Time in Quantum Cosmology

Time in quantum gravity is not a well-defined notion despite its central role in the very definition of dynamics. Using the formalism of quantum geometrodynamics, we briefly review the problem and illustrate it with two proposed solutions. Our main application is quantum cosmology—the application of quantum gravity to the Universe as a whole.

Bouncing with shear: implications from quantum cosmology

We consider the introduction of anisotropy in a class of bouncing models of cosmology. The presence of anisotropy often spells doom on bouncing models, since the energy density due to the anisotropic stress outweighs that of other matter components, as the universe contracts. Different suggestions have been made in the literature to resolve this pathology, classically. Here, we introduce a family of bouncing models, in which the shear density can be tuned to either allow or forbid classical bouncing scenarios. Following which, we show that quantum cosmological considerations can drastically change the above scenario. Most importantly, we find that quantum effects can enable a bounce, even when the anisotropic stress is large enough to forbid the same classically. We employ the solutions of the appropriate mini-superspace Wheeler-deWitt equation for homogeneous, but anisotropic cosmologies, with the boundary condition that the universe is initially contracting. Intriguingly, the solution to the Wheeler-deWitt equation exhibit an interesting phase transition-like behaviour, wherein, the probability to have a bouncing universe is precisely unity before the shear density reaches a critical value and then starts to decrease abruptly as the shear density increases further. We verified our findings using the tools of the Lorentzian quantum cosmology, along with the application of the Picard-Lefschetz theory. In particular, the semi-classical probability for bounce has been re-derived from the imaginary component of the on-shell effective action, evaluated at the complex saddle points. Implications and future directions have also been discussed.

Lorentzian quantum cosmology goes simplicial

We employ the methods of discrete (Lorentzian) Regge calculus for analysing Lorentzian quantum cosmology models with a special focus on discrete analogues of the no-boundary proposal for the early universe. We use a simple 4-polytope, a subdivided 4-polytope and shells of discrete 3-spheres as triangulations to model a closed universe with cosmological constant, and examine the semiclassical path integral for these different choices. We find that the shells give good agreement with continuum results for small values of the scale factor and in particular for finer discretisations of the boundary 3-sphere, while the simple and subdivided 4-polytopes can only be compared with the continuum in certain regimes, and in particular are not able to capture a transition from Euclidean geometry with small scale factor to a large Lorentzian one. Finally, we consider a closed universe filled with dust particles and discretised by shells of 3-spheres. This model can approximate the continuum case quite well. Our results embed the no-boundary proposal in a discrete setting where it is possibly more naturally defined, and prepare for its discussion within the realm of spin foams.

Classical and quantum cosmology in f(T)-gravity theory: A Noether symmetry approach

In the framework of [Formula: see text]-gravity theory, classical and quantum cosmology has been studied in this work for Friedmann Lemaitre Robertson Walker Metric (FLRW) space-time model. The Noether symmetry, a point-like symmetry of the Lagrangian, is used to the physical system and a specific functional form of [Formula: see text] is determined. A point transformation in the 2D augmented space restricts one of the variables to be cyclic so that the Lagrangian as well as the field equations are simplified so that they are solvable. Lastly, for quantum cosmology, the WD equation is constructed and a possible solution has been evaluated.

Quantization ambiguities and the robustness of effective descriptions of primordial perturbations in hybrid Loop Quantum Cosmology

We study the imprint that certain quantization ambiguities may leave in effective regimes of the hybrid loop quantum description of cosmological perturbations. More specifically, in the case of scalar perturbations we investigate how to reconstruct the Mukhanov-Sasaki field in the effective regime of Loop Quantum Cosmology, taking as starting point for the quantization a canonical formulation in terms of other perturbative gauge invariants that possess different dynamics. This formulation of the quantum theory, in terms of variables other than the Mukhanov-Sasaki ones, is crucial to arrive at a quantum Hamiltonian with a good behavior, elluding the problems with ill defined Hamiltonian operators typical of quantum field theories. In the reconstruction of the Mukhanov-Sasaki field, we ask that the effective Mukhanov-Sasaki equations adopt a similar form and display the same Hamiltonian structure as the classical ones, a property that has been widely assumed in Loop Quantum Cosmology studies over the last decade. This condition actually restricts the freedom inherent to certain quantization ambiguities. Once these ambiguities are removed, the reconstruction of the Mukhanov-Sasaki field naturally identifies a set of positive-frequency solutions to the effective equations, and hence a choice of initial conditions for the perturbations. Our analysis constitutes an important and necessary test of the robustness of standard effective descriptions in Loop Quantum Cosmology, along with their observational predictions on the primordial power spectrum, taking into account that they should be the consequence of a more fundamental quantum theory with a well-defined Hamiltonian, in the spirit of Dirac’s long-standing ideas.

Quantum cosmology with vector torsion

We extend the treatment of quantum cosmology to a manifold with torsion. We adopt a model of Einstein-Cartan-Sciama-Kibble compatible with the cosmological principle. The universe wavefunction is shown to be subject to a PT-symmetric Hamiltonian. With a vanishing energy-momentum tensor, the universe evolution in the semiclassical and classical regimes is shown to suggest a two-stage inflationary process induced by torsion.