Extended matter bounce scenario in ghost free $f(R,\mathcal{G})$ gravity compatible with GW170817

Understand

In the context of a ghost free $f(R,\mathcal{G})$ model, an extended matter bounce scenario is studied where the form of the scale factor is given by $a(t) = (a_0t^2 + 1)^n$.

• The ghost free character of the model is ensured by the presence of a Lagrange multiplier, as developed in \cite{Nojiri:2018ouv}.
• 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 $\ddot{h} = \dot{h}H$, with $H$ the Hubble parameter.