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We present simple solutions of IKKT-type matrix models describing a quantized homogeneous and isotropic cosmology with k = − 1 , finite density of microstates and a resolved Big Bang. At late times, a linear coasting cosmology a ( t ) ∝ t is obtained, which is remarkably close to observation. The solution consists of two sheets with opposite intrinsic chiralities, which are connected in a Euclidean pre-big bang era. [ABSTRACT FROM AUTHOR]

We consider the field equations for a flat FRW cosmological model, given by Eq. (??), in an a priori generic gravity model and cast them into a, completely normalized and dimensionless, system of ODEs for the scale factor and the function , with respect to the scalar curvature . It is shown that under reasonable assumptions, namely for power-law functional form for the gravity model, one can produce simple analytical and numerical solutions describing bouncing cosmological models where in addition there are late-time accelerating. The power-law form for the gravity model is typically considered in the literature as the most concrete, reasonable, practical and viable assumption [see S. D. Odintsov and V. K. Oikonomou, Phys. Rev. D 90 (2014) 124083, arXiv:1410.8183 [gr-qc]]. However even without assuming a power-law form for the gravity model, the formulation of the field equations, that is suggested in this paper, is according to the author's viewpoint quite generic in order to analyze the resulting field equations, without any further assumptions. Possibility of extending these results is briefly discussed. [ABSTRACT FROM AUTHOR]

The Fock quantization of free fields propagating in cosmological backgrounds is in general not unambiguously defined due to the nonstationarity of the space-time. For the case of a scalar field in cosmological scenarios, it is known that the criterion of unitary implementation of the dynamics serves to remove the ambiguity in the choice of Fock representation (up to unitary equivalence). Here, applying the same type of arguments and methods previously used for the scalar field case, we discuss the issue of the uniqueness of the Fock quantization of the Dirac field in the closed FRW space-time proposed by D’Eath and Halliwell. [ABSTRACT FROM AUTHOR]

We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under the symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize the part of the dynamics governed by the Dirac equation that is unitarily implementable. The uniqueness of the Fock vacuum is attained then once a physically motivated convention for the concepts of particles and antiparticles is fixed. [ABSTRACT FROM AUTHOR]

In this paper we study the third quantized super-group field cosmology, a model in multiverse scenario, in Batalin-Vilkovisky (BV) formulation. Further, we propose the superfield/super-antifield dependent BRST symmetry transformations. Within this formulation we establish connection between the two different solutions of the quantum master equation within the BV formulation. [ABSTRACT FROM AUTHOR]

In this paper, we analyse the Wheeler–DeWitt equation in the third quantized formalism. We will demonstrate that for certain operator ordering, the early stages of the universe are dominated by quantum fluctuations, and the universe becomes classical at later stages during the cosmic expansion. This is physically expected, if the universe is formed from quantum fluctuations in the third quantized formalism. So, we will argue that this physical requirement can be used to constrain the form of the operator ordering chosen. We will explicitly demonstrate this to be the case for two different cosmological models. [ABSTRACT FROM AUTHOR]

The inflationary paradigm is an important cornerstone of the concordance cosmological model. However, standard inflation cannot fully address the transition from an early homogeneous and isotropic stage, to another one lacking such symmetries corresponding to our present universe. In previous works, a self-induced collapse of the wave function has been suggested as the missing ingredient of inflation. Most of the analysis regarding the collapse hypothesis has been solely focused on the characteristics of the spectrum associated to scalar perturbations, and within a semiclassical gravity framework. In this Letter, working in terms of a joint metric-matter quantization for inflation, we calculate, for the first time, the tensor power spectrum and the tensor-to-scalar ratio corresponding to the amplitude of primordial gravitational waves resulting from considering a generic self-induced collapse. [ABSTRACT FROM AUTHOR]

