IR finite graviton propagators in de Sitter spacetime

Mir Faizal,Sudhaker Upadhyay,Bhabani Prasad Mandal

doi:10.1140/epjc/s10052-016-4008-x

Abstract

Graviton propagator diverges in certain gauges in de Sitter spacetime. We address this problem in this work by generalizing the infinitesimal BRST transformations in de Sitter spacetime to finite field-dependent BRST (FFBRST) transformations. These FFBRST transformations are symmetry of the classical action, but do not leave path integral measure invariant for the graviton theory in de Sitter spacetime. Due to the non-trivial Jacobian of such finite transformation the path integral measure changes and hence FFBRST transformation is capable of relating theories in two different gauges. We explicitly construct FFBRST transformation which relates theory with diverging graviton two-point function to theory with infrared (IR) finite graviton. The FFBRST transformation thus establishes that divergence in graviton two-point function may be only a gauge artifact.

Highlights

The observations from type I supernovae indicate that our universe has a positive cosmological constant and may approach de Sitter spacetime asymptotically [1,3,4,5,6]
We argue that the IR divergent graviton propagators with β = −n(n+3)/3 are related to the IR finite graviton propagators with other values of β
It has been possible to gauge away these IR divergences in the graviton two-point function in de Sitter spacetime using an finite field-dependent BRST (FFBRST) transformation

Summary

Introduction

The observations from type I supernovae indicate that our universe has a positive cosmological constant and may approach de Sitter spacetime asymptotically [1,3,4,5,6]. In this work we extend the FFBRST formulation [30] in de Sitter spacetime and construct an appropriate finite fielddependent parameter to relate the generating functionals corresponding to the effective theories with graviton propagator for various values of β. We will rather demonstrate that a graviton propagator in a certain gauge, in which a certain kind of IR divergences occurs, can be related to the graviton propagator in a different gauge where such IR divergences do not occur This can be done using the FFBRST transformations, as the FFBRST transformations are a symmetry of the generating functional and not of the effective action, which is obtained by adding the gauge fixing and ghosts terms to the original action.

Perturbative quantum gravity

FFBRST transformation

Recovering IR finite the graviton propagators

F F B RST

Conclusion