Quantum Cosmology Research Articles

Analytic and numerical study of scalar perturbations in loop quantum cosmology

Analytic and numerical study of scalar perturbations in loop quantum cosmology

Classical and Quantum Cosmology in Weyl Integrable Gravity: A Noether Symmetry Approach

Classical and Quantum Cosmology in Weyl Integrable Gravity: A Noether Symmetry Approach

Gravitational lensing of dark energy models and ΛCDM using observational data in loop quantum cosmology

This paper investigates the accelerated cosmic expansion in the late Universe by examining two dark energy models, viscous modified Chaplygin gas (VsMCG) and variable modified Chaplygin gas (VMCG), within loop quantum cosmology alongside the ΛCDM model. The objective is to constrain cosmic parameters using the ΛCDM model and 30 of the latest H(z) measurements from cosmic chronometers (CC), including Type Ia Supernovae, Gamma-Ray Bursts (GRB), Quasars, and 24 uncorrelated baryon acoustic oscillations (BAO) measurements across a redshift range from 0.106 to 2.33. The latest Hubble constant measurement from Riess in 2022 is included to enhance constraints. In the ΛCDM, VsMCG, and VMCG frameworks, best-fit parameters for the Hubble parameter (H0) and sound horizon (rd) are obtained. The results highlight significant disparities between H0 and rd values from late-time observational measurements, reflecting the known H0 and rd tensions. The gravitational lensing optical depth of the two dark energy models is studied by plotting log⁡(τ(zl)/H0−3τN) vs zl. The probability of finding gravitational lenses (optical depth) in both models increases with lens redshift zl. The change in optical depth behavior for different parameter constraints is graphically analyzed. A joint analysis of VsMCG and VMCG with ΛCDM is conducted. While the models diverge in the early Universe, they are indistinguishable at low redshift. Using the Akaike information criteria, the analysis indicates that neither dark energy model can be dismissed based on the latest observations.

Unruh-DeWitt particle detectors in bouncing cosmologies

We study semi-classical particle production in non-singular bouncing cosmologies by employing the Unruh-DeWitt model of a particle detector propagating in this class of spacetimes. The scale factor for the bouncing cosmology is derived analytically and is inspired by the modified Friedmann equation employed in the loop quantum cosmology literature. We examine how the detector response varies with the free parameters in this model such as the equation of state during the contraction phase and the critical energy density during the bounce phase. We also investigate whether such a signature in the particle detector survives at late times.

Unveiling the evolution of rotating black holes in loop quantum cosmology

In this work, we aim to discuss about the evolution of rotating black holes (RBHs) within the context of loop quantum cosmology. Here, the main part of our research work focuses on the impacts of angular momentum based rotating parameter and accretion efficiency on the lifetime of RBHs. Our study reveals that accretion of dark energy would not significantly affect the evolution of RBHs, however higher value of rotating parameter could slightly delay the evaporation times of RBHs. Our analysis also depicts that the maximum value of rotating parameter for evolution of any RBH is 10-8Mi2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-8}M_i^2$$\\end{document}, where Mi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_i$$\\end{document} is the formation mass of RBH. Moreover, from our calculation we found that the maximum mass of a presently existing supermassive black hole would be 1048g\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{48}\ ext {g}$$\\end{document}, if it undergoes rotation. Also from astrophysical constraint analysis, we found that there is a greater tendency for formation of black holes in loop quantum cosmology than standard model of cosmology.

Lorentzian Quantum Cosmology from Effective Spin Foams

Effective spin foams provide the most computationally efficient spin foam models yet and are therefore ideally suited for applications, e.g., to quantum cosmology. Here, we provide the first effective spin foam computations of a finite time evolution step in a Lorentzian quantum de Sitter universe. We will consider a setup that computes the no-boundary wave function and a setup describing the transition between two finite scale factors. A key property of spin foams is that they implement discrete spectra for the areas. We therefore study the effects that are induced by the discrete spectra. To perform these computations, we had to identify a technique to deal with highly oscillating and slowly converging or even diverging sums. Here, we illustrate that high-order Shanks transformation works very well and is a promising tool for the evaluation of Lorentzian (gravitational) path integrals and spin foam sums.

