Conformal inflation in the metric-affine geometry

¹ Department of Physics, Nagoya University - Nagoya 464-8602, Japan
² Kobayashi Maskawa Institute, Nagoya University - Chikusa, Aichi 464-8602, Japan
³ Kavli IPMU (WPI), UTIAS, The University of Tokyo - Kashiwa, Chiba 277-8583, Japan

^(a) mikura.yusuke@e.mbox.nagoya-u.ac.jp
^(b) tada.yuichiro@e.mbox.nagoya-u.ac.jp
^(c) shu@kmi.nagoya-u.ac.jp

Received: 21 August 2020
Accepted: 20 October 2020

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 being 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 SO(1, 1) or O(2), leading to the well-known α-attractor or natural inflation, respectively. The inflaton, can be understood as their pseudo–Nambu-Goldstone boson.