Anisotropic massive Brans\u2013Dicke gravity extension of the standard Lambda CDM model

Abstract

We present an explicit detailed theoretical and observational investigation of an anisotropic massive Brans–Dicke (BD) gravity extension of the standard Lambda CDM model, wherein the extension is characterized by two additional degrees of freedom; the BD parameter, omega , and the present day density parameter corresponding to the shear scalar, Omega _{sigma ^2,0}. The BD parameter, determining the deviation from general relativity (GR), by alone characterizes both the dynamics of the effective dark energy (DE) and the redshift dependence of the shear scalar. These two affect each other depending on omega , namely, the shear scalar contributes to the dynamics of the effective DE, and its anisotropic stress – which does not exist in scalar field models of DE within GR – controls the dynamics of the shear scalar deviating from the usual propto (1+z)^6 form in GR. We mainly confine the current work to non-negative omega values as it is the right sign – theoretically and observationally – for investigating the model as a correction to the Lambda CDM. By considering the current cosmological observations, we find that omega gtrsim 250, Omega _{sigma ^2,0}lesssim 10^{-23} and the contribution of the anisotropy of the effective DE to this value is insignificant. We conclude that the simplest anisotropic massive BD gravity extension of the standard Lambda CDM model exhibits no significant deviations from it all the way to the Big Bang Nucleosynthesis. We also point out the interesting features of the model in the case of negative omega values; for instance, the constraints on Omega _{sigma ^2,0} could be relaxed considerably, the values of omega sim -1 (relevant to string theories) predict dramatically different dynamics for the expansion anisotropy.