Noether symmetry analysis in f(T,TG) gravity theory: A study of classical cosmology

This work deals with [Formula: see text] gravity in the background of homogeneous and isotropic flat Friedmann–Lemaître–Robertson–Walker (FLRW) space-time model. The main aim of this work is to examine whether the model supports the observational data or not. By using the Noether symmetry analysis, not only the symmetry vector is obtained, but also the coupling function [Formula: see text] in the Lagrangian has been determined. Also, the symmetry analysis identifies a transformation from [Formula: see text] to [Formula: see text] in such a way that one of the new variables become cyclic along the direction symmetry vector and as a result the field equations become solvable. Then the solution is analyzed from the observational point of view. Finally, quantum cosmology has been formulated for the present model and the wave function of the universe has been evaluated by solving the Wheeler–DeWitt equation with some assumptions.

A non-perturbative and background-independent formulation of quadratic gravity

A non-perturbative and background-independent quantum formulation of quadratic gravity is provided. A canonical quantization procedure introduced in previous works, named after Dirac and Pauli, is here applied to quadratic gravity to obtain, as required by consistency, a well-defined Euclidean path integral. The theory is unitary: all probabilities are non negative and they sum up to one. We obtain path-integral expressions for the transition amplitudes, Green's functions and generic matrix elements of time-ordered products of the metric. As a byproduct, similar results are also obtained for a scalar-field four-derivative interacting model. In this way, among other things, previous perturbative and background-dependent calculations are justified. The (quantum) quadratic gravity effective action, whose field equations determine the vacuum expectation value of the metric in the presence of a generic energy-momentum tensor, is constructed. The classical limit of the effective action turns out to be equivalent to the starting classical action of quadratic gravity, whose runaway rates were previously shown to be slow enough to be compatible with observations. Finally, the constructed non-perturbative and background-independent quantum quadratic gravity is applied to quantum cosmology to obtain a path-integral expression for the wave function of the universe, which satisfies a sort of Wheeler-DeWitt equation. This application allows us to understand at the quantum level why our universe is nearly homogeneous and isotropic.

On the evolution of the volume in Loop Quantum Cosmology

The dynamics of the expectation value of the volume is one of the key ingredients behind the replacement of the Big Bang singularity by a bounce in Loop Quantum Cosmology. As such, it is of great importance that this quantity is mathematically well-defined in the space of physical states of the theory. A number of caveats have been raised about such a definition entering in conflict with the quantum evolution of states, motivated by the situation found in quantum geometrodynamics. We show that there are ways around these caveats, all of which are related to the existence of quantization prescriptions leading to a nondegenerate curvature operator in Loop Quantum Cosmology. Interestingly, the properties of the curvature operator that may allow for a good behavior of the volume are only possible thanks to the discreteness of the geometry characteristic of the loop quantization procedure.

Adiabatic approach to the trans-Planckian problem in loop quantum cosmology

We study the scalar modes that, being observable today, were trans-Planckian before inflation, within the context of hybrid loop quantum cosmology (LQC). We analyze the dynamics of these highly ultraviolet modes by introducing modified dispersion relations to their equations of motion and discuss the impact that these relations would introduce in the power spectrum by computing the adiabaticity coefficient. More precisely, we consider two different models compatible with observations for the standard linear dispersion relation which are based on different initial conditions for the perturbations and background. One of these models avoids the issue altogether by generating less e-folds of inflation, so that the observable modes are never trans-Planckian, whereas the other suffers (arguably softly) from the trans-Planckian problem. This shows that the existence of the trans-Planckian problem in LQC is model dependent. Published by the American Physical Society 2024

Gravastar in the framework of Loop Quantum Cosmology

Gravastar in the framework of Loop Quantum Cosmology

Fermion-antifermion pairs in a magnetized space-time with non-zero cosmological constant

We analyze a fermion-antifermion pair within the (2+1)-dimensional Bonnor-Melvin magnetic (BMM) spacetime featuring a nonzero cosmological constant (Λ>0). To do this, we rigorously investigate analytical solutions to the corresponding form of a fully-covariant two-body Dirac equation. We derive a non-perturbative wave equation and obtain an exact closed-form analytical solution for the system under consideration. In this magnetic background spacetime, described by a surface with positive Gaussian curvature, we noticed that fermion-antifermion pairs display a collective behavior resembling that of a single quantum oscillator, carrying a total rest mass of the particles and oscillating with a frequency (ωo∝Λ), even in the absence of mutual interaction between the particles. This indicates a compelling correlation between the cosmological constant and the energy spectrum of fermion-antifermion systems, implying connections between quantum realms and cosmology.

