B-Inflation

TL;DR

This work addresses the lack of a uniquely compelling high-energy inflation model by introducing Box-inflation, where the scalar field Lagrangian is a convex function of the d'Alembert operator, $Q(\Box \phi)$. In a flat FRW background the dynamics form a hyperbolic system that generically evolves toward a de Sitter attractor driven by the kinetic sector, with $\varepsilon$ and $p$ determined by $Q$ and the evolving variables; inflation can occur without a potential. A graceful exit is achieved by reintroducing first-order derivatives through a $K(\phi)X$ term, causing inflation to end when the effective mass $m(\phi)=\sqrt{-K(\phi)}$ becomes relevant, after which the residual energy behaves like dust ($\langle p\rangle\to0$) and reheating can proceed via standard couplings. Numerical examples illustrate the exit for representative $K(\phi)$, supporting the viability of this EFT-based inflation and suggesting a robust alternative to potential-driven models, with perturbations and detailed observational consequences left for future work.

Abstract

We propose a novel model of inflation based on a large class of covariant effective actions containing only the second derivatives of a scalar field. The initial conditions leading to the inflationary solutions in this model are rather generic. The graceful exit from the inflationary regime is natural once the first order derivative terms are included.

Figures (10)

• Figure 1: Here we plot a spherical region around the origin of the phase space $(\dot\phi,\dot B,B)$. The colored volume represents the region where energy density $\varepsilon$ is negative. The surface of this volume which does not belong to the surface of the depicted sphere is the surface of zero energy density $\varepsilon=0$. Note that this forbidden regions are in the quarters of the $(\dot \phi, \dot B)$ plane where the $\dot \phi\dot B\geq0$ and consequently $w\leq-1$. The red curves represent the two fixed lines given by Eq. (\ref{['fixed']}).
• Figure 2: The evolution of the dimensionless parameters $\phi$ and $B$ is plotted versus dimensionless time $t$. Function $Q(B)$ is chosen to be $B^2/2$. The initial values are $\dot\phi=0.1$, $B=0.1$, $\dot B=-0.025$
• Figure 3: The evolution of the energy density $\varepsilon$, pressure $p$ and the equation of state $w=p/\varepsilon$ is shown on this plot. Function $Q(B)$ is chosen to be $B^2/2$. The initial values are $\dot\phi=0.1$, $B=0.1$, $\dot B=-0.025$. The system quickly evolves into a nearly de Sitter regime.
• Figure 4: Here we plot the equation of state $w$ versus number of e-folds $N$ for various initial data. The function $Q(B)$ is chosen to be $\frac{1}{2} B^2$. The initial date are: for the red curve: $\dot\phi=0.1$, $B=0.08$, $\dot B=-0.05$, for the black curve: $\dot\phi=2$, $B=0.05$, $\dot B=-0.05$ for the blue one: $\dot\phi=0.03$, $B=0.5$, $\dot B=1$. The equation of state $w$ evolves to the nearly de Sitter value $w=-1$ within approximately one e-fold.
• Figure 5: Here we plot the $(\varepsilon,p)$-trajectories originating from a point where the universe is decelerating. The blue region cannot be reached by the system.