Pole inflation from extended metric-affine gravity

TL;DR

This paper explores inflation within extended metric-affine F(R) gravity, revealing that inflationary predictions are governed by pole structures in the scalar-tensor formulation, and identifies conditions for viable, ghost-free models with realistic observables.

Contribution

It introduces a comprehensive analysis of inflation in extended metric-affine F(R) gravity, emphasizing the role of poles and relaxing ghost-free conditions to expand viable models.

Findings

Inflationary predictions depend mainly on pole structure, not on specific F(R) form.

Models with second-order poles can be ghost-free or allow controlled ghosts.

Relaxing ghost constraints near the inflationary pole broadens the set of viable models.

Abstract

We study inflation in the framework of extended metric-affine F(R) gravity, where all even-parity quadratic invariants of torsion and non-metricity are included in the Lagrangian alongside the F(R) term. The extended theory admits a scalar-tensor description with a non-canonical kinetic term featuring poles. As a result, the inflationary dynamics and predictions for observables of this model are insensitive to the specific form of F(R), since they are dominated by the structure of the poles (order and residue). We analyze both a simplified version analytically and the full eleven-parameter theory, and we classify the models based on whether they feature second-order poles, whether they are free from ghosts, and whether they predict a sufficiently small tensor-to-scalar ratio. By relaxing the ghost-free requirement to only exclude ghosts near the pole (where inflation occurs), we demonstrate that we can significantly enlarge the set of viable models. We thus show that extended metric-affine F(R) gravity can act as a robust framework for inflation, reproducing the attractor predictions for the spectral index and tensor-to-scalar ratio.