"Graceful" Old Inflation

TL;DR

This work shows that old inflation from a false vacuum can yield a successful cosmology if a spectator scalar field non-minimally coupled to gravity slows the de Sitter expansion and triggers a transition via bubble nucleation. The framework yields a two-phase inflation: an initial exponential stage that can produce perturbations, followed by a Brans-Dicke–like phase that ends inflation through nucleation, with stringent constraints to avoid large bubbles and to achieve sufficient e-folds. Perturbations generated by the non-minimally coupled field tend to yield a red-tilted scalar spectrum (n_S ≈ 1 − 8β) incompatible with observations unless an additional curvaton is invoked to generate curvature perturbations with the observed amplitude. The model offers interesting observational signatures, including small-scale bubble imprints, a potential running of the spectral index, and possible gravitational waves from bubble dynamics, while outlining strategies to recover Einstein gravity at late times.

Abstract

We show that Inflation in a False Vacuum becomes viable in the presence of a spectator scalar field non minimally coupled to gravity. The field is unstable in this background, it grows exponentially and slows down the pure de Sitter phase itself, allowing then fast tunneling to a true vacuum. We compute the constraint from graceful exit through bubble nucleation and the spectrum of cosmological perturbations.

Figures (3)

• Figure 1: The evolution of the Hubble parameter as a function of time in our model (solid black line), compared to a power-law evolution $H=\alpha/t$ (red dashed line). Here $\beta=1/56, H_I=10^{-5}M$.
• Figure 2: The evolution of $r\equiv \Gamma_{\rm{vac}}/H^4$ as a function of the number of e-folds N (with $\beta=1/56,\, H_I=10^{-5} M, \, r_0=10^{-7}$). Time goes from right to left: $r=r_0$ at the beginning and then it grows to ${\cal O}(1)$.
• Figure 3: In grey we show the regions of allowed parameter space, for different $\Delta N$ (from left to right $\Delta N=-8,-4,0$). The region on the top and the region on the right are excluded because of the constraint on the production of large bubbles (this is independent on the value of $H_I/M$). For $\beta$ becoming bigger than what is shown in the plot, the scenario is still viable except when $\beta$ gets closer to ${\cal O}(0.1)$, where sufficient inflation might become difficult to obtain (depending also on the value of $H_I/M$).