Some exact results on quantum Newtonian cosmology (original) (raw)
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Quantum Newtonian cosmology revisited
2021
We formulate the Lagrangian of the Newtonian cosmology where the cosmological constant is also introduced. Following the affine quantization procedure, the Hamiltonian operator is derived. The wave functions of the Newtonian universe and the corresponding eigenvalues for the case of matter dominated by a negative cosmological constant are given.
Quantum Newtonian cosmology and the biconfluent Heun functions
Journal of Mathematical Physics, 2015
Using the Lagrangian formulation of the Newtonian cosmology we write the Hamiltonian operator of the Schrödinger equation for a particle (galaxy) moving in a universe constituted of incoherent matter, that is, in a cosmological substratum which is comprised of dust. In the phase space defined by the fixed rectangular coordinate (comoving), the exact solution for wave function of the Newtonian Universe is obtained in terms of the biconfluent Heun functions. We obtain the first few Heun polynimials of the biconfluent case. In this scenario, the cosmological constant is taken into account and the role of their presence in this solution is emphasized as well as an exact expression for the energy levels is obtained.
Some exact results on quantum relativistic cosmology: dynamical interpretation and tunneling phase
arXiv: General Relativity and Quantum Cosmology, 2019
In this work the wave functions associated to the quantum relativistic universe, which is described by the Wheeler-DeWitt equation, are obtained. Taking into account all forms of energy density, namely, matter, radiation, vacuum, dark energy, and quintessence, we discuss some aspects of the quantum dynamics. In all these cases, the wave functions of the quantum relativistic universe are given in terms of the triconfluent Heun functions. We investigate the expansion of the universe using these solutions and found that the asymptotic behavior for the scale factor is a(t)simmboxeta(t) \sim \mbox{e}^{t}a(t)simmboxet for whatever the form of energy density is. On the other hand, we analyze the behavior at early stages of the universe and found that a(t)simt1/2a(t) \sim t^{1/2}a(t)simt1/2. We also calculate and analyze the transmission coefficient through the effective potential barrier.
The Cosmological Constant: 2nd Order Quantum-Mechanical Correction to the Newton Gravity
OALib
The work shows that the associated Einstein-like gravity for the Klein-Gordon field shows the spontaneous emergence of the "cosmological" pressure tensor density (CPTD) that in the classical limit leads to the cosmological constant (CC). Even if the classical cosmological constant is set to zero, the model shows, that exists a residual theory-derived quantum CPTD. The work shows that the cosmological constant can be considered as a second order quantum-mechanical correction to the Newtonian gravity. The outputs of the theory show that the expectation value of the CPTD is independent by the zero-point vacuum energy density and that it takes contribution only from the space where the mass is localized (and the space-time is curvilinear) while tending to zero as the space-time approaches to the flat vacuum. A developed model of scalar matter universe shows an overall cosmological effect of the CPTD on the motion of the galaxies that agrees with the astronomical observations.
Quantum relativistic cosmology: Dynamical interpretation and tunneling universe
International Journal of Modern Physics D, 2020
In this work, the wave functions associated to the quantum relativistic universe, which is described by the Wheeler–DeWitt equation, are obtained. Taking into account different kinds of energy density, namely, matter, radiation, vacuum, dark energy and quintessence, we discuss some aspects of the quantum dynamics. In all these cases, the wave functions of the quantum relativistic universe are given in terms of the triconfluent Heun functions. We investigate the expansion of the universe using these solutions and found that the asymptotic behavior for the scale factor is [Formula: see text] for whatever the form of energy density is. On the other hand, we analyze the behavior at early stages of the universe and found that [Formula: see text]. We also calculate and analyze the transmission coefficient through the effective potential barrier.
Quantum Cosmology from Three Different Perspectives
The Eleventh Marcel Grossmann Meeting, 2008
Our review is devoted to three promising research lines in quantum cosmology and the physics of the early universe. The nonperturbative renormalization programme is making encouraging progress that we here assess from the point of view of cosmological applications: Lagrangian and Hamiltonian form of pure gravity with variable G and Λ; power-law inflation for pure gravity; an accelerating universe without dark energy. In perturbative quantum cosmology, on the other hand, diffeomorphism-invariant boundary conditions lead naturally to a singularity-free one-loop wave function of the Universe. Last, but not least, in the braneworld picture one discovers the novel concept of cosmological wave function of the bulk space-time. Its impact on quantum cosmology and singularity avoidance is still, to a large extent, unexplored.
Newtonian cosmology with a quantum bounce
The European Physical Journal C, 2016
It has been known for some time that the cosmological Friedmann equation deduced from General Relativity can be also obtained within the Newtonian framework under certain assumptions. We use this result together with quantum corrections to the Newtonian potentials to derive a set a of quantum corrected Friedmann equations. We examine the behavior of the solutions of these modified cosmological equations paying special attention to the sign of the quantum corrections. We find different quantum effects crucially depending on this sign. One such a solution displays a qualitative resemblance to other quantum models like Loop Quantum Gravity or non-commutative geometry.
In this work, we demonstrate that the recently introduced linear form of the Friedmann equations corresponds to the first-order WKB expansion of a quantum cosmological equation, indicating that both General Relativity (GR) contains aspects of Quantum Mechanics (QM) and that GR itself is part of a more general theory. Solutions of this quantum Friedmann equation are built in terms of a quantum scale factor that encapsulates the quantum effects on a free-falling particle. The quantummodified scale factor reshapes the dynamics of the universe, removing the singularity due to the vanishing of the scale factor. A detailed example within the radiation-dominated context illustrates how these quantum solutions connect to Seiberg-Witten theory, recently applied to black holes, and incorporate resurgence phenomena and complex metrics as developed by Kontsevich, Segal, and Witten. As a result, this reveals an invariance of time parametrization under Γ(2) transformations of the wave function.
Quantum Cosmology in the Unified Field
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.
QUANTUM SPACE AND THE EXPANSION OF THE UNIVERSE
We present a dynamical model of space that considers it to be made up of energy quanta. The theory is used along with a thermodynamic approach to give a new view of cosmic evolution based on well known physical-chemical processes and provide an insight into the nature of dark energy and dark matter. The universe started from an atomic size volume at very high temperature and pressure near the Planck epoch. Upon expansion and cooling, phase transitions occurred resulting in the formation of radiation, fundamental particles, and matter. These nucleate and grow into stars, galaxies, and clusters. From a phase diagram of cosmic composition, we obtained a correlation between dark energy and the energy of space. Using the Friedmann equations, data from WMAP studies of the composition of the universe at 3.8 x 105 (a=5.25 x 10-3) years and at present (a=1), are well fitted by our model with an equation of state parameter, w= -0.7. The accelerated expansion of the universe, starting at about 7 billion years, determined by BOSS measurements, also correlates well with the dominance of dark energy at 7.25 x 109 years ( a= 0.65). Fitting with a Cosmological Constant yielded a time of 8.75 x 109 years (a=0.74). The expansion is thus better attributed to Quintessence with a space force arising from a quantum space field. From our phase diagram, we also find a correlation suggesting that dark matter is a plasma form of matter similar to that which existed during the photon epoch immediately prior to recombination. The BOSS data indicate that thermodynamics of expansion of the universe was adiabatic with the rate decelerating during the first 6 billion years after the Big Bang. This is consistent with our Quantum Space model. However, it became non-adiabatic and accelerating thereafter. This implies an influx of energy from a source outside the universe. It warrants further study.