Cosmic Microwave Background Temperature and Polarization Anisotropy in Brans-Dicke Cosmology

We develop a formalism for calculating cosmic microwave background (CMB) temperature and polarization anisotropies in cosmological models with BransDicke gravity. We then modify publicly available Boltzmann codes to calculate numerically the temperature and polarization power spectra. Results are illustrated with a few representative models. Comparing with the generalrelativistic model with the same cosmological parameters, both the amplitude and the width of the acoustic peaks are different in the Brans-Dicke models. We use a covariance-matrix calculation to investigate whether the effects of Brans-Dicke gravity are degenerate with those of variation in other cosmological parameters and to simultaneously determine whether forthcoming CMB maps might be able to distinguish Brans-Dicke and general-relativistic cosmology. Although the predicted power spectra for plausible Brans-Dicke models differ from those in general relativity only slightly, we find that MAP and/or the Planck Surveyor may in principle provide a test of Brans-Dicke theory that is competitive to solar-system tests. For example, if all other parameters except for the CMB normalization are fixed, a value of the Brans-Dicke parameter ω as large as 500 could be identified with MAP, and for Planck, values as large as ω ' 3000 could be identified; these sensitivities are decreased roughly by a factor of 3 if we marginalize over the baryon density, Hubble constant, spectral index, and reionization optical depth. In more general scalar-tensor theories, ω may evolve with time, and in this case, the CMB probe would be complementary to that from solar-system tests. Typeset using REVTEX ∗Email: [email protected] †Email: [email protected]