Constraints on scalar-tensor theories of gravity from observations

Abstract

In spite of their original discrepancy, both dark energy and modified theory of gravity can be parameterized by the effective equation of state (EOS) ω for the expansion history of the Universe. A useful model independent approach to the EOS of them can be given by so-called ChevallierPolarski-Linder (CPL) parametrization where two parameters of it (ω 0 and ω a ) can be constrained by the geometrical observations which suffer from degeneracies between models. The linear growth of large scale structure is usually used to remove these degeneracies. This growth can be described by the growth index parameter γ and it can be parameterized by γ 0 + γ a (1 − a) in general. We use the scalar-tensor theories of gravity (STG) and show that the discernment between models is possible only when γ a is not negligible. We show that the linear density perturbation of the matter component as a function of redshift severely constrains the viable subclasses of STG in terms of ω and γ. From this method, we can rule out or prove the viable STG in future observations. When we use Z(φ) = 1, F shows the convex shape of evolution in a viable STG model. The viable STG models with Z(φ) = 1 are not distinguishable from dark energy models when we strongly limit the solar system constraint.

Conformal (In)Equality

“…The evolution equations for the background and the matter perturbation in the flat FriedmannLemaitre-Robertson-Walker (FLRW) metric are given by [6] …”

Conformal Frame Dependence on Cosmological Observations in Scalar-Tensor Theories of Gravity

“…Thus, one needs complementary methods beyond the background evolution of the Universe to break degeneracies among models. The growth rate of the large scale structure, f (a) ≡ d ln δ m (a)/d ln a is one of these discriminators of models [4,5,6,7,8,9,10,11,12,13,14]. This is due to the fact that the matter perturbations of the different gravity theories might have the different Poisson terms (source terms) for the same background evolution (friction term).…”

“…For the scalar-tensor theories of gravity (STG) [28,29,30], one can obtain the specific γ for the certain STG model [31,32,33]. One of the common parametrizations for all models is given by γ = γ 0 + γ a (1 − a) as similar to that of ω [11].…”

“…However, one needs to reconstruct theory without any specific theory a priori. Thus, we use both background and growth history parameters (ω, γ) which can be obtained from observations to find the viable subclasses of STG [11]. However, this process is done in the so-called Jordan frame (JF) where the metric tensor is minimally coupled to the matter sector.…”

“…Thus, we assume that both ω and γ is determined from the observations. We briefly review how to reconstruct STG model functions F (φ) and U (φ) as a function of redshift, z in a JF by using ω and γ in the next section [11]. In Sec.…”