Self-sustained, out-of-equilibrium inflation

TL;DR

This work shows that holographically realized, non-conformal QFTs in de Sitter space can sustain exponential inflation via out-of-equilibrium dynamics within the semiclassical gravity regime, revealing multiple ds-invariant states whose horizon areas signal continuous entropy production. The authors construct a bottom-up Einstein–scalar holographic model with a tunable parameter φ_M that yields coexisting ds branches with O(M^4) energy densities, and they demonstrate that the required fine-tuning to realize small H is only logarithmic in M_sp/H due to the AdS warp factor. They compare curvature-driven (quantum) and thermal phase transitions, illustrating how ds and thermal branches share structural similarities while differing in symmetry constraints and entropy interpretation. Finally, they discuss cosmological implications, showing that a late-time ds-invariant attractor could arise from an FLRW universe after an initial out-of-equilibrium evolution, though a complete inflationary phenomenology (perturbations, exit, reheating) remains to be developed.

Abstract

We use holography to study dS-invariant states of non-conformal, strongly coupled quantum field theories in four-dimensional de Sitter space. We show that out-of-equilibrium effects can sustain the exponential inflation within the regime of validity of semiclassical gravity, $H \ll M \ll M_\mathrm{sp}$, with $H$ the Hubble parameter, $M$ the characteristic scale of the quantum field theory, $M_\mathrm{sp} = M_\mathrm{p}/N$ the species scale, $M_\mathrm{p}$ the Planck scale, and $N^2$ the number of matter fields. In the holographic description, the required fine-tuning scales only logarithmically with the ratio $M_\mathrm{sp}/H$. The resulting solutions exhibit apparent horizons whose increasing area indicates a continuous growth of the comoving entropy density. We suggest that this inflationary regime can arise as the late-time limit of a dynamical evolution starting from an initial Friedmann-Lemaître-Robertson-Walker universe.

Figures (14)

• Figure 1: Energy density of dS-invariant states of a QFT in our family (corresponding to $\phi_M=0.59$) as a function of the dS Hubble parameter. Multiple states coexist for the same value of $H$ down to a small value $H_{\text{min}} \ll M$, indicated by a solid vertical line on the left, with a finite energy gap between them. States with the lowest Euclidean action are shown in solid green. The dashed vertical line on the right indicates the point at which these states jump from one branch to another. The blue branches lie very close to each other and intersect only at $H=H_{\text{min}}$.
• Figure 2: Bulk scalar potential for several values of $\phi_M$ that will be of interest below.
• Figure 3: Relation between the Hubble rate of the QFT in dS and the value of the scalar field at the horizon in the dual bulk for the model with $\phi_M=0.59$. Multiple states coexist in the range of $H$ between the maximum and the minimum. $\phi_E$ corresponds to the first positive minimum of the potential $V(\phi)$.
• Figure 4: Energy (left) and free energy (right) densities as functions of the Hubble rate for the model with $\phi_M=0.59$. The plots exhibit multiple states separated by a finite energy-density gap down to small values of $H$. The branches of the phase transition are shown in solid green for globally stable states and dashed blue for the remaining states. The dashed vertical line corresponds to the critical de Sitter temperature of the phase transition. In our renormalization scheme, the energy density at small $H$ in this and similar plots is slightly negative---see the comment below \ref{['stress']}.
• Figure 5: Entropy density per unit physical volume of the QFT in a de Sitter–invariant state for the model with $\phi_M$=0.59, extracted from the area of the apparent horizon of the dual bulk solution. The branches of the phase transition are shown in solid green for globally stable states and dashed blue for globally unstable states. The dashed vertical line corresponds to the critical de Sitter temperature of the phase transition.