Covariant quantum corrections to a scalar field model inspired by nonminimal natural inflation

Abstract

We calculate the covariant one-loop quantum gravitational effective action for a scalar field model inspired by the recently proposed nonminimal natural inflation model. Our calculation is perturbative, in the sense that the effective action is evaluated in orders of background field, around a Minkowski background. The effective potential has been evaluated taking into account the finite corrections. An order-of-magnitude estimate of the one-loop corrections reveals that gravitational and non-gravitational corrections have same or comparable magnitudes.

Covariant Effective Action for Scalar-Tensor Theories of Gravity

“…Note that the calculations throughout this work have been carried out for a constant background scalar field. In this limit, the mass correction for the minimal coupling case is in agreement with the results found in [20], [22], and [48], and a similar agreement can be found with the results in [31] if instead of Γ…”

“…The main issue encountered in this formalism is in the choice of configuration-space metric. While Vilkovisky advocated obtaining the operator from the highest derivative term in the action, several past works like [20][21][22] have instead explicitly chosen diagonal metric forms that seem easier to deal with. The calculations consequently yield inaccurate results with missing terms attributed to the off-diagonal components of the metric.…”

“…So far, the attempts at evaluating the one-loop covariant effective action have not been entirely successful. In [31], the calculations were performed using a non-covariant method which was evident due to lack of Vilkovisky-DeWitt connections, while in [20][21][22], the explicit choice of a trivial field-space metric led to inaccurate results. In this paper, we perform these calculations using the extended Schwinger-DeWitt approach and compare them with existing literature.…”