We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann–Lemaître–Robertson–Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar–Barbero connection, the expansion and shear scalars in the effective theories of the Bianchi type II and Bianchi type IX models have upper bounds, and these are in exact agreement with the bounds found in the effective theories of the Friedmann–Lemaître–Robertson–Walker and Bianchi type I models in loop quantum cosmology. We also comment on some ambiguities present in the definition of inverse triad operators and their role. [ABSTRACT FROM AUTHOR]

The state space of Loop Quantum Gravity admits a decomposition into orthogonal subspaces associated to diffeomorphism equivalence classes of spin-network graphs. In this paper I investigate the possibility of obtaining this state space from the quantization of a topological field theory with many degrees of freedom. The starting point is a 3-manifold with a network of defect-lines. A locally-flat connection on this manifold can have non-trivial holonomy around non-contractible loops. This is in fact the mathematical origin of the Aharonov-Bohm effect. I quantize this theory using standard field theoretical methods. The functional integral defining the scalar product is shown to reduce to a finite dimensional integral over moduli space. A non-trivial measure given by the Faddeev-Popov determinant is derived. I argue that the scalar product obtained coincides with the one used in Loop Quantum Gravity. I provide an explicit derivation in the case of a single defect-line, corresponding to a single loop in Loop Quantum Gravity. Moreover, I discuss the relation with spin-networks as used in the context of spin foam models. [ABSTRACT FROM AUTHOR]

In this paper, the expression of the adiabatic invariant quantity is presented in the dragged–Painlevé coordinate system. Via revisited adiabatic invariant quantity, using Bohr–Sommerfeld quantization rule and the first law of the black hole thermodynamics, we derive the spectroscopy of the black hole. The result shows that the area and entropy spectra are respectively equally spaced and independent of black hole parameters and the area spectrum of the black hole is $\Delta A=8\pi l_{P}^{2}$ , which confirms the initial proposal of Bekenstein, and there is no need to impose the small angular momentum limit in contrast to the quasinormal mode method. [ABSTRACT FROM AUTHOR]

In this paper, we discuss wild embeddings like Alexanders horned ball and relate them to fractal spaces. We build a C*-algebra corresponding to a wild embedding. We argue that a wild embedding is the result of a quantization process applied to a tame embedding. Therefore, quantum states are directly the wild embeddings. Then we give an example of a wild embedding in the four-dimensional spacetime. We discuss the consequences for cosmology. [ABSTRACT FROM AUTHOR]

We present a model of the gravitational field based on two symmetric tensors. Gravity is affected by the new field, but if Tμv = 0, the predictions of the model coincide exactly with general relativity, so all classical tests are satisfied. We find that massive particles do not follow a geodesic, while massless particles trajectories are null geodesics of an effective metric. We study the cosmological case, where we obtain an accelerated expansion of the Universe without dark energy. [ABSTRACT FROM AUTHOR]

The entropy spectrum of a spherically symmetric black hole was derived via the Bohr-Sommerfeld quantization rule in Majhi and Vagenas's work. Extending this work to charged and rotating black holes, we quantize the horizon area and the entropy of an Einstein-Maxwell-Dilaton-Axion black hole via the Bohr-Sommerfeld quantization rule and the adiabatic invariance. The result shows the area spectrum and the entropy spectrum are respectively equally spaced and independent on the parameters of the black hole. [ABSTRACT FROM AUTHOR]

In this paper, we consider the quantization of the 2D BF model coupled to topological matter. Guided by the rigid supersymmetry, this system can be viewed as a super-BF model, where the field content is expressed in terms of superfields. A canonical analysis is done and the constraints are then implemented at the quantum level in order to construct the Hilbert space of the theory under the perspective of loop quantum gravity methods. [ABSTRACT FROM AUTHOR]

In recent years, theories in which the Einstein-Hilbert Lagrangian is replaced by a function f (R) of the Ricci Scalar have been extensively studied in four-dimensional spacetime. In this paper we carry out an analysis of such theories in two-dimensional spacetime with focus on cosmological implications. Solutions to the cosmological field equations are obtained and their properties are analysed. Inflationary solutions are also obtained and discussed. Quantization is then carried out, the Wheeler-DeWitt equation is set up, and its exact solutions are obtained. [ABSTRACT FROM AUTHOR]

