# Renormalization of Yukawa model with sterile scalar in curved space-time

## TL;DR

This paper investigates the quantum properties and renormalization of a sterile scalar field coupled to fermions in curved space-time, revealing new non-minimal couplings and odd potential terms with implications for gravity and inflation.

## Contribution

It introduces a novel renormalization framework for a scalar field with odd potential terms and new non-minimal couplings in curved space-time, extending previous models.

## Key findings

- Identification of odd powers in the scalar potential.
- Discovery of a new non-minimal coupling term $f\,\varphi R$.
- Implications for low-energy gravity and inflationary physics.

## Abstract

We explore the classical and quantum properties of a sterile scalar field coupled to $N$ copies of Dirac fermions in an external gravitational field. We find that the self-interaction scalar potential of a model that is consistent at the quantum level, includes odd (first and third) powers of a scalar. In particular, one has to consider, besides the standard non-minimal coupling of the form $\xi \varphi^2 R$, the new type of non-minimal coupling of the form $f\varphi R$ with new non-minimal parameter $f$. We study the one-loop renormalization of such a theory including renormalization of the new non-minimal coupling. Also, we calculate the one-loop effective potential using the renormalization group and show how the renormalization group analysis should be extended compared to the standard expression which was derived in 1980-ies. This conclusion is supported by the direct calculation of effective potential using normal coordinates and covariant cut-off regularization. The important features of the classical theory with a sterile scalar are related to the presence of the qualitatively new terms in the induced action of gravity, coming from the odd terms. We show that this new feature of the theory may have phenomenologically relevant consequences, both in the low-energy gravitational physics and at the high energies, corresponding to inflation.