Abstract
In the context of a ghost free f(R,G) model, an extended matter bounce scenario is studied where the form of the scale factor is given by a(t)=(a0t2+1)n. The ghost free character of the model is ensured by the presence of a Lagrange multiplier, as developed in [1]. The conditions under which, in this model, the speed of gravitational waves becomes equal to the speed of light (equal to one, in natural units), thus becoming compatible with the striking event GW170817, is investigated. It is shown that this happens for a class of Gauss-Bonnet (GB) coupling functions (h(t)) which satisfies a constraint equation of the form h¨=h˙H, with H the Hubble parameter. This constraint is then imposed on the ghost free f(R,G) gravity theory to be consistent with the GW170817 event, subsequently, the corresponding non-singular bouncing cosmology with the aforementioned scale factor is extensively studied. The forms of the coupling function and Lagrange multiplier in the “low curvature limit” of the theory are reconstructed, yielding a viable approximation for n<1/2. Correspondingly, by solving the cosmological perturbation equation, the main observable quantities, namely the spectral index, tensor to scalar ratio, and the running index are determined and confronted with the latest Planck 2018 data. Consistency with the data is proven for those parametric regimes that which correspond to n<1/2. This makes the low curvature approximation a viable one for calculating the scalar and tensor power spectra.
Highlights
A major issue in theoretical cosmology is to ascertain whether the Universe was created from an initial singular or if, on the contrary, the Universe initiated its expansion from a non-singular, bounce-like stage
The implications of GW170817 on non-singular bounce has been investigated, but in a different context i.e from a degenerate higher order scalar-tensor (DHOST) theory [79], unlike to the present paper where we discuss the bouncing scenario from ghost free f (R, G) gravity model taking the constraint of GW170817 into account
In the present paper we have considered an extended matter bounce scenario in a ghost free f (R, G) gravity, in particular, for the f (R, G) =
Summary
A major issue in theoretical cosmology is to ascertain whether the Universe was created from an initial singular or if, on the contrary, the Universe initiated its expansion from a non-singular, bounce-like stage. The implications of GW170817 on non-singular bounce has been investigated, but in a different context i.e from a degenerate higher order scalar-tensor (DHOST) theory [79], unlike to the present paper where we discuss the bouncing scenario from ghost free f (R, G) gravity model taking the constraint of GW170817 into account. We will consider a Hubble parameter which leads to an an extended matter bounce cosmology In this context, it is worth mentioning that the presence of the potential term V (χ) in f (R, G) model to realize a non-singular bounce cosmology which is consistent with c2T = 1. We shall extensively discuss the bouncing scenario of this f (R, G) model, which is both ghost free and compatible with the GW170817 event
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