# Inflationary Cosmology in Scalar-Tensor Gravity: Reconstructing Higgs-Like Potentials

## TL;DR

This paper explores scalar-tensor cosmology with a focus on reconstructing Higgs-like potentials, showing that certain solutions naturally lead to a Mexican hat potential, providing insights into inflationary models.

## Contribution

It demonstrates that scalar-tensor gravity models can naturally produce Higgs-like potentials without being explicitly assumed, offering a new perspective on inflationary cosmology.

## Key findings

- Reconstructed Higgs-like potentials from scalar-tensor models.
- Solutions avoid pre-inflationary collapse in standard cosmology.
- Potential shapes depend on initial conditions and universe curvature.

## Abstract

We study cosmology in scalar-tensor (Bergmann Wagoner) gravity, restricting the coupling function, ${\omega}({\phi})$ to be constant. Rather than specify the form of the cosmological function, ${\lambda}({\phi})$, the scalar field is modelled as a function which decays to its present value ${\phi}=1$. Solutions of the field equations are found for which ${\lambda}({\phi})$ evolves from a large value (approximately 1) near the singularity to a small, non-zero value at later times, avoiding the problem of pre-inflationary collapse in standard general relativistic cosmology. Interpreting the model within the framework of Brans-Dicke theory with a scalar potential, we find that for suitable initial conditions, the reconstructed potential at late times for flat, open and closed universes is well described by a Higgs-like Mexican hat potential, quartic in ${\phi}$, though this was not built in to the initial assumptions.