Abstract
New corrections to General Relativity are considered in the context of modified f(R) gravity, that satisfy cosmological and local gravity constraints. The proposed models behave asymptotically as R − 2Λ at large curvature and show the vanishing of the cosmological constant at the flat spacetime limit. The chameleon mechanism and thin shell restrictions for local systems were analyzed, and bounds on the models were found. The steepness of the deviation parameter m at late times leads to measurable signal of scalar-tensor regime in matter perturbations, that allows to detect departures form the ΛCDM model. The theoretical results for the evolution of the weighted growth rate fσ8(z), from the proposed models, were analyzed.
Highlights
Background evolutionTo solve numerically the field equations we use the variables introduced in [45, 50] yH H2 μ2 a−3, yR R μ2 − 3a−3 (2.19)and work with the e-fold variable ln a, where (’) indicates d/d ln a
The steepness of the deviation parameter m at late times leads to measurable signal of scalartensor regime in matter perturbations, that allows to detect departures form the ΛCDM model
In the present paper we propose f (R) models that satisfy the stability conditions f (R) > 0, f (R) > 0, comply with cosmological and local gravity constraints and can lead to signals of scalar-tensor regime measurable at late times
Summary
Given that y yds, in a high curvature regime the parameter α is not so relevant in the expression (3.24) (unless it is large enough), so the power η becomes the dominant parameter Another case of the model (3.5) is obtained by setting α = 1/η, giving f (R) = R −. Taking into account that the condition μ2 R follows, the effective potential for the models (3.5) and (3.36) can be written respectively as (we will use Ve(ff1) for the model (3.5) and Ve(ff2) for the model (3.36) and likewise for the corresponding scalar fields) Note that in this last case the curvature R cannot be expressed explicitly in terms of the scalar field, but the scalar field can be expressed in terms of R via the conformal transformation (3.56). In both models the last bound can be disregarded since they become indistinguishable from ΛCDM model
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