Quantum Cosmology from Three Different Perspectives

1999

A crucial problem in quantum cosmology is a careful analysis of the one-loop semiclassical approximation for the wave function of the universe, after an appropriate choice of mixed boundary conditions. The results for Euclidean quantum gravity in four dimensions are here presented, when linear covariant gauges are implemented by means of the Faddeev-Popov formalism. On using ζ-function regularization and a mode-by-mode analysis, one finds a result for the one-loop divergence which agrees with the Schwinger-DeWitt method only after taking into account the non-trivial effect of gauge and ghost modes. For the gravitational field, however, the geometric form of heat-kernel asymptotics with boundary conditions involving tangential derivatives of metric perturbations is still unknown. Moreover, boundary effects are found to be responsible for the lack of one-loop finiteness of simple supergravity, when only one bounding three-surface occurs. This work raises deep interpretative issues about the admissible backgrounds and about quantization techniques in quantum cosmology.

2010

Quantum cosmology from the late sixties into the early XXI st century is reviewed and appraised in the form of a debate, set up by two presentations on mainly the Wheeler-DeWitt quantization and on loop quantum cosmology, respectively. (Open) questions, encouragement and guiding lines shared with the audience are provided here.

Cosmology is the branch of astrophysics concerned with the large-scale structure of the cosmos and (in the current interpretation) the origin of the universe. Yet the scientific method employed in other branches of physics consists in equating the origins of the constituents of the physical world-the particles and fields that appear in it-to the ends of other elements: science seeks to explain the world from a principle of conservation. It thus appears incongruous that an explanation of the large-scale structure of the universe should require the addition of another "origin", that of the universe as a whole. If the universe had a beginning, then matter and motion, space and time, had to be created. This point of view is obviously incompatible with a principle of conservation. A model that is consistent with the conservation principle, and therefore requires no cosmic beginning, can be investigated by examining the current conception of the large-scale structure of space and time in the light of physical theory. Analysis reveals that the conservation-violating universe model contradicts other theoretical principles which have received confirmation from empirical measurement. An alternative model is proposed to circumvent these difficulties, and an extension of general relativity theory is posited. ================================================================== Cosmology in the twentieth century has been dominated by two major advances: one observational, the other theoretical. The former-the discovery that the spectral lines of light emitted by external galaxies were shifted toward the red in proportion to distance-constitutes the primary empirical foundation for a cosmological model. How this correspondence between redshift and distance is interpreted in the light of theory determines the model. Astronomers presently acknowledge that a universe model must be predicated upon the analytical framework established by the second scientific advance-the general theory of relativity. But unlike the present model for cosmology, relativity unambiguously retains a conservation theorem for momentum and energy. If the accepted universe model is found to exhibit further inconsistencies with relativity, then it is necessary to abandon this model in favour of one that concurs rigorously with theoretical principles.

Physics of the Dark Universe, 2017

We endorse the context that the cosmological constant problem is a quantum cosmology issue. Therefore, in this paper we investigate the q-deformed Wheeler-DeWitt equation of a spatially closed homogeneous and isotropic Universe in the presence of a conformally coupled scalar field. Specifically, the quantum deformed Universe is a quantized minisuperspace model constructed from quantum Heisenberg-Weyl U q (h 4) and U q (su(1, 1)) groups. These intrinsic mathematical features allow to establish that (i) the scale factor, the scalar field and corresponding momenta are quantized and (ii) the phase space has a non-equidistance lattice structure. On the other hand, such quantum group structure provides us a new framework to discuss the cosmological constant problem. Subsequently, we show that a ultraviolet cutoff can be obtained at 10 −3 eV , i.e., at a scale much larger than the expected Planck scale. In addition, an infrared cutoff, at the size of the observed Universe, emerges from within such quantum deformation of Universe. In other words, the spectrum of the scale factor is upper bounded. Moreover, we show that the emerged cosmological horizon is a quantum sphere S 2 q or, alternatively, a fuzzy sphere S 2 F which explicitly exhibits features of the holographic principle. The corresponding number of fundamental cells equals the dimension of the Hilbert space and hence, the cosmological constant can be presented as a consequence of the quantum deformation of the FLRW minisuperspace.

arXiv (Cornell University), 2004

We study a classical model of gravitation in which a self interacting scalar field is coupled to gravity with the metric undergoing a continuous signature transition. We show that by appropriate duality transformations on the parameters of the scalar field potential one obtains dual signature changing classical solutions for the Einstein field equations. These dual classical solutions correspond to the same quantum cosmology. This suggests that, if the solutions of the Wheeler-DeWitt equation are assumed to be more primitive than the classical solutions, we may arrange for a reasonable jump of dual classical solutions passing through the signature changing hypersurface, provided we introduce a distribution of such dual potentials over Euclidean and Lorentzian regions. This may serve as an alternative scenario for the quantum creation of the Lorentzian universe in which the quantum jumps of dual signature changing classical solutions may play the role of a finite inflation, accompanied by phase transitions, in the early universe. A solution for the cosmological constant problem is proposed based on the self-duality of quantum cosmology.

