The Finslerian quantum cosmology

Modern Physics Letters A, 2018

We consider a very general scenario of our universe where its geometry is characterized by the Finslerian structure on the underlying spacetime manifold, a generalization of the Riemannian geometry. Now considering a general energy–momentum tensor for matter sector, we derive the gravitational field equations in such spacetime. Further, to depict the cosmological dynamics in such spacetime proposing an interesting equation of state identified by a sole parameter [Formula: see text] which for isotropic limit is simply the barotropic equation of state [Formula: see text] ([Formula: see text] being the barotropic index), we solve the background dynamics. The dynamics offers several possibilities depending on this sole parameter as follows: (i) only an exponential expansion, or (ii) a finite time past singularity (big bang) with late accelerating phase, or (iii) a nonsingular universe exhibiting an accelerating scenario at late time which finally predicts a big rip type singularity. We ...

2006

We show that the Friedmann-Lemaitre-Robertson-Walker equations with scalar field and perfect fluid matter source are equivalent to a suitable non-linear Schrodinger type equation. This provides for an alternate method of obtaining exact solutions of the Einstein field equations for a homogeneous, isotropic universe.

2009

We consider a time independent Schrödinger type equation derived from the equations of motion that drives a single scalar field in a standard cosmology model for inflation in a flat space-time with a Friedman-Robertson-Walker (FRW) metric with a cosmological constant. We find that all the 1-dimensional bound state solutions of quantum mechanics lead to at least one exact solution for the dynamical equations of standard cosmology, and that these solutions resemble the most recurrent inflationary solutions found in the literature. The analogies derived from this approach may be used to realize a deeper understanding of the dynamics of the model.

International Journal of Physical Sciences, 2013

Friedmann equations play a central role in cosmology for describing the evolution of the universe. Initially, the Friedmann equations were derived by Alexander Friedmann in 1922. He derived the equations from Einstein's field equations for a universe which is spatially homogeneous and isotropic. The equations were again derived from Newtonian mechanics by Milne. However in this paper, we derive the spatially flat Friedmann equation from Wheeler-DeWitt equation. We apply the Bohm-de Broglie interpretation to the wave function of universe. In addition, we also set a condition to the wave function, where a large scale factor of the universe is needed.

2008

In "extended phase space" approach to quantum geometrodynamics numerical solutions to Schrodinger equation corresponding to various choice of gauge conditions are obtained for the simplest isotropic model. The "extended phase space" approach belongs to those appeared in the last decade in which, as a result of fixing a reference frame, the Wheeler - DeWitt static picture of the world is replaced by evolutionary quantum geometrodynamics. Some aspects of this approach were discussed at two previous PIRT meetings. We are interested in the part of the wave function depending on physical degrees of freedom. Three gauge conditions having a clear physical meaning are considered. They are the conformal time gauge, the gauge producing the appearance of Lambda-term in the Einstein equations, and the one covering the two previous cases as asymptotic limits. The interpretation and discussion of the obtained solutions is given.

2008

Abstract We present perfect fluid Friedmann–Robertson–Walker quantum cosmological models in the presence of negative cosmological constant. In this work the Schutz's variational formalism is applied for radiation, dust, cosmic string, and domain wall dominated Universes with positive, negative, and zero constant spatial curvature. In this approach the notion of time can be recovered. These give rise to Wheeler–DeWitt equations for the scale factor. We find their eigenvalues and eigenfunctions by using Spectral Method.

Gravitation and Cosmology, 2015

We discuss the issue of unitarity in particular quantum cosmological models with scalar field. The time variable is recovered, in this context, by using the Schutz's formalism for a radiative fluid. Two cases are considered: a phantom scalar field and an ordinary scalar field. For the first case, it is shown that the evolution is unitary provided a convenient factor ordering and inner product measure are chosen; the same happens for the ordinary scalar field, except for some special cases for which the Hamiltonian is not self-adjoint but admits a self-adjoint extension. In all cases, even for those cases not exhibiting unitary evolution, the formal computation of the expectation value of the scale factor indicates a non-singular bounce. The importance of the unitary evolution in quantum cosmology is briefly discussed.

In previous works, it was shown that the Lagrangians and Hamiltonians of cosmological linear scalar, vector and tensor perturbations of homogeneous and isotropic space-times with flat spatial sections containing a perfect fluid can be put in a simple form through the implementation of canonical transformations and redefinitions of the lapse function, without ever using the background classical equations of motion. In this paper, we generalize this result to general fluids, which includes entropy perturbations, and to arbitrary spacelike hypersurfaces through a new method together with the Faddeev-Jackiw procedure for the constraint reduction. A simple second order Hamiltonian involving the Mukhanov-Sasaki variable is obtained, again without ever using the background equations of motion.

