Viable non-singular cosmic bounce in holonomy improved F(R) gravity endowed with a Lagrange multiplier

Understand

Matter and quasi-matter bounce scenarios are studied for an F(R) gravity model with holonomy corrections and a Lagrange multiplier, with a scale factor $a(t) = \left(a_0t^2 + 1 \right)^n$, where the Hubble parameter squared has a linear and a quadratic dependence on the effective energy density.

• Provided $n < 1/2$, it is shown that the primordial curvature perturbations are generated deeply into the contracting era, at large negative time, which makes the low-curvature limit a good approximation for calculating the perturbation power spectrum.
• Moreover, it is shown that, for $n$ within this range, the obtained cosmological quantities are fully compatible with the Planck constraints, and that the &#34;low curvature limit&#34; comes as a viable approximation to calculate the power spectra of both scalar and tensor perturbations.
• Using reconstruction techniques for F(R) gravity with the Lagrange multiplier, the precise form of the effective F(R) gravity is found, from which one determines the power spectra of scalar and tensor perturbations in such bouncing scenario.