We propose a new cosmological test of gravity, by using the observed mass fraction of X-ray-emitting gas in massive galaxy clusters. The cluster gas fraction, believed to be a fair sample of the average baryon fraction in the Universe, is a well-understood observable, which has previously mainly been used to constrain background cosmology. In some modified gravity models, such as f(R) gravity, gas temperature in a massive cluster is determined by the effective mass (the mass that would have produced the same gravitational effect assuming standard gravity as the cluster actually does in f(R) gravity) of that cluster, which can be larger than its true mass. On the other hand, X-ray luminosity is determined by the true gas density, which in both modified gravity and Λ-cold-dark-matter models depends mainly on Ωb/Ωm and hence the true total cluster mass. As a result, the standard practice of combining gas temperatures and X-ray surface brightnesses of clusters to infer their gas fractions can, in modified gravity models, lead to a larger – in f(R) gravity this can be 1/3 larger – value of Ωb/Ωm than that inferred from other observations such as the cosmic microwave background. Our quick calculation shows that the Hu–Sawicki n = 1 f(R) model with |f¯R0|=5×10−5|f¯R0|=5×10−5 is in tension with the gas fraction data of the 42 clusters analysed by Allen et al. We also discuss the implications for other modified gravity models.
Li, B., He, J., & Gao, L. (2016). Cluster gas fraction as a test of gravity. Monthly Notices of the Royal Astronomical Society, 456(1), 146-155. https://doi.org/10.1093/mnras/stv2650