Abstract: Campbellʼs theorem ensures that all vacuum space–times in general relativity can be embedded in five dimensions, with the 4D scalar curvature expressed as an effective cosmological ‘constant’ Λ which depends on the extra coordinate. This Λ-landscape can be used to give insight to certain physical phenomena, such as the big bang and quantized particles. [Copyright &y& Elsevier]

Space-time quantum contributions to the classical Einstein equations of General Relativity are determined. The theoretical background is provided by the non-perturbative theory of manifestly-covariant quantum gravity and the trajectory-based representation of the related quantum wave equation in terms of the Generalized Lagrangian path formalism. To reach the target an extended functional setting is introduced, permitting the treatment of a non-stationary background metric tensor allowed to depend on both space-time coordinates and a suitably-defined invariant proper-time parameter. Based on the Hamiltonian representation of the corresponding quantum hydrodynamic equations occurring in such a context, the quantum-modified Einstein field equations are obtained. As an application, the quantum origin of the cosmological constant is investigated. This is shown to be ascribed to the non-linear Bohm quantum interaction of the gravitational field with itself in vacuum and to depend generally also on the realization of the quantum probability density for the quantum gravitational field tensor. The emerging physical picture predicts a generally non-stationary quantum cosmological constant which originates from fluctuations (i.e., gradients) of vacuum quantum gravitational energy density and is consistent with the existence of quantum massive gravitons. [ABSTRACT FROM AUTHOR]

It has been shown that black holes can be quantized by using Bohr's idea of quantizing the motion of an electron inside the atom. We apply these ideas to the universe as a whole. This approach reinforces the suggestion that it may be a way to unify gravity with quantum theory. [ABSTRACT FROM AUTHOR]

We exhibit a relation between the SU(2) invariant matrix model arising from the quantization of the 11-dimensional supermembrane in the light cone gauge and supersymmetric quantum cosmology. We use a Dirac-like gamma matrix representation for the fermionic degrees of freedom and find explicit solutions to reduced lower dimensional SU(2) matrix models for the zero energy states. One of the solutions we encounter in the matrix model resembles exactly a wave function found independently in the context of SUSY quantum cosmology; this allows us to give these regularized models a physical meaning and shows a direct relation between the SU(2) matrix model and SUSY quantum cosmology. [ABSTRACT FROM AUTHOR]

It is shown that like the Bianchi I, V and IX models, a Kantowski–Sachs cosmological model also allows unitary evolution on quantization. It has also been shown that this unitarity is not at the expense of anisotropy. Non-unitarity, if there is any, cannot escape notice here, as the evolution is studied against a properly oriented time parameter fixed by the evolution of the fluid. Furthermore, we have constructed a wave packet by superposing different energy eigenstates, thereby establishing unitarity in a non-trivial way, which is a stronger result than an energy eigenstate trivially giving a time independent probability density. For , we have proved that the Hamiltonian admits a self-adjoint extension under a reasonable assumption, using a standard theorem. This consolidates the fact that the problem of non-unitarity cannot be a generic problem of anisotropy. [ABSTRACT FROM AUTHOR]

We construct a new vacuum and representation for loop quantum gravity. Because the new vacuum is based on BF theory, it is physical for (2+1)-dimensional gravity, and much closer to the spirit of spin foam quantization in general. To construct this new vacuum and the associated representation of quantum observables, we introduce a modified holonomy–flux algebra that is cylindrically consistent with respect to the notion of refinement by time evolution suggested in Dittrich and Steinhaus (2013 arXiv:1311.7565). This supports the proposal for a construction of the physical vacuum made in Dittrich and Steinhaus (2013 arXiv:1311.7565) and Dittrich (2012 New J. Phys.14 123004), and for (3+1)-dimensional gravity. We expect that the vacuum introduced here will facilitate the extraction of large scale physics and cosmological predictions from loop quantum gravity. [ABSTRACT FROM AUTHOR]