Metric-affine formalism of higher derivative scalar fields in cosmology

Abstract

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