drain energy from the Galileon, initiating defrosting; a non-minimal coupling further accelerates this transfer. Reintroducing gravity alters the background evolution (e.g., $H(t)\sim -1/t^3$ near the would-be singularity) and enhances the growth of $\sigma$ fluctuations, producing a UV blue tilt and a Lambert $W$-dependent freeze-out, such that $\bar{\rho}_\sigma$ ultimately dominates $\rho_\pi$ and preheating proceeds. The results indicate a graceful exit to a radiation-dominated FRW phase, with backreaction consistently damping the Galileon, and reveal both parallels and differences with inflationary reheating, alongside open questions about curvature perturbations sourced by entropy modes. Overall, the work clarifies a viable defrosting pathway for Galileon-based cosmologies with potential observational implications.

Abstract

We study the transition from an Emergent Galileon condensate phase of the early universe to a later expanding radiation phase. This "defrosting" or "preheating" transition is a consequence of the excitation of matter fluctuations by the coherent Galileon condensate, in analogy to how preheating in inflationary cosmology occurs via the excitation of matter fluctuations through coupling of matter with the coherent inflaton condensate. We show that the "minimal" coupling of matter (modeled as a massless scalar field) to the Galileon field introduced by Creminelli, Nicolis and Trincherini in order to generate a scale-invariant spectrum of matter fluctuations is sufficient to lead to efficient defrosting, provided that the effects of the non-vanishing expansion rate of the universe are taken into account. If we neglect the effects of expansion, an additional coupling of matter to the Galileon condensate is required. We study the efficiency of the defrosting mechanism in both cases.

Figures (2)

• Figure 1: Evolution of the power spectrum of the $\sigma_k$ perturbations after freeze-out. The level curves show constant amplitudes of perturbations. On the colour map, blue means smaller amplitude and red means larger amplitude. Modes bellow the dotted line are frozen out, while modes with paler colour are still oscillating. If we choose for a chosen value of $H_0 = 5\times10^{-4}$, the green region corresponds to an amplitude of perturbation of $\sim10^{-5}$. The horizontal axis shows the time-evolution of the perturbations for a given k mode, while the vertical axis shows the k spectrum at a given time. In the IR end (i.e. for $k<H_0$), the spectrum is scale invariant and constant until the onset of preheating after $t = -H_0^{-1}$, at which point the amplitude of the fluctuations starts to grow. On the other side, the UV end of the spectrum is slightly red and its amplitude increases slightly with time.
• Figure 2: Power spectrum of $\sigma_k$ fluctuations after freezeout when the full background with gravitational coupling is considered, obtained by solving numerically the differential equation f or the background $\pi$ and $H$ and the time-dependent mass in (\ref{['UVgravTimeDepMass']}). The colour map is logarithmic in the amplitude of the power spectrum, and increases from blue to red. The horizontal axis shows the time evolution of the perturbations for a given k mode, while the vertical axis shows the logarithm of the k spectrum at a given time. Modes below the dotted line are frozen out with the indicated amplitude, while modes with paler colour above the dotted line are still oscillating. The first thing to note is that the spectrum is now constant for all modes that are frozen out. At the IR end (i.e. for $k\lesssim H_0$), the spectrum is almost scale-invariant and slightly red-tilted until the end of that regime after $t=-H_0^{-1}$. On the other side, the UV end of the spectrum is very tilted towards the blue, and the onset of this UV regime marks the onset of preheating. In between the two regimes, the graph shows an interesting feature in the power spectrum: a small trough between $k=10^{-4}$ and $k=10^{-3}$. This feature allows for a red-tilted power spectrum during the fake de Sitter phase, or IR regime, where the spectrum is almost scale invariant, at the same time as an efficient preheating with a blue spectrum in the UV end, so that the power spectrum becomes highly dominated by UV modes as defrosting proceeds.