Conformal $\alpha$-attractor Inflation with Weyl Gauge Field

TL;DR

This paper explores conformal symmetry breaking during inflation, introducing a formalism with Weyl gauge fields, revealing new symmetries, and presenting models consistent with current and future cosmological observations.

Contribution

It systematically analyzes local conformal inflation models with Weyl gauge fields, identifying SO(2) symmetry possibilities and providing analytic solutions relating Jordan and Einstein frames.

Findings

Identified SO(2) as an alternative symmetry with Weyl gauge fields.

Derived all analytic solutions connecting Jordan and Einstein frames.

Proposed inflation models fitting current observations and testable by future experiments.

Abstract

Conformal scaling invariance should play an important role for understanding the origin and evolution of universe. During inflation period, it appears to be an approximate symmetry, but how it is broken remains uncertain. The appealing $\alpha$-attractor inflation implements the spontaneous breaking of conformal symmetry and a mysterious SO(1,1) global symmetry. To better understand the SO(1,1) symmetry, here we present a systematic treatment of the inflation models with local conformal symmetry in a more general formalism. We find SO(2) is the other possible symmetry in the presence of Weyl gauge field. We also obtain all the analytic solutions that relate the inflation fields between Jordan frame and Einstein frame. We illustrate a class of inflation models with the approximate SO(2) symmetry and trigonometric potential, and find that it can fit the current observations and will be probed by future CMB experiments.