Conformally Invariant Equations for Graviton

TL;DR

This paper derives conformally invariant wave equations for massless spin-2 fields in de Sitter space, aiming to advance the understanding of quantum gravity and the role of conformal symmetry in gravitational theories.

Contribution

It introduces conformally invariant equations for massless spin-2 fields in de Sitter space, addressing a gap in the invariance properties of linearized gravity.

Findings

Derived conformally invariant wave equations for massless spin-2 fields.

Showed that previous linearized Einstein equations are not conformally invariant.

Suggested conformal invariance as a potential key to quantum gravity.

Abstract

Recent astrophysical data indicate that our universe might currently be in a de Sitter (dS) phase. The importance of dS space has been primarily ignited by the study of the inflationary model of the universe and the quantum gravity. As we know Einstein's theory of gravitation (with a nonzero cosmological constant) can be interpreted as a theory of a metric field; that is, a symmetric tensor field of rank-2 on a fixed de Sitter background. It has been shown that the massless spin-2 Fierz-Pauli wave equation (or the linearized Einstein equation) is not conformally invariant. This result is in contrary with what we used to expect for massless theories. In this thesis we obtain conformally invariant wave equation for the massless spin-2 in the dS space. This study is motivated by the belief that conformal invariance may be the key to a future theory of quantum gravity.