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

TL;DR

The paper addresses testing Brans-Dicke scalar-tensor gravity with cosmic microwave background anisotropies by developing a complete formalism and modifying a public Boltzmann code to compute BD temperature and polarization spectra. It reveals how BD alters the amplitude and width of acoustic peaks relative to general relativity with the same parameters and uses a covariance-matrix analysis to assess parameter degeneracies and detectability. The results indicate that MAP could constrain $\omega$ to about 500 and Planck to about 3000 (with other parameters fixed), with reductions by roughly a factor of 3 when marginalizing over $\Omega_b h^2$, $H_0$, $n_s$, and $\tau$, making the CMB a competitive, complementary probe to solar-system tests, especially if $\omega$ evolves with time. Overall, the work provides a BD-specific framework for CMB analysis and demonstrates the potential of CMB observations to test scalar-tensor gravity in regimes not accessible to weak-field experiments.

Abstract

We develop a formalism for calculating cosmic microwave background (CMB) temperature and polarization anisotropies in cosmological models with Brans-Dicke 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 general-relativistic 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 omega as large as 500 could be identified with MAP, and for Planck, values as large as omega \simeq3000 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, omega may evolve with time, and in this case, the CMB probe would be complementary to that from solar-system tests.