Exiting Inflation with a Smooth Scale Factor

TL;DR

This paper investigates the mathematical smoothness of the universe's expansion transition from inflation to subsequent eras, analyzing interpolating functions and their physical implications on universe size and particle production.

Contribution

It introduces a geometric model to examine smooth transition functions between inflation and later cosmological phases, highlighting the effects of smoothness constraints.

Findings

Order-of-magnitude increase in universe size at transition

Identification of a cusp in direct inflation-to-era transition

Impact on boson production during preheating

Abstract

The expectation that the physical expansion of space occurs smoothly may be expressed mathematically as a requirement for continuity in the time derivative of the metric scale factor of the Friedmann-Robertson-Walker cosmology. We explore the consequences of imposing such a smoothness requirement, examining the forms of possible interpolating functions between the end of inflation and subsequent radiation- or matter-dominated eras, using a straightforward geometric model of the interpolating behavior. We quantify the magnitude of the cusp found in a direct transition from the end of slow roll inflation to the subsequent era, analyze the validity several smooth interpolator candidates, and investigate equation-of-state and thermodynamic constraints. We find an order-of-magnitude increase in the size of the universe at the end of the transition to a single-component radiation or matter era. We also evaluate the interpolating functions in terms of the standard theory of preheating and determine the effect on the number of bosons produced.