an essential difference with respect to theories such as General Relativity (GR) or LQC in the [*deformed algebra approach*]{}, where the dynamical equation for the potential $\Phi$ decouples ($\delta\phi$ does not appear, see for instance [@mukhanovbook; @grain]).

Once these equations are obtained, we study some characteristics of the matter-ekpyrotic bounce scenario [@cw; @haa] as the calculation of some spectral quantities and the reheating temperature via the gravitational particle production of massless particles, in the contracting regime, during the phase transition from matter domination to the ekpyrotic regime.

The manuscript is organized as follows: In Section II we present our class of modified gravitational theories and obtain the corresponding dynamical equations. We study them at the background level and find which is the model that leads to the simple bounce predicted by holonomy corrected LQC. A Hamiltonian analysis of our theory is performed in Section III, which leads to the conclusion that the present theory, as in the case of mimetic gravity, has one more degree of freedom than GR. In section IV, we study scalar and tensor perturbations. For scalar perturbations, working in the longitudinal gauge, we obtain the equations for the Newtonian potential and for the perturbed part of 