Quantized Cosmology

2004

I discuss the problem of inflation in the context of Friedmann-Robertson-Walker Cosmology and show how, after a simple change of variables, to quantize the problem in a way which parallels the classical discussion. The result is that two of the Einstein equations arise as exact equations of motion and one of the usual Einstein equations (suitably quantized) survives as a constraint equation to be imposed on the space of physical states. However, the Friedmann equation, which is also a constraint equation and which is the basis of the Wheeler-deWitt equation, acquires a welcome quantum correction that becomes significant for small scale factors. To clarify how things work in this formalism I briefly outline the way in which our formalism works for the exactly solvable case of de-Sitter space.

2004

I discuss the problem of inflation in the context of Friedmann-Robertson-Walker Cosmology and show how, after a simple change of variables, to quantize the problem in a way which parallels the classical discussion. The result is that two of the Einstein equations arise as exact equations of motion and one of the usual Einstein equations (suitably quantized) survives as a constraint equation to be imposed on the space of physical states. However, the Friedmann equation, which is also a constraint equation and which is the basis of the Wheeler-deWitt equation, acquires a welcome quantum correction that becomes significant for small scale factors. To clarify how things work in this formalism I briefly outline the way in which our formalism works for the exactly solvable case of de-Sitter space.

2004

This paper discusses the problem of inflation in the context of Friedmann-Robertson-Walker Cosmology. We show how, after a simple change of variables, to quantize the problem in a way which parallels the classical discussion. The result is that two of the Einstein equations arise as exact equations of motion and one of the usual Einstein equations (suitably quantized) survives as a constraint equation to be imposed on the space of physical states. However, the Friedmann equation, which is also a constraint equation and which is the basis of the Wheeler-deWitt equation, acquires a welcome quantum correction that becomes significant for small scale factors. We discuss the extension of this result to a full quantum mechanical derivation of the anisotropy (δρ/ρ) in the cosmic microwave background radiation, and the possibility that the extra term in the Friedmann equation could have observable consequences. To clarify the general formalism and explicitly show why we choose to weaken the statement of the Wheeler-deWitt equation, we apply the general formalism to de Sitter space. After exactly solving the relevant Heisenberg equations of motion we give a detailed discussion of the subtleties associated with defining physical states and the emergence of the classical theory. This computation provides the striking result that quantum corrections to this long wavelength limit of gravity eliminate the problem of the big crunch. We also show that the same corrections lead to possibly measurable effects on the CMB radiation. For the sake of completeness, we discuss the special case, Λ = 0, and its relation to Minkowski space. Finally, we suggest interesting ways in which these techniques can be generalized to cast light on the question of chaotic or eternal inflation. In particular, we suggest one can put an experimental lower bound on the distance to a universe with a scale factor very different from our own, by looking at its effects on our CMB radiation.

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.

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.

Gravitation and Cosmology, 2015

We propose a model of cosmological evolution of the early and late Universe which is consistent with observational data and naturally explains the origin of inflation and dark energy (DE). We show that the de Sitter accelerated expansion of the FLRW space with no matter fields (hereinafter "empty space") is its natural state, and the model does not require either a scalar field or cosmological constant or any other hypotheses. Mathematically, this is due to the fact that the de Sitter state is an exact solution of the rigorous, mathematically consistent equations of one-loop quantum gravity for the empty FLRW space that are finite off the mass shell. Physically, this is due to the fact that the natural quantum metric fluctuations have the backreaction effect on the FLRW background, forming a self-polarized de Sitter graviton-ghost condensate which describes the condensation of gravitons on the horizon scale of the nonstationary Universe leading to its exponential expansion. The energy required to maintain the accelerated expansion is drawn from the graviton vacuum. At the start and the end of cosmological evolution, the Universe is assumed to be empty, which means that de Sitter expansion is a natural state of the Universe at the start and end of its cosmological evolution. The emptiness of the Universe at the start of its cosmological evolution automatically generates inflation. With an increase in the energy density of a new-born matter during inflation, the expansion begins to deviate from the de Sitter law, and eventually stops when the energy density of new-born matter reaches the first threshold which is the energy density of instantons. After that, the standard Big Bang cosmology begins. With a decrease in the energy density of matter by the end of the cosmological evolution of the Universe, the expansion first passes through the second threshold which again is the energy density of instantons. Here the quasi-de Sitter expansion (i.e. DE) is born, and then as the Universe empties, approaches the de Sitter law and asymptotically becomes such when the Universe becomes completely empty. This is observed as the DE effect. This scenario seems consistent with observational data. Existence of the first threshold explains the reason why the inflation is stopped. Existence of the second threshold explains why the DE acceleration is happening during the contemporary epoch of matter domination (coincidence problem). The Universe starts and ends with de Sitter expansion but the evolutionary process runs in these cases in opposite directions. It leads to the prediction that the signs of the parameter 1 w + should be opposite in both cases, and this fact is consistent with observations. The fluctuations of the number of gravitons lead to fluctuations of their energy density which in turn leads to the observed CMB temperature anisotropy of the order of 5 10 −  and CMB polarization. In the frame of this scenario, it is not a hypothetical scalar field that generates inflation and relic gravitational waves but on the contrary, the gravitational waves (gravitons) generate DE, inflation, CMB anisotropy and polarization.

Physical Review D, 2012

We quantize to completion an inflationary universe with small inhomogeneities in the framework of loop quantum cosmology. The homogeneous setting consists of a massive scalar field propagating in a closed, homogeneous scenario. We provide a complete quantum description of the system employing loop quantization techniques. After introducing small inhomogeneities as scalar perturbations, we identify the true physical degrees of freedom by means of a partial gauge fixing, removing all the local degrees of freedom except the matter perturbations. We finally combine a Fock description for the inhomogeneities with the polymeric quantization of the homogeneous background, providing the quantum Hamiltonian constraint of the composed system. Its solutions are then completely characterized, owing to the suitable choice of quantum constraint, and the physical Hilbert space is constructed. Finally, we consider the analog description for an alternate gauge and, moreover, in terms of gauge-invariant quantities. In the deparametrized model, all these descriptions are unitarily equivalent at the quantum level.

International Journal of Theoretical Physics, 2013

In the present work, we study the quantum cosmology description of two Friedmann-Robertson-Walker models in the presence of a stiff matter perfect fluid and a negative cosmological constant. The models differ from each other by the constant curvature of the spatial sections, taken to be either positive or zero. We work in the Schutz's variational formalism, quantizing the models and obtaining the appropriate Wheeler-DeWitt equations. In these models there are bound states. Therefore, we compute, for each one, the discrete energy spectrum and the corresponding eigenfunctions. After that, we use the eigenfunctions in order to construct wave packets and evaluate the time-dependent expectation values of the scale factors. Each model shows bounded oscillations for the expectation value of the scalar factor, which is never zero, which can be interpreted as an initial indication that these models may not have singularities at the quantum level.