How can holonomy corrections be introduced in $f(R)$ gravity?

Abstract

We study the introduction of holonomy corrections in $f(R)$ gravity. We will show that there are infinitely many ways, as many as canonical transformations, to introduce this kind of corrections, depending on the canonical variables (two coordinates and its conjugate momenta) used to obtain the Hamiltonian. In each case, these corrections lead, at effective level, to different modified holonomy corrected Friedmann equations in $f(R)$ gravity, which are in practice analytically unworkable, i.e. only numerical analysis can be used to understand its dynamics. Finally, we give arguments in favour of one preferred set of variables, the one that conformally maps $f(R)$ to Einstein gravity, because for these variables the dynamics of the system has a clear physical meaning: the same as in standard Loop Quantum Cosmology, where the effective dynamics of a system can be analytically studied.

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• Accelerating Cosmology and Phase Structure of F(R) Gravity with Lagrange Multiplier Constraint: Mimetic Approach
• The bounce universe history from unimodular $F(R)$ gravity
• Bounce universe from string-inspired Gauss-Bonnet gravity
• Cosmological bouncing solutions in extended teleparallel gravity theories
• Quasi-matter domination parameters in bouncing cosmologies
• Bounce Loop Quantum Cosmology Corrected Gauss-Bonnet Gravity
• Correction to Lagrangian for Bouncing Cosmologies in $f(Q)$ Gravity
• Mimetic $F(R)$ inflation confronted with Planck and BICEP2/Keck Array data
• The effective dynamics of loop quantum $R^2$ cosmology
• Loop Quantum Cosmology Matter Bounce Reconstruction from $F(R)$ Gravity Using an Auxiliary Field
• Viable non-singular cosmic bounce in holonomy improved F(R) gravity endowed with a Lagrange multiplier
• Anamorphic Quasiperiodic Universes in Modified and Einstein Gravity with Loop Quantum Gravity Corrections