A diffeomorphism invariant family of metric-affine actions for loop cosmologies

In loop quantum cosmology (LQC) the big bang singularity is generically resolved by a bigbounce. This feature holds even when modified quantization prescriptions of the Hamiltonianconstraint are used such as in mLQC-I and mLQC-II. While the later describes an effectivedescription qualitatively similar to that of standard LQC, the former describes an asymmetricevolution with an emergent Planckian de-Sitter pre-bounce phase even in the absence of apotential. We consider the potential relation of these canonically quantized non-singular modelswith effective actions based on a geometric description. We find a 3-parameter family ofmetric-affine f(ℛ) theories which accurately approximate the effective dynamics of LQCand mLQC-II in all regimes and mLQC-I in the post-bounce phase. Two of the parameters are fixed byenforcing equivalence at the bounce, and the background evolution of the relevant observables canbe fitted with only one free parameter. It is seen that the non-perturbative effects of these loopcosmologies are universally encoded by a logarithmic correction that only depends on the bouncecurvature of the model. In addition, we find that the best fit value of the free parameter can bevery approximately written in terms of fundamental parameters of the underlying quantumdescription for the three models. The values of the best fits can be written in terms of thebounce density in a simple manner, and the values for each model are related to one another by aproportionality relation involving only the Barbero-Immirzi parameter.

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19 pages, 4 figures and 3 tables

quantum cosmology
modified gravity
cosmic singularity
quantum cosmology: loop space
effect: nonperturbative
big bang: singularity
constraint: Hamiltonian
diffeomorphism: invariance
bounce
family

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