Quantum Oppenheimer–Snyder–Swiss Cheese model

The quantum Oppenheimer–Snyder (qOS) model in loop quantum cosmology is combined with the quantum Swiss Cheese (qSC) model. While in the qOS model, the interior Ashtekar–Pawlowski–Singh (APS) semiclassical metric is joined to an exterior static spherically symmetric metric, in the qSC model an exterior APS metric is joined to an interior spherically symmetric metric. The qOS model represents a deformed Schwarzschild black hole containing a collapsing APS ball. On the other hand, the qSC describes a deformed Schwarzschild black hole surrounded by a quantum-modified Friedmann–Robertson–Walker universe i.e., APS metric. In this Letter, we apply the concept of the Thin-Shell Wormhole (TSW) to combine the two individual models in a single model that is called the quantum Oppenheimer–Snyder–Swiss Cheese (qOSSC) model. Unlike qOS and qSC, in which the interior and exterior metrics are glued smoothly without an energy–momentum tensor on the interface hypersurface, in the qOSSC model there exists an exotic surface fluid on the throat which satisfies a dark energy equation of state. The dynamic of the throat is investigated, and the universe may bounce from the minimum radius without forming a black hole.

Noether symmetry analysis for fourth-order modified gravity theory: Cosmological solution and evolution

A modified fourth-order gravity theory namely the [Formula: see text] theory is considered in flat FLRW model to investigate both classical and quantum cosmology. The field equations are reduced to second-order differential equations by considering the technique of Lagrange multiplier. Noether symmetry analysis has been used both for obtaining classical solution and the wave function of the Universe in quantum cosmology. Finally the cosmological solutions are examined from observational view point.

Axial perturbations in Kantowski-Sachs spacetimes and hybrid quantum cosmology

Axial perturbations in Kantowski-Sachs spacetimes and hybrid quantum cosmology

Spectral solutions for fractional Klein–Gordon models of distributed order

The Klein–Gordon equation is a fundamental theoretical physics concept, governing the behavior of relativistic quantum particles with spin-zero. Its numerical solution is crucial in fields like quantum field theory, particle physics, and cosmology. The study explores numerical methodologies for solving this equation, highlighting their significance and challenges. This study uses the collocation method to approximate fractional Klein–Gordon models of distributed order based on Shifted Jacobi orthogonal polynomials and Shifted fractional order Jacobi orthogonal functions. While, the distributed term (integral term) was treat using Legendre–Gauss–Lobatto quadrature. It assesses residuals through finite expansion and yields accurate numerical results. The method is more factual and fair when initial and boundary conditions are enforced. Numerical simulations are presented to demonstrate the method’s accuracy, particularly in fractional Klein–Gordon models of distributed order. Furthermore, we offer a few numerical test scenarios to show that the method is able to maintain the non-smooth solution of the underlying issue.

Quantum cosmology in teleparallel gravity with a boundary term

We quantize a homogeneous and isotropic universe for two models of modified teleparallel gravity: one wherein an arbitrary function of the boundary term, namely B, is present in the action, and in the other model, a scalar field that is non-minimally coupled to both the torsion and boundary term. In this regard, we study exact solutions of both the classical and quantum frameworks by utilizing the corresponding Wheeler–DeWitt (WDW) equations of the models. To correspond to the comprehensive classical and quantum levels, in the second model, we propose an appropriate initial condition for the wave packets and observe that they closely adhere to the classical trajectories and reach their peak. We quantify this correspondence using the de Broglie–Bohm interpretation of quantum mechanics. According to this proposal, the classical and Bohmian trajectories coincide when the quantum potential vanishes along the Bohmian paths. Furthermore, we apply the de-parameterization technique to our model in the realm of the problem of time in quantum cosmological models based on the WDW equation, utilizing the global internal time denoted as χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi $$\\end{document}, which represents a scalar field.

