Cosmological constraints on post-Newtonian parameters in effectively massless scalar-tensor theories of gravity

Abstract

We study the cosmological constraints on the variation of the Newton's constant and on post-Newtonian parameters for simple models of scalar-tensor theory of gravity beyond the extended Jordan-Brans-Dicke theory. We restrict ourselves to an effectively massless scalar field with a potential V ∝ F 2 , where F (σ) = N 2 pl + ξσ 2 is the coupling to the Ricci scalar considered. We derive the theoretical predictions for cosmic microwave background (CMB) anisotropies and matter power spectra by requiring that the effective gravitational strength at present is compatible with the one measured in a Cavendish-like experiment and by assuming adiabatic initial condition for scalar fluctuations. When comparing these models with P lanck 2015 and a compilation of baryonic acoustic oscilation (BAO) data, all these models accomodate a marginalized value for H0 higher than in ΛCDM. We find no evidence for a statistically significant deviation from Einstein's general relativity. We find ξ < 0.064 (|ξ| < 0.011) at 95% CL for ξ > 0 (for ξ < 0, ξ = −1/6). In terms of post-Newtonian parameters, we find 0.995 < γPN < 1 and 0.99987 < βPN < 1 (0.997 < γPN < 1 and 1 < βPN < 1.000011) for ξ > 0 (for ξ < 0). For the particular case of the conformal coupling, i.e. ξ = −1/6, we find constraints on the post-Newtonian parameters of similar precision to those within the Solar System. the more general Horndeski theory [13]:where χ = −g µν ∂ µ σ∂ ν σ, R is the Ricci scalar, G µν = R µν − g µν R/2, and L m is the density Lagrangian for the rest of matter. The eJBD theory corresponds to G 3 = G 5 = 0, G 2 = ω BD χ/σ − V (σ), G 4 = σ (in the equivalent induced gravity (IG) formulation with a standard kinetic term the two last conditions become G 2 = χ/2 − V (σ), G 4 = ξσ 2 /2 with ξ = 1/(4ω BD )).Cosmology puts to severe test eJBD theories. The constraints from P lanck 2015 and a compilation of baryon acoustic oscillations (BAO) data lead to a 95% CL upper bound ξ < 0.00075, weakly dependent on the index for a power-law potential [4] (see [3] for the P lanck 2013 constraints obtained with the same methodology). In terms of the first post-Newtonian parameter γ PN = (1 + ω BD )/(2 + ω BD ) = (1 + 4ξ)/(1 + 8ξ), the above 95% CL constraint read as |γ PN − 1| < 0.003 [4]. With the same data, a 95% CL bound is obtained on the relative time variation of the effective Newton's constant

Larger value for H0 by an evolving gravitational constant

“…By our embedding of a massless σ in ΛCDM, we focus on the early type of modification in this paper. In the case of a negative coupling ξ < 0, the scalar field decreases because of the coupling to matter, leading to cosmological post-Newtonian parameters which can be naturally consistent with the Solar System constraints γ PN − 1 ¼ ð2.1 AE 2.3Þ × 10 −5 at 68% CL [39] and β PN − 1 ¼ ð4.1 AE 7.8Þ × 10 −5 at 68% CL [40], extending what already emphasized for a conformal coupling (CC, i.e., ξ ¼ −1=6) in [37]. We also investigate to the case where N eff , which describes the effective number of relativistic species, is included in the analysis.…”

“…The n ¼ 2 case has been studied in Refs. [37,41] with a potential V ∝ F 2 , which is, however, close to a flat potential for the range of ξ allowed by observations. 3 The Friedmann and the Klein-Gordon equations in the spatially flat Friedmann-Lemaitre-Robinson-Walker (FLRW) background are given by…”

“…2 of Ref. [37] and their Eqs. (13) and (14) for the definitions of ρ DE and p DE ) and the contribution of the scalar field 4 to the total expansion rate HðzÞ thus resembles the one from an extra dark radiation component.…”

“…GeV is the reduced Planck mass, and n is taken as an even and positive integer, to reduce the H 0 tension. This simple model relies on the degeneracy between a nonminimal coupling to the Ricci curvature and the Hubble parameter which has been studied in previous works on the constraints on scalar-tensor theories of gravity 2 [35][36][37][38]. In general, scalar-tensor models modify both the early (in a way that resembles a contribution of an extra dark radiation component) and late-time expansion of the Universe [37].…”

Anisotropic massive Brans–Dicke gravity extension of the standard $$\Lambda $$CDM model

“…[116]. The constraints from Planck 2015 (2013) and a compilation of baryon acoustic oscillations (BAO) data are ω > 333 (ω > 208) at the 2σ C.L., weakly dependent on the exponent n > 0 for a power-law potential U (ϕ) ∝ ϕ n mimicking Λ in the late universe [117,118] (also see [119] for a recent work considering a more complicated potential). The BBN leads to ω 277 (for a universe containing dust, radiation and conventional vacuum energy), which assumes power-law solutions and, by using general solutions, can be somewhat altered depending on the behaviour of the Jordan field in the early universe [120].…”