Recent Advances on Inflation

TL;DR

This paper reviews recent developments in inflationary models within modified gravity theories, including string-inspired models, Chern-Simons theories, and $f(R)$ gravity, highlighting their potential to address early universe problems.

Contribution

It provides a comprehensive overview of various modified gravity frameworks for inflation, including new models and techniques for analyzing gravitational wave signatures.

Findings

Inflation can be realized in multiple string-inspired models with Gauss-Bonnet and higher derivative couplings.

Vacuum $f(R)$ gravity offers viable inflationary scenarios consistent with observations.

Modified gravity effects can significantly alter gravitational wave waveforms.

Abstract

We review recent trends on inflationary dynamics in the context of viable modified gravity theories. After providing a general overview of the inflationary paradigm emphasizing on what problems of hot Big Bang theory inflation solves, and a somewhat introductory presentation of single field inflationary theories with minimal and non-minimal couplings, we review how inflation can be realized in terms of several string motivated models of inflation, which involve Gauss-Bonnet couplings of the scalar field, higher order derivatives of the scalar field, and some subclasses of viable Horndeski theories. We also present and analyze inflation in the context of Chern-Simons theories of gravity, including various subcases and generalizations of string corrected modified gravities which also contain Chern-Simons correction terms, with the scalar field being identified with the invisible axion, which is the most viable to date dark matter candidate. We also provide a detailed account of vacuum $f(R)$ gravity inflation, and also inflation in $f(R,\phi)$ and kinetic-corrected $f(R,\phi)$ theories of gravity. In the end of the review we discuss the technique for calculating the overall effect of modified gravity on the waveform of the standard general relativistic gravitational wave form.