Symmetry reduction of loop quantum gravity

We investigate the dynamics of single and multiple scalar fields with exponential potentials, leading to power-law and assisted inflation, in loop quantum cosmology. Unlike in the classical theory, dynamical trajectories in loop quantum cosmology are generically nonsingular, with a big bounce replacing classical big bang in the Planck regime. Post bounce, after a phase of super-inflation, dynamical trajectories evolve towards the classical attractor in the inflationary scenarios. Depending on the initial conditions, bounce is shown to occur in kinetic as well as potential dominated regimes. We analyze the number of e-foldings resulting from the phase of super-inflation, and find the dependence of the maximum possible number of e-foldings on the equation of state at the bounce and on the steepness of the potential.We find that if the potential is not steep, this phase can lead to large number of e-foldings in power-law inflation. For the assisted inflation scenario, an increase in the number of fields can yield a significant increase in the number of e-foldings during super-inflation.

Section: Discussionmentioning

confidence: 99%

Nonsingular power-law and assisted inflation in loop quantum cosmology

Ranken

Singh

2012

“…(Some progress on the latter question has recently been made [37,38,39], but so far without indications on the minisuperspace question.) The kinematical side of a possible reduction of loop quantum cosmology from loop quantum gravity is still being analyzed [40,41,42,43,44,45,46,47], and possible dynamical relations between minisuperspace models and the full theory are tentative. A recent idea uses condensate states in order to describe homogeneous space-times, either as an approximation [48] or as a reduction from a full theory defined by group-field theories [49,50,51,52,53,54,55].…”

Section: Minisuperspace Truncation Vs Approximationmentioning

confidence: 99%

Minisuperspace models as infrared contributions

Bojowald

Brahma

2016

A direct correspondence of quantum mechanics as a minisuperspace model for a self-interacting scalar quantum-field theory is established by computing, in several models, the infrared contributions to 1-loop effective potentials of Coleman-Weinberg type. A minisuperspace approximation rather than truncation is thereby obtained. By this approximation, the spatial averaging scale of minisuperspace models is identified with an infrared scale (but not a regulator or cut-off) delimiting the modes included in the minisuperspace model. Some versions of the models studied here have discrete space or modifications of the Hamiltonian expected from proposals of loop quantum gravity. They shed light on the question of how minisuperspace models of quantum cosmology can capture features of full quantum gravity. While it is shown that modifications of the Hamiltonian can well be described by minisuperspace truncations, some related phenomena such as signature change, confirmed and clarified here for modified scalar field theories, require at least a perturbative treatment of inhomogeneity beyond a strict minisuperspace model. The new methods suggest a systematic extension of minisuperspace models by a canonical effective formulation of perturbative inhomogeneity.

“…Within loop quantum gravity (LQG), there has been a lot of recent interest in this subject, see e.g. [1][2][3][4][5][6][7][8][9]. Different strategies can be employed towards this goal, the most active one being the identification of suitable symmetry reduced states directly within the full, not classically gauge fixed, quantum theory.…”

Section: Introductionmentioning

confidence: 99%

Quantum reduction to Bianchi I models in loop quantum gravity

Bodendorfer

2015

We propose a quantum symmetry reduction of loop quantum gravity to Bianchi I spacetimes. To this end, we choose the diagonal metric gauge for the spatial diffeomorphism constraint at the classical level, leading to an R Bohr gauge theory, and quantise the resulting theory via loop quantum gravity methods. Constraints which lead classically to a suitable reduction are imposed at the quantum level. The dynamics of the resulting model turn out to be very simple and manifestly coincide with those of a polymer quantisation of a Bianchi I model for the simplest choice of full theory quantum states compatible with the Bianchi I reduction. In particular, the "improved" µ dynamics of loop quantum cosmology can be obtained by modifying the regularisation of the Hamiltonian constraint with similar ideas, in turn yielding insights into the full theory dynamics.