Cosmological perturbations in a class of fully covariant modified theories: Application to models with the same background as standard LQC

Understand

Bouncing cosmologies are obtained by adding to the Einstein-Hilbert action a term of the form $\sqrt{-g}f(\chi)$, with $\chi$ a scalar depending on the Hubble parameter only, not on its derivatives, and which is here shown to arise from the divergence of the unitary time-like eigenvector of the stress tensor.

• At background level, the dynamical equations for a given $f$-theory are calculated, showing that the simplest bouncing cosmology resulting leads to exactly the same equations as those for holonomy corrected Loop Quantum Cosmology (LQC).
• When dealing with perturbations, the equation for tensor ones is the same as in General Relativity (GR); for scalar perturbations, when one uses the $f$-theory which leads to the same background as the standard version of holonomy corrected LQC, one obtains similar equations (although a bit more elaborated) as those coming from LQC in the so-called deformed algebra approach.