Journal of High Energy …, 2003

Pramana, 2018

Considering a homogeneous and isotropic universe characterized by the Friedmann-Lemaître-Robertson-Walker (FLRW) line element, in this work, we have prescribed a general formalism for the cosmological solutions when the equation of state of the cosmic substance follows a general structure φ(p, ρ) = 0, where p, ρ are respectively the pressure and the energy density of the cosmic substance. Using the general formalism we recover some well known solutions, namely, when the cosmic substance obeys the linear equation of state, a Chaplygin type equation of state, or a nonlinear equation of state. Thus, the current work offers a new technique to solve the cosmological solutions without any prior relation between p and ρ.

Arxiv preprint gr-qc/9803025, 1998

The Wheeler-DeWitt equation is solved for some scalar-tensor theories of gravitation in the case of homogeneous and isotropic cosmological models. We present general solutions corresponding to cosmological term: (i)λ(φ) = 0 and (ii)λ(φ) = qφ.

Physical Review D, 2007

Effective equations often provide powerful tools to develop a systematic understanding of detailed properties of a quantum system. This is especially helpful in quantum cosmology where several conceptual and technical difficulties associated with the full quantum equations can be avoided in this way. Here, effective equations for Wheeler-DeWitt and loop quantizations of spatially flat, isotropic cosmological models sourced by a massive or interacting scalar are derived and studied. The resulting systems are remarkably different from that given for a free, massless scalar. This has implications for the coherence of evolving states and the realization of a bounce in loop quantum cosmology.

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.

Physical Review D, 1996

In this work we show a procedure to obtain a canonical description of standard cosmology. It is based on the fact that, within the framework of Einstein's general relativity, the dynamics of a spatially homogeneous and isotropic perfect fluid is governed by two equations for a pair of physical variables (rho,theta) (the comoving proper density of matter and the inverse

Quantum Cosmology in the Unified Field, 2023

Quantum Cosmology describes the nature of the universe from a perspective of an unobserved and largely unseen microcosm forming the basis for an experienced and observed macrocosm. It so presents a cosmogenesis, a description of the origins as an ontology for cosmological models. The building blocks of an experienced physical reality in atomic, molecular and subatomic constituents then emerge in models and paradigms of science from an observed and measured wave-particle duality which couples the microcosm of the quantum realm to its macrocosmic cooperator within a collectivized physical reality. Quantum Cosmology proposes the emergence of the quantum world manifesting in an experienced spacetime of energy interactions for a thermodynamically expanding universe to derive from a preexisting timespace forming the reason and purpose for the existence of a physical reality experienced in the world of the macrocosm. The relevant physics for the kaleidoscope and interplay of energy describing the universe modelled in the physics of a Planck-Einstein black body radiator then utilizes the emitted electromagnetic radiation spectrum to derive and apply the initial and boundary conditions for the cosmology manifesting in the experienced spacetime. Quantum Cosmology expands on the premises of Special and General Relativity for a description of spacetime in introducing the concept of Quantum Relativity (QR), emerging from the timespace to become the cornerstone for a Unified Field of Quantum Relativity (UFoQR). The Unified Field defines the parameters for the microcosmic reality experienced and observed in spacetime from the platform of the timespace in the emergence of space and time from an algorithmically defined energy matrix described in a multidimensional setting of mathematical logistical statements and principles. The birth of space in the formulation of an inflaton and the birth of time in the form of an instanton follow the self-generation of dimensions from a prior abstractly defined existence in timespace to become a multidimensional physicalized reality in the spacetime. The abstract nature of the timespace as originator for the spacetime is defined as a form of universalized consciousness and as a concept of being 'self-aware' of occupying the spacetime from a prior state of being unaware in the spacelessness and timelessness of the timespace. In particular the occupancy of spacetime volumars as the basis universalized consciousness is defined in Quantum Relativity as a spacial awareness in the form of a radius independent form of quantum spin-acceleration as the frequency over time differential df/dt defining an initializing maximized frequency permutation count. The square of frequency then forms a basis to couple maximized and minimized energy states, modelled on a multidimensional 12-dimensional cosmology described as a T-duality modular mirror duality. The nature of quantum gravitation, for example, then is described in gravitational waves using the squared frequency state (as G times density) to couple to the universalized consciousness quantization in the form of the gravitational parameter GM with mensuration units identical to the universal consciousness quantum as the magnetic charge of a Dirac monopole and as evidenced in the charge formulation of Newman-Kerr black hole s(r)ingularities (manifold singularity without thickness). The spacetime realism intersecting the timespace abstraction then becomes the multidimensional energy continuum for the wave-particle duality enabling the microcosm to self-replicate in holographic fractalization to evolve into an observable and measurable macrocosmic physical reality. This book is presented for the scientifically literate reader and researcher and can be said to follow a Newtonian tradition and to be inclusive of an holistic metaphysically overviewing cosmology.