Isotropic Universe Research Articles

Product manifolds as realizations of general linear symmetries

This paper considers the relationship between geometry, symmetry and fundamental interactions — gravity and those mediated by gauge fields. We explore product spacetimes which (a) have the necessary symmetries for gauge interactions and four-dimensional gravity and (b) reduce to an [Formula: see text]-dimensional isotropic universe in their flat space limit. The key technique is looking at orbits of the operator form of symmetric rank-two tensors under changes of coordinate system. Orbits containing diagonal matrices are seen to correspond to product manifolds. The [Formula: see text] symmetry of the decompactified universe acts nonlinearly on such a product spacetime. We explore the resulting Kaluza–Klein theories, in which the internal symmetries act indirectly on space of the extra dimensions, and give two examples: a six-dimensional model in which the gauge symmetry is [Formula: see text] and a seven-dimensional model in which it is [Formula: see text]. We identify constraints that can be placed on any rank-two symmetric tensor to obtain such spacetimes: relationships between polynomial invariants. The multiplicities of its eigenvalues determine the dimensionalities of the factor spaces and hence the gauge symmetries. If the tensor in question is the Ricci tensor, other than two-dimensional factor spaces all the factor spaces are Einstein manifolds. This situation represents the classical vacuum of the Kaluza–Klein theory.

Larger H0 values in the CMB dipole direction

Based on the assumption that quasars (QSOs) and gamma-ray bursts (GRBs) represent standardizable candles, we provide evidence that the Hubble constant ${H}_{0}$ adopts larger values in hemispheres aligned with the cosmic microwave background (CMB) dipole direction. If substantiated, this trend signals a departure from Friedmann-Lema\^{\i}tre-Robertson-Walker cosmology. In particular, QSOs show a definite trend, whereas our findings in GRBs are consistent with an isotropic universe, but we show in a sample of GRBs calibrated with type Ia supernovae (SNe) that this conclusion may change as one focuses on GRBs more closely (mis)aligned with the CMB dipole direction. The statistical significance in QSOs alone is $\ensuremath{\gtrsim}2\ensuremath{\sigma}$, and when combined with similar trends in strong lensing, type Ia SNe, and calibrated GRBs, this increases to $\ensuremath{\sim}3\ensuremath{\sigma}$. Our findings are consistent with reported discrepancies in the cosmic dipole and anisotropies in galaxy cluster scaling relations. The reported variations in ${H}_{0}$ across the sky suggest that Hubble tension may be a symptom of a deeper cosmological malaise.

Large-scale structure with superhorizon isocurvature dark energy

The standard cosmological model assumes a homogeneous and isotropic universe as the background spacetime on large scales called the cosmological principle. However, some observations suggest the possibility of an inhomogeneous and anisotropic universe at large scales. In this paper, we investigate a model of the Universe with random inhomogeneities and anisotropies on very large scales, motivated by the supercurvature dark energy model in Nan et al. [Phys. Rev. D 99, 103512 (2019)]. In this model, the authors introduced a scalar field with $\mathcal{O}(1)$ inhomogeneities on a scale sufficiently larger than the current horizon scale (superhorizon scale), and the potential energy of the scalar field explains the accelerating expansion, with slight deviations from the cosmological principle. We aim at clarifying the theoretical prediction on the large-scale structure (LSS) of the matter component in this model. Based on the work on the superhorizon scale fluctuations (superhorizon mode) presented in Y. Nan and K. Yamamoto [Phys. Rev. D 105, 063518 (2022)], we derive the equations that the perturbative components to the LSS obey as a generalization of the cosmological perturbations theory, which is solved to find the influence of the dark energy inhomogeneities on the formation of the LSS. Finally, we show that the model can be consistent with observations by comparing the ${\ensuremath{\sigma}}_{8}$ predicted by the numerical solution of the model with the ${\ensuremath{\sigma}}_{8}$ indicated by observations such as Planck and the Sloan Digital Sky Survey.

