the scalar field, showing that they are coupled. Moreover, we derive the corresponding Mukhanov-Sasaki equations for our theory. Then, dealing with tensor perturbations, we show that, since the modification of our theory is performed on the matter sector, the equations must be the same as for GR. Section V is devoted to the comparison, at the perturbative level, of our model which leads to the same background as holonomy corrected LQC, with other theories which also lead to the same background, as: LQC in the [*deformed algebra approach*]{} [@grain; @caitelleau; @vidotto], teleparallel LQC [@cai; @haro13], extrinsic curvature LQC [@ha17] and mimetic LQC [@mukhanov1; @langlois; @Norbert]. In Section VI, we study the matter-ekpyrotic scenario applied to the model that leads the same background as LQC. We calculate the spectral index and its running and show that they match the most recent observational data. Moreover, we study the reheating process via gravitational massless particle production. Finally, the last Section is devoted to conclusions.

The units used throughout the paper are $\hbar=c=1=M_{pl}=1$, where $M_{pl}$ is the reduced Planck mass with the convention that a temporal vector $v_{\mu}$ satisfies $v_{\mu}v^{\mu}<0$ and with the notation:

1.  $\varphi_{,\mu}\equiv\partial_{\mu}\varphi=\nabla_{\mu}\varphi$ for a given scalar $\varphi$.

2.  $\bar{g}$ is 