2014

The development of a quantum theory of gravity has been ongoing in the theoretical physics community for about 80 years, yet it remains unsolved. In this dissertation, we review the loop quantum gravity approach and its application to cosmology, better known as loop quantum cosmology. In particular, we present the background formalism of the full theory together with its main result, namely the discreteness of space on the Planck scale. For its application to cosmology, we focus on the homogeneous isotropic universe with free massless scalar field. We present the kinematical structure and the features it shares with the full theory. Also, we review the way in which classical Big Bang singularity is avoided in this model. Specifically, the spectrum of the operator corresponding to the classical inverse scale factor is bounded from above, the quantum evolution is governed by a difference rather than a differential equation and the Big Bang is replaced by a Big Bounce.

We argue that the Lorentzian path integral is a better starting point for quantum cosmology than the Euclidean version. In particular, we revisit the mini-superspace calculation of the Feynman path integral for quantum gravity with a positive cosmological constant. Instead of rotating to Euclidean time, we deform the contour of integration over metrics into the complex plane, exploiting Picard-Lefschetz theory to transform the path integral from a conditionally convergent integral into an absolutely convergent one. We show that this procedure unambiguously determines which semiclassical saddle point solutions are relevant to the quantum mechanical amplitude. Imposing "no-boundary" initial conditions, i.e., restricting attention to regular, complex metrics with no initial boundary, we find that the dominant saddle contributes a semiclassical exponential factor which is precisely the inverse of the famous Hartle-Hawking result. * Electronic address: [email protected] † Electronic address: [email protected] ‡ Electronic address: [email protected]

Advances in Astronomy, 2009

The cosmological constant problem is principally concerned with trying to understand how the zero-point energy of quantum fields contributes to gravity. Here we take the approach that by addressing a fundamental unresolved issue in quantum theory, we can gain a better understanding of the problem. Our starting point is the observation that the notion of classical time is external to quantum mechanics. Hence there must exist an equivalent reformulation of quantum mechanics which does not refer to an external classical time. Such a reformulation is a limiting case of a more general quantum theory which becomes nonlinear on the Planck mass/energy scale. The nonlinearity gives rise to a quantum-classical duality which maps a “strongly quantum, weakly gravitational” dynamics to a “weakly quantum, strongly gravitational” dynamics. This duality predicts the existence of a tiny nonzero cosmological constant of the order of the square of the Hubble constant, which could be a possible source ...

2008

Despite its great successes in accounting for the current observations, the so called `standard' model of cosmology faces a number of fundamental unresolved questions. Paramount among these are those relating to the nature of the origin of the universe and its early evolution. Regarding the question of origin, the main difficulty has been the fact that within the classical general relativistic framework, the `origin' is almost always a singular event at which the laws of physics break down, thus making it impossible for such an event, or epochs prior to it, to be studied. Recent studies have shown that Loop Quantum Cosmology may provide a non-singular framework where these questions can be addressed. The crucial role here is played by quantum effects, i.e.\ corrections to the classical equations of motion, which are incorporated in effective equations employed to develop cosmological scenarios. In this chapter we shall consider the three main types of quantum effects expected to be present within such a framework and discuss some of their consequences for the effective equations. In particular we discuss how such corrections can allow the construction of non-singular emergent scenarios for the origin of the universe, which are past-eternal, oscillating and naturally emerge into an inflationary phase. These scenarios provide a physically plausible picture for the origin and early phases of the universe, which is in principle testable. We pay special attention to the interplay between these different types of correction terms. Given the absence, so far, of a complete derivation of such corrections in general settings, it is important to bear in mind the questions of consistency and robustness of scenarios based on partial inclusion of such effects.

Classical and Quantum Gravity, 2011

Loop quantum cosmology (LQC) is the result of applying principles of loop quantum gravity (LQG) to cosmological settings. The distinguishing feature of LQC is the prominent role played by the quantum geometry effects of LQG. In particular, quantum geometry creates a brand new repulsive force which is totally negligible at low space-time curvature but rises very rapidly in the Planck regime, overwhelming the classical gravitational attraction. In cosmological models, while Einstein's equations hold to an excellent degree of approximation at low curvature, they undergo major modifications in the Planck regime: For matter satisfying the usual energy conditions any time a curvature invariant grows to the Planck scale, quantum geometry effects dilute it, thereby resolving singularities of general relativity. Quantum geometry corrections become more sophisticated as the models become richer. In particular, in anisotropic models there are significant changes in the dynamics of shear potentials which tame their singular behavior in striking contrast to older results on anisotropies in bouncing models. Once singularities are resolved, the conceptual paradigm of cosmology changes and one has to revisit many of the standard issues-e.g., the 'horizon problem'-from a new perspective. Such conceptual issues as well as potential observational consequences of the new Planck scale physics are being explored, especially within the inflationary paradigm. These considerations have given rise to a burst of activity in LQC in recent years, with contributions from quantum gravity experts, mathematical physicists and cosmologists. The goal of this article is to provide an overview of the current state of the art in LQC for three sets of audiences: young researchers interested in entering this area; the quantum gravity community in general; and, cosmologists who wish to apply LQC to probe modifications in the standard paradigm of the early universe. An effort has been made to streamline the material so that each of these communities can read only the sections they are most interested in, without a loss of continuity.