Cosmological parameter constraints for Horndeski scalar-tensor gravity

Abstract

We present new cosmological parameter constraints for general Horndeski scalartensor theories, using CMB, redshift space distortion, matter power spectrum and BAO measurements from the Planck, SDSS/BOSS and 6dF surveys. We focus on theories with cosmological gravitational waves propagating at the speed of light, c GW = c, implementing and discussing several previously unaccounted for aspects in the constraint derivation for such theories, that qualitatively affect the resulting constraints. In order to ensure our conclusions are robust, we compare results for three different parametrisations of the free functions in Horndeski scalartensor theories, identifying several parametrisation-independent features of the constraints. We also consider models, where c GW = c in cosmological settings (still allowed after GW170817 for frequency-dependent c GW ) and show how this affects cosmological parameter constraints.

Cosmological constraints on dark energy in light of gravitational wave bounds

“…Cosmological parameter constraints for the dark energy c B and c M parameters, using the α i = c i ·a (left triangle plot) and α i = c i ·Ω DE (right triangle plot) parametrisations and different combinations of datasets and priors (see section III). All constraints shown assume α T = 0, but note that constraints in the c M − c B plane, as shown here, are only mildly affected by allowing α T = 0 [34]. Contours mark 68% and 95% confidence intervals, computed using just Planck data (P15), Planck data plus RSD, BAO and matter power spectrum measurements (P15 + LSS), and P15 + LSS with an additional prior ensuring the absence of GW-induced instabilities (P15 + LSS + GW).…”

“…3 below we show that P15 + LSS + GW and P15 + GW lead to near identical constraints. Dotted lines mark c i = 0 (the GR value), c B = 2 (a singular line physical models cannot cross in the α i = c i a parametrisation -see [34][35][36] for details) and c M = −c B (constraint derived from the GW prior). instability constraints introduces one additional class of interactions not constrained by current GW bounds [12].…”

“…5 As discussed above, we consider such perturbations around an FRW background. More specifically we will assume this background to be ΛCDM-like (motivated by the observed proximity to such 5 For a comparison with cosmological parameter constraints on models without the α T constraint (and employing the same parametrisations as in this paper), see [17,34]. a solution) and constrain perturbations around it.…”

“…parameters Ω cdm , Ω b , θ s , A s , n s and τ reio -for technical details regarding the MCMC implementation (as well as for additional details on the implementation and use of the data sets involved) see [34]. For related cosmological parameter constraints on deviations from GR using general parameterised approaches and a variety of (current and forecasted) experimental data, see [17,18,34,[48][49][50][51][52][53][54][55][56][57][58][59][60] All the constraints computed here assume α T = 0 as a prior to ensure compatibility with the speed of gravity constraints from GW170817 (as discussed in detail above), but we consider constraints with and without the further prior (7) from requiring the absence of GW-induced gradient instabilities. For reference throughout the remainder of this section, we adopt the following shorthands in referring to the datasets we use (as well as the additional GW prior):…”

“…• LSS: Here we include baryon acoustic oscillation (BAO) measurements from SDSS/BOSS [63,64], constraints from the SDSS DR4 LRG matter power spectrum shape [65] and redshift space distortion (RSD) constraints from BOSS and 6dF [66,67]. Of these large scale structure measurements, RSDs have the strongest constraining power for general Horndeski theories [34].…”