Conformal inflation in the metric-affine geometry

TL;DR

This paper explores inflationary models within metric-affine geometry, emphasizing how local conformal symmetry and global symmetries influence model construction, exemplified by two-scalar models related to well-known inflationary scenarios.

Contribution

It demonstrates that metric-affine geometry allows local conformal invariance in each term of the Lagrangian, enabling new inflationary models with broken global symmetries.

Findings

Metric-affine geometry preserves local conformal symmetry in each Lagrangian term.

Two-scalar models with broken SO(1,1) or O(2) symmetries are connected to α-attractor and natural inflation.

Inflaton fields can be interpreted as pseudo Nambu-Goldstone bosons.

Abstract

Systematic understanding for classes of inflationary models is investigated from the viewpoint of the local conformal symmetry and the slightly broken global symmetry in the framework of the metric-affine geometry. In the metric-affine geometry, which is a generalisation of the Riemannian one adopted in the ordinary General Relativity, the affine connection is an independent variable of the metric rather than given e.g. by the Levi-Civita connection as its function. Thanks to this independency, the metric-affine geometry can preserve the local conformal symmetry in each term of the Lagrangian contrary to the Riemannian geometry, and then the local conformal invariance can be compatible with much more kinds of global symmetries. As simple examples, we consider the two-scalar models with the broken $\mathrm{SO}(1,1)$ or $\mathrm{O}(2)$, leading to the well-known $\alpha$-attractor or natural inflation, respectively. The inflaton can be understood as their pseudo Nambu-Goldstone boson.