Singular Inflation

TL;DR

This paper demonstrates that certain scalar field cosmologies with power-law potentials inevitably develop finite-time weak singularities, termed 'singular inflation', which occur at the end of inflationary evolution.

Contribution

It introduces the concept of 'singular inflation' by showing that models with specific power-law potentials lead to finite-time weak singularities at inflation's end.

Findings

Models with $0<n<1$ develop weak singularities at finite time.

A broad class of models with $n>1$ exhibit even weaker singularities.

These singularities occur when the universe's expansion rate remains finite but higher derivatives diverge.

Abstract

We prove that a homogeneous and isotropic universe containing a scalar field with a power-law potential, $V(\phi )=A\phi ^{n}$, with $0<n<1$ and $A>0$ always develops a finite-time singularity at which the Hubble rate and its first derivative are finite, but its second derivative diverges. These are the first examples of cosmological models with realistic matter sources that possess weak singularities of 'sudden' type. We also show that a large class of models with even weaker singularities exist for non-integer $n>1$. More precisely, if $k<n<k+1$ where $k$ is a positive integer then the first divergence of the Hubble rate occurs with its ($k+2)$th derivative. At early times these models behave like standard large-field inflation models but they encounter a singular end-state when inflation ends. We term this singular inflation.