Gravitational Waves in Viable f(R) Models

TL;DR

This paper investigates the properties of gravitational waves in viable f(R) gravity models with non-zero background curvature, highlighting the scalar mode's mass and potential detectability by future gravitational wave observatories.

Contribution

It provides a detailed analysis of scalar gravitational wave modes in viable f(R) models, including exponential and Starobinsky models, under realistic cosmological conditions.

Findings

Scalar mode mass is about 10^{-33} eV in vacuum for both models.

In matter-rich environments like galaxies, the scalar mode can become very heavy or vanish.

Starobinsky model predicts a detectable scalar mode frequency around 10^{-9} Hz.

Abstract

We study gravitational waves in viable $f(R)$ theories under a non-zero background curvature. In general, an $f(R)$ theory contains an extra scalar degree of freedom corresponding to a massive scalar mode of gravitational wave. For viable $f(R)$ models, since there always exits a de-Sitter point where the background curvature in vacuum is non-zero, the mass squared of the scalar mode of gravitational wave is about the de-Sitter point curvature $R_{d}\sim10^{-66}eV^{2}$. We illustrate our results in two types of viable $f(R)$ models: the exponential gravity and Starobinsky models. In both cases, the mass will be in the order of $10^{-33}eV$ when it propagates in vacuum. However, in the presence of matter density in galaxy, the scalar mode can be heavy. Explicitly, in the exponential gravity model, the mass becomes almost infinity, implying the disappearance of the scalar mode of gravitational wave, while the Starobinsky model gives the lowest mass around $10^{-24}eV$, corresponding to the lowest frequency of $10^{-9}$ Hz, which may be detected by the current and future gravitational wave probes, such as LISA and ASTROD-GW.