Group theoretical interpretation of the modified gravity in de Sitter space

TL;DR

This paper develops a group theoretical framework for interpreting modified gravity in de Sitter space, linking the field equations to unitary irreducible representations of the de Sitter group and analyzing their properties.

Contribution

It introduces a novel group theoretical approach to modified gravity in de Sitter space, connecting the linearized field equations to specific UIRs of the de Sitter group.

Findings

The linearized modified gravitational field equation corresponds to two UIRs of the dS group.

The solutions are expressed as a product of polarization tensors and scalar fields.

The two-point function is de Sitter invariant and free of theoretical issues.

Abstract

A frame work has been presented for theoretical interpretation of various modified gravitational models which is based on the group theoretical approach and unitary irreducible representations (UIR's) of de Sitter (dS) group. In order to illustrate the application of the proposed method, a model of modified gravity has been investigated. The background field method has been utilized and the linearized modified gravitational field equation has been obtained in the 4-dimensional dS space-time as the background. The field equation has been written as the eigne-value equation of the Casimir operators of dS space using the flat 5-dimensional ambient space notations. The Minkowskian correspondence of the theory has been obtained by taking the zero curvature limit. It has been shown that under some simple conditions, the linearized modified field equation transforms according to two of the UIR's of dS group labeled by $\Pi^\pm_{2,1}$ and $\Pi^\pm_{2,2}$ in the discrete series. It means that the proposed modified gravitational theory can be a suitable one to describe the quantum gravitational effects in its linear approximation on dS space. The field equation has been solved and the solution has been written as the multiplication of a symmetric rank-2 polarization tensor and a massless scalar field using the ambient space notations. Also the two-point function has been calculated in the ambient space formalism. It is dS invariant and free of any theoretical problem.