Galaxy clusters and a possible variation of the fine structure constant

Abstract

Galaxy clusters have been used as a cosmic laboratory to verify a possible time variation of fundamental constants. Particularly, it has been shown that the ratio $Y_{SZ}{D}_A^2/C_{XZS}{Y}_X$, which is expected to be constant with redshift, can be used to probe a variation of the fine structure constant, $\alpha$. In this ratio, $Y_{SZ}{D}_A^2$ is the integrated comptonization parameter of a galaxy cluster obtained via Sunyaev-Zel'dovich (SZ) effect observations multiplied by its angular diameter distance, $D_A$, $Y_X$ is the X-ray counterpart and $C_{XSZ}$ is an arbitrary constant. Using a combination of SZ and X-ray data, a recent analysis found $Y_{SZ}{D}_A^2/C_{XZS}{Y}_X=\mathrm{C}\alpha (z{)}^{3.5}$, where $\mathrm{C}$ is a constant. In this paper, following previous results that suggest that a variation of $\alpha$ necessarily leads to a violation of the cosmic distance duality relation, $D_L/D_A(1+z{)}^2=1$, where $D_L$ is the luminosity distance of a given source, we derive a new expression, $Y_{SZ}{D}_A^2/C_{XSZ}{Y}_X=\mathrm{C}{\alpha }^{3.5}{\eta }^{-1}(z)$, where $\eta (z)=D_L/D_A(1+z{)}^2$. In particular, considering the direct relation $\eta (z)\propto \alpha (z{)}^{1/2}$, derived from a class of dilaton runaway models, %class of modified gravity theories, and 61 measurements of the ratio $Y_{SZ}{D}_A^2/C_{XSZ}{Y}_X$ provided by the Planck collaboration, we discuss bounds on a possible variation of $\alpha$. We also estimate the value of the constant $\mathrm{C}$, which is compatible with the unity at $2\sigma$ level, indicating that the assumption of isothermality for the temperature profile of the galaxy clusters used in the analysis holds.

JCAP Accepted, 8 pages, two figures, I table