Quantum reduced loop gravity: Semiclassical limit

Abstract

We discuss the semiclassical limit of Quantum Reduced Loop Gravity, a recently proposed model to address the quantum dynamics of the early Universe. We apply the techniques developed in full Loop Quantum Gravity to define the semiclassical states in the kinematical Hilbert space and evaluating the expectation value of the euclidean scalar constraint we demonstrate that it coincides with the classical expression, i.e. the one of a local Bianchi I dynamics. The result holds as a leading order expansion in the scale factors of the Universe and opens the way to study the subleading corrections to the semiclassical dynamics. We outline how by retaining a suitable finite coordinate length for holonomies our effective Hamiltonian at the leading order coincides with the one expected from LQC. This result is an important step in fixing the correspondence between LQG and LQC.

New loop quantum cosmology modifications from gauge-covariant fluxes

“…One promising method to get some hints on this issue is to study coherent states in some approximations of LQG which are peaked on semi-classical cosmological space times. Some computations of the expectation values of the scalar constraint motivated from LQG have shown agreement with those in LQC for certain regularizations [22][23][24]. These calculations have been improved, for example by considering regularizations of the scalar constraint which do not assume classical symmetries of Friedmann-Lemaître -Robertson-Walker (FLRW) spacetime [25][26][27].…”

Curvature operator for loop quantum gravity

“…Our hope is that the curvature operator we built will allow us to construct a more analytically manageable Hamiltonian operator and will give the possibility to construct solutions in order to get more insights on the dynamical sector of LQG both in the full theory [43,44] and in simplified models [45][46][47][48]. This will be the subject of upcoming works.…”

Challenges in recovering a consistent cosmology from the effective dynamics of loop quantum gravity

“…peaked about isotropic geometry data (c, p) and Hamiltonian operatorĤ = H(ĥ,Ê). For any polynomial O in the fundamental variables, the following holds: Several studies appeared in LQG which make (sometimes implicit) use of this conjecture [10,11], concluding that the LQG quantum dynamics of semiclassical states (supported on a single lattice) resembles the µ oscheme of LQC. This scheme, however, was shown to lead to physically inconsistent results within LQC (for example, it does not admit a proper infrared regulator removal limit [14]).…”