The Cosmic Black Hole

Concurrent with advancements in cosmology, various theories have been proposed about the origin of the universe or its ultimate fate. These theories include the Steady State Theory, Oscillating Universe Theory or Cyclic model, Multiverse Theory, String Theory/M-Theory, Quantum Gravity or Loop Quantum Cosmology, The Big Bang Theory, Inflationary Universe Theory, and the No-Boundary Proposal. Among these, the Big Bang theory has been widely accepted by most scientists, with the Inflation theory serving as its complementary addition. On the other hand, theories such as the big rip, flat universe, and big crunch have also addressed the ultimate fate of the cosmos. However, T-Consciousness Cosmology presents a new hypothesis to explain how the universe was born from a black hole named the ‘Cosmic Black Hole,’ or the initial seed of the universe. This hypothesis not only addresses how this particular type of black hole forms, contingent on the reversion of the cosmos according to the Spherical Cosmos model but also details its fundamental differences from known black holes, referred to as “intra-cosmic black holes.” The reversion of the cosmos in the ‘Spherical Cosmos Model,’ is described through a mechanism known as space Rebound, which is distinct from the Big Crunch. The Terminal Edge of the cosmos is defined as the maximum radius at which space mesh is capable of rebound during the universe's volume increase. In the process of the rebound of space to its ultimate extent, objects within the cosmos face complete disintegration and transform into waves called absolute waves. Due to the inherent rotation of the cosmos and its reversion from the Terminal Edge, these waves collide and create gravitational centers in the central regions of the spherical cosmos, forming new types of matter known as light-dark matter, dark-dark matter, and thermal matter. Each of these mentioned materials represents a new type of matter introduced by T-Consciousness Cosmology. Additionally, according to this model, the cosmos contracts into a very tiny point with a final quench, where all types of matter and fundamental forces unite, forming a new type of absolute matter called ‘Taheri Absolute Matter’ (TAM). The spherical cosmos model also divides time into various types: ‘Longitudinal’ and ‘Transverse,’ and unlike the theory of relativity, where time is considered a dimension, it classifies it as one of the types of transverse time introduced as an entropic force. In essence, this type of force (time) acts against the force of gravity and, by disintegrating all types of objects from fundamental to large scale, acts as an agent of stress or tension release from the space mesh.

Numerical simulation of coupled Klein–Gordon–Schrödinger equations: RBF partition of unity

The coupled Klein–Gordon–Schrödinger equations have significant implications in quantum field theory, particle physics, cosmology, and nonlinear dynamics. In this study, we propose an efficient method for numerically simulating this system. The proposed approach involves employing the radial basis function partition of unity for spatial discretization. This method utilizes scaled Lagrange basis functions with polyharmonic spline kernels, taking advantage of the scalability property of the polyharmonic kernel to ensure stability in the approximation process. The resulting spatially discretized system yields a nonlinear time-dependent set of differential equations. To solve this system, we combine an implicit central finite difference scheme with a predictor–corrector procedure to overcome the nonlinearity. In the numerical results section, we assess the efficiency, accuracy, and versatility of the proposed method by conducting several simulations in large domains over extended periods. We present and compare these results with those obtained using alternative methods, demonstrating the effectiveness of the proposed approach in accurately solving the coupled Klein–Gordon–Schrödinger equations.

An approximate application of quantum gravity to the rotation problem

Arbitrary initial conditions allow solutions of Einstein’s field equations for General Relativity to have arbitrarily large relative rotation of matter and inertial frames. The ‘Rotation Problem’ is to explain why the measured relative rotation rate is so small. As it turns out, nearly any reasonable theory of quantum gravity can solve the rotation problem by phase interference. Even as early as about a quarter of a second after the initial simgularity, quantum cosmology would limit the cosmologies that contribute significantly to a path integral calculation to have relative rms rotation rates less than about 10−51 radians per year. Those calculations are based on using 50 e-foldings during inflation. For 55 or 60 e-foldings, the cosmologies contributing significantly to the path integral would have even smaller relative rotation rates. In addition, although inflation dominates the calculation, even if there had been no inflation, the cosmologies contributing significantly to the path integral would have relative rotation rates less than about 10−32 radians per year at about a quarter of a second after the initial singularity. These calculations are insensitive to the details of the theory of quantum gravity because the main factor depends only on the size of the visible Universe, the Planck time, the free-space speed of light, the Hubble parameter, and the number of e-foldings during inflation. These calculations use the Einstein–Hilbert action in quantum gravity, including large-scale relative rotation of inertial frames and the matter distribution, in which each ‘path’ is a cosmology with a different rms relative rotation rate. The calculations include inflation for 50, 55, and 60 e-foldings, and for values of the dependence of relative rotation rate on cosmological scale factor a as a −m for various values of m. The calculation shows that the action is an extremum at zero rms relative rotation rate.