New loop quantum cosmology modifications from gauge-covariant fluxes

Abstract

Loop quantum cosmology is a symmetry reduced quantization of cosmological spacetimes based on loop quantum gravity. While it has been succsessful in resolution of various cosmological singularities and connecting Planck scale physics to phenomenology, its connection with loop quantum gravity has remained elusive. It is therefore important to integrate more and more features of the full theory into this framework and understand the reliability of physical predictions. In particular, if one wishes to connect the effective Hamiltonian in loop quantum cosmology to an expectation value of the scalar constraint operator in suitable coherent states for the full theory, one has to go beyond the standard setting of loop quantum cosmology. One possibility is to introduce gauge-covariant fluxes, which become necessary because the presence of a finite regularization parameter causes functions build out of the standard discretized variables to be in general not gauge invariant. Following the construction of gauge-covariant fluxes pioneered by Thiemann in [1], we show that the physics of loop quantum cosmology is affected in a non-trivial way. The bounce turns out to be generically asymmetric with a rescaling of the Newton's constant in the pre-bounce branch. Gauge-covariant fluxes result in a higher order quantum difference equation in comparison to loop quantum cosmology. Even the behavior of matter, which behaves innocuously in loop quantum cosmology, is enriched resulting in an effective non-minimal coupling. These effects are shown to be common to different choices of regularization parameters.

Some physical implications of regularization ambiguities in SU(2) gauge-invariant loop quantum cosmology

“…We also mention that upon solving the constraint for the energy density, we obtain an expression that is not invariant under residual diffeomorphisms. This effect is analogous to the one discussed in [51].…”

“…In this section, we review the construction of gauge-covariant fluxes and its application to isotropic, spatially-flat cosmology. Our notation will follow [51], which the reader can refer for details.…”

“…Computing the holonomies and gauge-covariant fluxes for a lattice Γ with lattice spacing in coordinate distance, we find for a suitable choice of paths ρ x (see [51] for further details):…”

The Effect of a Positive Cosmological Constant on the Bounce of Loop Quantum Cosmology

“…As a consequence, the two branches of the Universe (pre and post-bounce) tend, in general, to different classical trajectories. Even though this is the first time that an asymmetric bounce has resulted from this quantization procedure, we note that other prescriptions within the context of LQC have been found to generate an asymmetry between the pre and post-bounce epochs [30][31][32][33].…”

Gauge-invariant bounce from loop quantum gravity

“…The coherent state Ψ = ⊗ e ψ e in H Γ := ⊗ e H e can now be peaked for each edge e on the holonomies h e , and for either version of the fluxes: E(S e ) or P (e) := P (e(0), S e ). If e is oriented along direction I, one finds [12] E(S e ) = p ǫ 2 τ I ,…”