Intrinsic quantum dynamics of particles in brane gravity

The Newtonian dynamics of particles in brane gravity is investigated. Due to the coupling of the particles' energy-momentum tensor to the tension of the brane, the particle is semi-confined and oscillates along the extra dimension. We demonstrate that the frequency of these oscillations is proportional to the kinetic energy of the particle in the brane. We show that the classical stability of particle trajectories on the brane gives us the Bohr--Sommerfeld quantization condition. The particle's motion along the extra dimension allows us to formulate a geometrical version of the uncertainty principle. Furthermore, we exhibited that the particle's motion along the extra dimension is identical to the time-independent Schr\"odinger equation. The dynamics of a free particle, particles in a box, a harmonic oscillator, a bouncing particle, and tunneling are re-examined. We show that the particle's motion along the extra dimension yields a quantized energy spectrum for bound states.Comment: 17 pages, 4 figures, to appear in Annal of Physic

Deviation from the Standard Uncertainty Principle and the Dark Energy Problem

Quantum fluctuations of a real massless scalar field are studied in the context of the Generalized Uncertainty Principle (GUP). The dynamical finite vacuum energy is found in spatially flat Friedmann-Robertson- Walker (FRW) spacetime which can be identified as dark energy to explain late time cosmic speed-up. The results show that a tiny deviation from the standard uncertainty principle is necessary on cosmological ground. By using the observational data we have constraint the GUP parameter even more stronger than ever.Comment: 9 pages, no figures, to appear in Gen. Rel. Gra

Collapse and dispersal of a homogeneous spin fluid in Einstein-Cartan theory

In the present work, we revisit the process of gravitational collapse of a spherically symmetric homogeneous dust fluid which is known as the Oppenheimer-Snyder (OS) model [1]. We show that such a scenario would not end in a spacetime singularity when the spin degrees of freedom of fermionic particles within the collapsing cloud are taken into account. To this purpose, we take the matter content of the stellar object as a homogeneous Weyssenhoff fluid which is a generalization of perfect fluid in general relativity (GR) to include the spin of matter. Employing the homogeneous and isotropic FLRW metric for the interior spacetime setup, it is shown that the spin of matter, in the context of a negative pressure, acts against the pull of gravity and decelerates the dynamical evolution of the collapse in its later stages. Our results bode a picture of gravitational collapse in which the collapse process halts at a finite radius whose value depends on the initial configuration. We thus show that the spacetime singularity that occurs in the OS model is replaced by a non-singular bounce beyond which the collapsing cloud re-expands to infinity. Depending on the model parameters, one can find a minimum value for the boundary of the collapsing cloud or correspondingly a threshold value for the mass content below which the horizon formation can be avoided. Our results are supported by a thorough numerical analysis.Comment: 16 pages, 5 figures, revised versio

The shadows of quantum gravity on Bell's inequality

This study delves into the validity of quantum mechanical operators in the context of quantum gravity, recognizing the potential need for their generalization. A primary objective is to investigate the repercussions of these generalizations on the inherent non-locality within quantum mechanics, as exemplified by Bell's inequality. Additionally, the study scrutinizes the consequences of introducing a non-zero minimal length into the established framework of Bell's inequality. The findings contribute significantly to our theoretical comprehension of the intricate interplay between quantum mechanics and gravity. Moreover, this research explores the impact of quantum gravity on Bell's inequality and its practical applications within quantum technologies, notably in the realms of device-independent protocols, quantum key distribution, and quantum randomness generation

Signature change from Schutz's canonical quantum cosmology and its classical analogue

We study the signature change in a perfect fluid Friedmann-Robertson-Walker quantum cosmological model. In this work the Schutz's variational formalism is applied to recover the notion of time. This gives rise to a Schrodinger-Wheeler-DeWitt equation with arbitrary ordering for the scale factor. We use the eigenfunctions in order to construct wave packets and evaluate the time-dependent expectation value of the scale factor which coincides with the ontological interpretation. We show that these solutions exhibit signature transitions from a finite Euclidean to a Lorentzian domain. Moreover, such models are equivalent to a classical system where, besides the perfect fluid, a repulsive fluid is present.Comment: 15 pages, 4 figures, to appear in PR

Estimated Age of the Universe in Fractional Cosmology

Our proposed cosmological framework, which is based on fractional quantum cosmology, aims to address the issue of synchronicity in the age of the universe. % Please check intended meaning is retained. To achieve this, we have developed a new fractional $\Lambda$CDM cosmological model. We obtained the necessary formalism by obtaining the fractional Hamiltonian constraint in a general minisuperspace. This formalism has allowed us to derive the fractional Friedmann and Raychaudhuri equations for a homogeneous and isotropic cosmology. Unlike the traditional de Sitter phase, our model exhibits a power-law accelerated expansion in the late-time universe, when vacuum energy becomes dominant. % Please check intended meaning is retained. By fitting the model's parameters to cosmological observations, we determined that the fractional parameter of L\'{e}vy equals $\alpha=1.986$. Additionally, we have calculated the age of the universe to be 13.8196 Gyr. Furthermore, we have found that the ratio of the age to Hubble time from the present epoch to the distant future is finite and confined within the interval $0.9858\leq Ht<95.238$.Comment: 24 pages, 9 figure

Non-commutative multi-dimensional cosmology

A non-commutative multi-dimensional cosmological model is introduced and used to address the issues of compactification and stabilization of extra dimensions and the cosmological constant problem. We show that in such a scenario these problems find natural solutions in a universe described by an increasing time parameter.Comment: 9 pages, 1 figure, to appear in JHE

Multi-dimensional classical and quantum cosmology: Exact solutions, signature transition and stabilization

We study the classical and quantum cosmology of a $(4+d)$-dimensional spacetime minimally coupled to a scalar field and present exact solutions for the resulting field equations for the case where the universe is spatially flat. These solutions exhibit signature transition from a Euclidean to a Lorentzian domain and lead to stabilization of the internal space, in contrast to the solutions which do not undergo signature transition. The corresponding quantum cosmology is described by the Wheeler-DeWitt equation which has exact solutions in the mini-superspace, resulting in wavefunctions peaking around the classical paths. Such solutions admit parametrizations corresponding to metric solutions of the field equations that admit signature transition.Comment: 15 pages, two figures, to appear in JHE

Quantization of the interior Schwarzschild black hole

We study a Hamiltonian quantum formalism of a spherically symmetric space-time which can be identified with the interior of a Schwarzschild black hole. The phase space of this model is spanned by two dynamical variables and their conjugate momenta. It is shown that the classical Lagrangian of the model gives rise the interior metric of a Schwarzschild black hole. We also show that the the mass of such a system is a Dirac observable and then by quantization of the model by Wheeler-DeWitt approach and constructing suitable wave packets we get the mass spectrum of the black hole.Comment: 12 pages, 1 figure, revised versio