Cosmological Constraints on Brans-Dicke Theory

Abstract

We report strong cosmological constraints on the Brans-Dicke (BD) theory of gravity using cosmic microwave background data from Planck. We consider two types of models. First, the initial condition of the scalar field is fixed to give the same effective gravitational strength Geff today as the one measured on Earth, GN. In this case, the BD parameter ω is constrained to ω>692 at the 99% confidence level, an order of magnitude improvement over previous constraints. In the second type, the initial condition for the scalar is a free parameter leading to a somewhat stronger constraint of ω>890, while Geff is constrained to 0.981<Geff/GN<1.285 at the same confidence level. We argue that these constraints have greater validity than for the BD theory and are valid for any Horndeski theory, the most general second-order scalar-tensor theory, which approximates the BD theory on cosmological scales. In this sense, our constraints place strong limits on possible modifications of gravity that might explain cosmic acceleration.

Constraints on the Brans-Dicke gravity theory with the Planck data

“…As pointed out by Ref. [18], comparing with their prior, our flat prior on ζ penalizes large ω, and hence for the same data set a "weaker" limit on ω would be obtained for our choice. We do not see a good theoretical reason to favor one prior on ω over the other, but our choice is again in agreement with our general philosophy of being conservative on constraining models.…”

“…This parameterization is more "conservative", so our limits appeared to be "weaker" than Ref. [18] even though we have used the newer and more precise Planck data.…”

“…Ref. [18] argued that if ω < −3/2 the Brans-Dicke field would be a ghost field, and they will therefore consider only positive ω. However, we would rather err on the conservative side, and use a more general form of parameterization which allows negative ω.…”

“…[15] and Ref. [18] considered flat prior on ln[1/ω] (though the exact parameter they used differs slightly). A limitation of this choice is that it could not treat the ω < 0 case.…”

“…Wu et al [16,17] excluded the region of −120 < ω < 97.8 by using the WMAP 5 year data and the Sloan Digital Sky Survey (SDSS) Luminous Red Galaxy (LRG) data. Considering only the possibility of ω > 0, Avilez and Skordis [18] derived a limit of ω > 288 at 95% confidence level. by combining the WMAP 7 year data and the data from the South Pole Telescope (SPT) and other small scale CMB experiments.…”