Covariant and infrared-free graviton two-point function in de Sitter spacetime

TL;DR

This paper derives a covariant, infrared-free two-point function for gravitons in de Sitter space using Krein space quantization, addressing infrared divergences and gauge issues in quantum gravity on curved backgrounds.

Contribution

It presents a covariant, infrared-free graviton two-point function in de Sitter space employing Krein space quantization, with a detailed analysis of gauge fixing and the pure-trace component.

Findings

The two-point function is free of infrared divergence.

Gauge fixing parameter is restricted to an optimal value.

Pure-trace part expressed via a conformally coupled scalar.

Abstract

In this paper, the two-point function of linearized gravitons on de Sitter (dS) space is presented. Technically, respecting the dS ambient space notation, the field equation is given by the coordinate-independent Casimir operators of the de Sitter group. Analogous to the quantization of the electromagnetic field in Minkowski space, the field equation admits gauge solutions. The notation allows us to exhibit the formalism of Gupta-Bleuler triplets for the present field in exactly the same manner as it occurs for the electromagnetic field. In this regard, centering on the spin-two part (the traceless part, ${\cal{K}}^t$), the field solution is written as a product of a generalized polarization tensor and a minimally coupled massless scalar field. Then, admitting a de Sitter-invariant vacuum through the so-called "Krein space quantization", the de Sitter fully covariant two-point function is calculated. This function is interestingly free of pathological large distance behavior (infrared divergence). Moreover, the spin-zero part (the pure-trace part; ${\cal{K}}^{pt}$) of the field is discussed in this paper. It is shown that the implications of the dS group unitary irreducible representations restrict the gauge-fixing parameter to the optimal value, which remarkably results in the pure-trace part be written in terms of a conformally coupled massless scalar field.