Dark sector evolution in Horndeski models

Abstract

We use the Equation of State (EoS) approach to study the evolution of the dark sector in Horndeski models, the most general scalar-tensor theories with second order equations of motion. By including the effects of the dark sector into our code EoS_class, we demonstrate the numerical stability of the formalism and excellent agreement with results from other publicly available codes for a range of parameters describing the evolution of the function characterising the perturbations for Horndeski models, α x , with x = {K, B, M, T}. After demonstrating that on sub-horizon scales (k 10 −3 Mpc −1 at z = 0) velocity perturbations in both the matter and the dark sector are typically subdominant with respect to density perturbations in the equation of state for perturbations, we find an attractor solution for the dark sector gauge-invariant density perturbation ∆ ds . Using this result, we provide simplified expressions for the equation-of-state functions: the dark sector entropy perturbations w ds Γ ds and anisotropic stress w ds Π ds . From this we derive a growth factor-like equation for both matter and dark sector and are able to capture the relevant physics for several observables with great accuracy. We finally present new analytical expressions for the well-known modified gravity phenomenological functions µ, η and Σ for a generic Horndeski model as functions of α x . We show that on small scales they reproduce expressions presented in previous works, but on large scales, we find differences with respect to other works.

Effective field theory of dark energy: A review

“…A collection of EB solvers based on the EFT framework has been compared and cross-calibrated recently [132,71]. Among them, there are: the Effective Field Theory for CAMB (EFTCAMB) [67,68], Horndeski in CLASS (hi class) [69], Cosmology Object Oriented Package (COOP) [70] and Equation of State for CLASS (EoS class) [71]. All are publicly available 8 .…”

“…The analysis of COOP, instead, shows that COOP achieves the required precision only for k < 1hMpc −1 . EoS class was cross-checked with hi class for the α-basis [71] and with EFTCAMB for the designer f (R)model [132] showing a sub-percent agreement. These results strengthened the confidence on these numerical codes making them efficient for precision constraints on cosmological and gravitational parameters.…”

“…The EFT approach allows thus to investigate the phenomenology of these effects at linear scales for large class of models [193,56,106,194,69,77,58,195,196,130,197,140,198,71]. In this case the connection with a specific operator in the action (5) or a physical effect enclosed in the α-basis can be easily identified by switching on/off single EFT functions per time.…”

“…The synergy between theory and observations is further exploited thanks to Einstein-Boltzmann (EB) codes constructed on top of the EFT framework. The latter are EFTCAMB [67,68], hi class [69], COOP [70] and EoS class [71] and they have been used to obtain cosmological constrains using a wide selection of data sets.…”

hi_class background evolution, initial conditions and approximation schemes

“…EFTCAMB [76], COOP [77]) and ones dealing with an approximation to it or specific models of gravity (e.g. DASh [78], GalCAMB [79], EoS_class [80] or EFCLASS [81]) reaching the level of accuracy needed by next-generation cosmological experiments [82]. Currently the publicly available version of the hi_class code incorporates Horndeski's scalar-tensor theory, a very general overarching framework that incorporates a large class of DE and beyond GR theories.…”