HYM-flation: Yang-Mills cosmology with Horndeski coupling

TL;DR

This paper introduces a novel inflation mechanism using a non-minimally coupled SU(2) Yang-Mills field with Horndeski gravity, leading to robust inflation with graceful exit and potential two-step inflation involving Higgs fields.

Contribution

It presents the first gauge covariant, ghost-free Yang-Mills theory with curvature-dependent action that induces inflation and can be extended to a two-step inflationary scenario.

Findings

Existence of de Sitter attractor solutions for the Yang-Mills field.

Robust inflation with a natural graceful exit.

Potential for a two-step inflation involving Higgs fields.

Abstract

We propose new mechanism for inflation using classical SU(2) Yang-Mills (YM) homogeneous and isotropic field non-minimally coupled to gravity via Horndeski prescription. This is the unique generally and gauge covariant ghost-free YM theory with the curvature-dependent action leading to second-order gravity and Yang-Mills field equations. We show that its solution space contains de Sitter boundary to which the trajectories are attracted for some finite time, ensuring the robust inflation with a graceful exit. The theory can be generalized to include the Higgs field leading to two-steps inflationary scenario, in which the Planck-scale YM-generated inflation naturally prepares the desired initial conditions for the GUT-scale Higgs inflation.