Massless and Partially Massless Limits in Quadratic Gravity

TL;DR

This paper investigates the limits of quadratic gravity theories, revealing how the presence of a cosmological constant influences the emergence of massless and partially massless spin-2 modes, with implications for high-energy behavior.

Contribution

It demonstrates the distinct massless and partially massless limits in quadratic gravity depending on the cosmological constant, and analyzes their implications for renormalizability and ghost behavior.

Findings

Massless limit occurs when the cosmological constant is zero.

Partially massless limit arises with a non-zero cosmological constant.

Interactions vanish in the partially massless limit.

Abstract

In the context of perturbative quantum field theory, the addition of quadratic-curvature invariants to the Einstein-Hilbert action makes it possible to achieve strict renormalizability in four dimensions. The additional terms $R^2$ and $C_{\mu\nu\rho\sigma} C^{\mu\nu\rho\sigma}$ are multiplied by dimensionless coefficients that are related to the masses of the extra gravitational degrees of freedom and to the interaction couplings. The aim of this paper is to study the limit of the theory in which the Weyl-squared coefficient tends to infinity. Remarkably, the result of this limit turns out to be sensitive to the presence of a cosmological constant: when the latter is zero we have a massless limit for the spin-2 ghost, while when the cosmological constant is different from zero we obtain a partially massless limit. We show that the renormalizability property and the ghost-like nature of the massive spin-$2$ field ensure that the two limits do not hit strong couplings, unlike standard ghost-free theories of massive gravity. In particular, in the partially massless limit the interactions mediated by the spin-$2$ sector vanish. We argue that our results can be useful for understanding the high-energy limit of Quadratic Gravity.