Limiting curvature mimetic gravity for group field theory condensates

Abstract

Nonsingular bouncing cosmologies are realized in limiting curvature mimetic gravity by means of a multivalued potential f ( φ) depending on the d'Alembertian of a scalar field φ. We determine the functional form of such a potential so as to exactly reproduce the cosmological background dynamics obtained in the group field theory approach to quantum gravity. The original proposal made by Chamseddine and Mukhanov [JCAP 1703[JCAP , no. 03, 009 (2017], which was shown to lead to a background dynamics reproducing the effective dynamics of loop quantum cosmology, is here recovered as a particular case for some specific choices of the parameters of our model. We also clarify some issues related to the multi-valuedness of the function f , showing in particular that its functional form can be unambiguously reconstructed by imposing appropriate matching conditions at the branching points.

Reconstruction of Mimetic Gravity in a Non-Singular Bouncing Universe from Quantum Gravity

“…Equation 2.6 can be interpreted as a conservation law for the Noether current associated with the global shift-symmetry of the action (2.1), see Refs. [19,34] Considering a flat FLRW model ds 2 = dt 2 − a 2 (t)δ ij dx i dx j , the field equations (2.3) lead to a modification of the Friedmann and Raychaudhuri equations 1 3…”

“…In Ref. [19] the reconstruction procedure outlined in Section 3 was successfully applied to the cosmological dynamics obtained from group field theory condensates in [5]. The evolution equation for such a model can be expressed in relational form by introducing a minimally coupled massless scalar field ψ [41].…”

“…(4.5) becomes the dominant one: the standard Friedmann evolution is thus recovered, and the quantum gravity corrections are sub-leading. The background evolution (4.5) can be exactly reproduced in mimetic gravity if the function f (χ) is given by [19] f (χ) = ρ ψ (χ) + 1 3…”

“…On a cosmological spacetime, f (χ) reduces to a function of the Hubble rate [20]. Multivaluedness of the potential is necessary for a consistent realisation of bouncing cosmologies in this framework [19,[21][22][23]. Non-singular black hole solutions have been studied in Refs.…”

“…In Section 4 we focus on the model of Ref. [19]: we discuss the background evolution, exhibit the form of the function f (χ) and derive its expansion in its two branches, corresponding to the region around the bounce and to a large universe. The model of Ref.…”