The Big Bang and Inflation United by an Analytic Solution

TL;DR

This paper presents an exact analytic solution linking the Big Bang and inflation within scalar-tensor gravity theories, successfully modeling inflation consistent with WMAP data and revealing new solution methods leveraging Weyl symmetry.

Contribution

It introduces a novel analytic solution method for scalar-tensor theories with hyperbolic potentials, connecting Big Bang and inflation, and utilizing Weyl symmetry for solving complex cosmological equations.

Findings

Model reproduces WMAP 7-year data constraints

Inflation and Big Bang are connected via a time delay

Solution reveals non-monotonic inflaton behavior and early non-slow-roll periods

Abstract

Exact analytic solutions for a class of scalar-tensor gravity theories with a hyperbolic scalar potential are presented. Using an exact solution we have successfully constructed a model of inflation that produces the spectral index, the running of the spectral index and the amplitude of scalar perturbations within the constraints given by the WMAP 7 years data. The model simultaneously describes the Big Bang and inflation connected by a specific time delay between them so that these two events are regarded as dependent on each other. In solving the Fridemann equations, we have utilized an essential Weyl symmetry of our theory in 3+1 dimensions which is a predicted remaining symmetry of 2T-physics field theory in 4+2 dimensions. This led to a new method of obtaining analytic solutions in 1T field theory which could in principle be used to solve more complicated theories with more scalar fields. Some additional distinguishing properties of the solution includes the fact that there are early periods of time when the slow roll approximation is not valid. Furthermore, the inflaton does not decrease monotonically with time, rather it oscillates around the potential minimum while settling down, unlike the slow roll approximation. While the model we used for illustration purposes is realistic in most respects, it lacks a mechanism for stopping inflation. The technique of obtaining analytic solutions opens a new window for studying inflation, and other applications, more precisely than using approximations.