Building cubic gravity with healthy and viable scalar and tensor perturbations

Petros Asimakis; Spyros Basilakos; Emmanuel N. Saridakis

doi:10.1140/epjc/s10052-024-12554-7

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 207
https://doi.org/10.1140/epjc/s10052-024-12554-7

Regular Article - Theoretical Physics

Building cubic gravity with healthy and viable scalar and tensor perturbations

Petros Asimakis¹^a, Spyros Basilakos²^,3^,4 and Emmanuel N. Saridakis²^,5^,6

¹ Department of Physics, National Technical University of Athens, Zografou Campus, 157 73, Athens, Greece
² National Observatory of Athens, 11852, Athens, Lofos Nymfon, Greece
³ Academy of Athens, Research Center for Astronomy and Applied Mathematics, Soranou Efesiou 4, 11527, Athens, Greece
⁴ School of Sciences, European University Cyprus, Diogenes Street, Engomi, 1516, Nicosia, Cyprus
⁵ CAS Key Laboratory for Researches in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of China, 230026, Hefei, Anhui, People’s Republic of China
⁶ Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, Casilla, 1280, Antofagasta, Chile

^a peterr321_@hotmail.com

Received: 8 December 2023
Accepted: 14 February 2024
Published online: 29 February 2024

Abstract

We investigate sufficient conditions under which cubic gravity is healthy and viable at the perturbation level. We perform a detailed analysis of the scalar and tensor perturbations. We impose the requirement that the two scalar potentials, whose ratio is the post-Newtonian parameter $γ$ $\gamma$ , should deviate only minimally form general relativity. Additionally, concerning tensor perturbations we impose satisfaction of the LIGO-VIRGO and Fermi Gamma-ray Burst observations, and thus we result to a gravitational-wave equation with gravitational-wave speed equal to the speed of light, and where the only deviation from general relativity appears in the dispersion relation. Furthermore, we show that cubic gravity exhibits an effective Newton’s constant that depends on the model parameter, on the background evolution, and on the wavenumber scale. Hence, by requiring its deviation from the standard Newton’s constant to be within observational bounds we extract the constraints on the single coupling parameter $β$ $\beta$ .

© The Author(s) 2024

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