Deriving loop quantum cosmology dynamics from diffeomorphism invariance

Abstract

We use the requirement of diffeomorphism invariance in the Bianchi I context to derive the form of the quantum Hamiltonian constraint. After imposing the correct classical behavior and making a certain minimality assumption, together with a certain restriction to "planar loops", we then obtain a unique expression for the quantum Hamiltonian operator for Bianchi I to both leading and subleading orders in . Specifically, this expression is found to exactly match the form proposed by Ashtekar and Wilson-Ewing in the loop quantum cosmology (LQC) literature. Furthermore, by using the projection map from the quantum states of the Bianchi I model to the states of the isotropic model, we constrain the dynamics also in the homogeneous isotropic case, and obtain, again to both leading and subleading order in , a quantum constraint which exactly matches the standard 'improved dynamics' of Ashtekar, Pawlowski and Singh. This result in the isotropic case does not require a restriction to planar loops, but only the minimality assumption. Our results strengthen confidence in LQC dynamics and its observational predictions as consequences of more basic fundamental principles. Of the assumptions made in the isotropic case, the only one not rigidly determined by physical principle is the minimality principle; our work also shows the exact freedom allowed when this assumption is relaxed.

New loop quantum cosmology modifications from gauge-covariant fluxes

“…As a result, the way Planck scale physics in LQC changes as we bring it closer to methods of LQG is an important question to be answered to understand robustness and reliability of phenomenological predictions. One way to answer these questions would be to explore the cosmological sector of LQG which has recently attracted a lot of activity [19][20][21][22][23][24][25][26]. A preliminary insight from these investigations is that the physics, at least of singularity resolution, should change from standard LQC [22][23][24][25][26].…”

“…Indeed, the properties of a system with gauge covariant fluxes will be vastly different than before and uncover many unexpected features as we will discuss below. Moreover, when restricting the µ 0 scheme to a compact torus, the dependence of the coordinate volume accounts merely to a diffeomorphism dependency [21]. Therefore to understand restrictions on any regularization one needs to carefully study diffeomorphism invariant observables.…”

“…In the last decade, while LQC has served well as a testbed to extract physics from LQG, the question of whether LQC is the cosmological sector of LQG (or any of its incarnations) has not yet been answered [17][18][19][20][21]. 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 physical implications of regularization ambiguities in SU(2) gauge-invariant loop quantum cosmology

“…standard [30,31,47] versus Thiemann regularization [41,43] and (iii) LQC based on holonomies and triads [31,47], or based on holonomies and gauge-covariant fluxes [50,51]. The first ambiguity has been well explored in standard LQC using conventional quantization based on holonomies and triads [32,53], but no such investigation has been carried out using gauge-covariant fluxes. Given that gauge-covariant fluxes radically change the nature of gravitational and matter parts of constraints, it is pertinent to explore the fate of µ 0 andμ-schemes when modifications due to gauge-covariant fluxes non-trivially affect the Hamiltonian constraint.…”

Gauge-invariant bounce from loop quantum gravity

“…While this success is extraordinary, so far little is known about relating LQG and LQC, and the derivation of the cosmological sector of LQG is an open issue [9]. Further, some of the field theoretical aspects of LQG are not yet fully incorporated in LQC.…”