Metric-Affine Formalism of Higher Derivative Scalar Fields in Cosmology

TL;DR

This paper explores higher derivative scalar fields in cosmology using the metric-affine formalism, revealing that it can produce significantly different cosmological predictions compared to the traditional metric approach, especially in dark energy models.

Contribution

It introduces the metric-affine formalism for higher derivative scalar fields in cosmology, highlighting differences from the metric approach and their potential impact on cosmic evolution.

Findings

Differences between formalisms are suppressed by the Planck mass but can be significant in some cases.

The metric-affine approach yields different future universe scenarios in dark energy models.

Potential observable deviations in cosmological predictions due to formalism choice.

Abstract

Higher derivative scalar field theories have received considerable attention for the potentially explanations of the initial state of the universe or the current cosmic acceleration which they might offer. They have also attracted many interests in the phenomenological studies of infrared modifications of gravity. These theories are mostly studied by the metric variational approach in which only the metric is the fundamental field to account for the gravitation. In this paper we study the higher derivative scalar fields with the metric-affine formalism where the connections are treated arbitrarily at the beginning. Because the higher derivative scalar fields couple to the connections directly in a covariant theory these two formalisms will lead to different results. These differences are suppressed by the powers of the Planck mass and are usually expected to have small effects. But in some cases they may cause non-negligible deviations. We show by a higher derivative dark energy model that the two formalisms lead to significantly different pictures of the future universe.