Emergent de Sitter epoch of the loop quantum cosmos: A detailed analysis

Abstract

We present a detailed analysis of a quantum model for Loop Quantum Cosmology based on strict application of the Thiemann regularization algorithm for the Hamiltonian in Loop Quantum Gravity, extending the results presented previously in our brief report. This construction leads to a qualitative modification of the bounce paradigm. Quantum gravity effects still lead to a quantum bounce connecting deterministically large classical Universes. However, the evolution features a large epoch of de Sitter Universe, with emergent cosmological constant of Planckian order, smoothly transiting into a spatially flat expanding Universe. Moreover, we present an effective Hamiltonian describing the quantum evolution to high accuracy and for which the dynamics can be solved analytically. *

Effective dynamics from coherent state path integral of full loop quantum gravity

“…Among many important achievements of LQG, one of the most profound physical predictions is the resolution of singularities by quantum effects e.g. [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. It is well-known that the classical theory of Einstein gravity breaks down at singularities, while the purpose of quantum gravity is to extend the gravity theory to describe the physics of singularities.…”

“…It is known that in LQC, the µ 0 -scheme suffers the problem that the bounce may happen at low critical density (or large critical volume), and the better scheme is theμ-scheme where the critical density is Plankian (see e.g. [5,8]). In Section 9, we comment on the problem of µ 0 -scheme from the full LQG point of view, and suggest that if we take into account of the continuum limit of the lattice γ, the critical density should be always high in our framework.…”

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

“…If, instead of gauge-covariant fluxes, one uses triads one obtains the expression of the Hamiltonian constraint for the Thiemann regularization studied earlier [41][42][43]:…”

“…In addition, different choices of regularized versions of constraints can result in strikingly different physical evolution even for the same choice of regulator . An example is the case of symmetric versus asymmetric bounce originating in standard [31] versus Thiemann-regularized scalar constraint in LQC [22,[41][42][43]. Recall that the standard form of the Hamiltonian constraint arises using classical symmetries of the FLRW spatially-flat spacetime by combining Euclidean and Lorentzian terms in the constraint, whereas in the Thiemann-regularization these terms are quantized independently.…”

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

“…For certain models admitting massless scalar field (including the flat FLRW universe with non-negative cosmological constant or negative curvature), the semiclassicality property defined above may not be preserved by the dynamics (see for example [38,39], also the discussion in [29,40]). In these cases the Dirac observables corresponding to p(t) may be ill defined on the physical Hilbert space, thus alternative observables encoding the same information need to be used [29,40]. Other choices of matter fields for an internal clock (like dust [26] or radiation [27]) are free from this deficiency.…”