Quantum gravity corrections to the matter dynamics in the presence of a reference fluid

We analyze the effect induced on standard quantum field theory (in a functional approach) by quantum gravity corrections to a pure classical background. In the framework of the Kucha\ifmmode \check{r}\else \v{r}\fi{} and Torre proposal for a gravity-matter theory constrained to a Gaussian reference frame, materialized as a fluid in the system evolution, we consider a Born-Oppenheimer separation of the system, regarding the gravity degrees of freedom as the slow varying component and the matter plus the Gaussian fluid as fast quantum coordinates. The slow gravity component obeys the Wheeler-DeWitt equation, and we consider a Wentzel-Kramer-Brillouin expansion of its quantum dynamics via a Planckian parameter. The main issue of the proposed scenario is that, on one hand, we recover a modified quantum field theory in the presence of a Hermitian Hamiltonian (not affected by nonunitarity as in other approaches) and, on the other hand, we get the Gaussian fluid as a physical clock for such an amended quantum theory (verifying the correct energy conditions). We also show its equivalence with the kinematical action method, used in a previous work, in the homogeneous setting. Then, we implement the proposed paradigm to describe the dynamics of a homogeneous free massless scalar field, living on an isotropic universe, in the presence of a cosmological constant. We completely solve the dynamics up to the first order correction in the Planckian parameter to the standard quantum field theory. We determine the explicit form of the modified scalar field wave function, due to quantum features of the cosmic scale factor evolution. Phenomenological considerations and discussions are provided.

Islands in closed and open universes

We show that spatial curvature has a significant effect on the existence of entanglement islands in cosmology. We consider a homogeneous, isotropic universe with thermal radiation purified by a reference spacetime. Arbitrarily small positive curvature guarantees that the entire universe is an island. Proper subsets of the time-symmetric slice of a closed or open universe can be islands, but only if the cosmological constant is negative and sufficiently large in magnitude.

Euclid: Forecast constraints on consistency tests of the ΛCDM model

Context. The standard cosmological model is based on the fundamental assumptions of a spatially homogeneous and isotropic universe on large scales. An observational detection of a violation of these assumptions at any redshift would immediately indicate the presence of new physics. Aims. We quantify the ability of the Euclid mission, together with contemporary surveys, to improve the current sensitivity of null tests of the canonical cosmological constant Λ and the cold dark matter (ΛCDM) model in the redshift range 0 < z < 1.8. Methods. We considered both currently available data and simulated Euclid and external data products based on a ΛCDM fiducial model, an evolving dark energy model assuming the Chevallier-Polarski-Linder parameterization or an inhomogeneous Lemaître-Tolman-Bondi model with a cosmological constant Λ, and carried out two separate but complementary analyses: a machine learning reconstruction of the null tests based on genetic algorithms, and a theory-agnostic parametric approach based on Taylor expansion and binning of the data, in order to avoid assumptions about any particular model. Results. We find that in combination with external probes, Euclid can improve current constraints on null tests of the ΛCDM by approximately a factor of three when using the machine learning approach and by a further factor of two in the case of the parametric approach. However, we also find that in certain cases, the parametric approach may be biased against or missing some features of models far from ΛCDM. Conclusions. Our analysis highlights the importance of synergies between Euclid and other surveys. These synergies are crucial for providing tighter constraints over an extended redshift range for a plethora of different consistency tests of some of the main assumptions of the current cosmological paradigm.

Semiclassical and quantum features of the Bianchi I cosmology in the polymer representation

We analyze the Bianchi I cosmology in the presence of a massless scalar field and describe its dynamics via a semiclassical and quantum polymer approach by adopting three different sets of configurational variables: the natural Ashtekar connections, a set of anisotropic volumelike coordinates and the Universe volume plus two anisotropy coordinates (the latter two sets of variables would coincide in the case of an isotropic Universe). In the semiclassical analysis we demonstrate that the big bounce clearly emerges in all the sets of variables. Moreover, when adopting the proper volume variables (i.e. when defining the Universe volume itself on the polymer lattice) we also derive the exact polymer-modified Friedmann equation for the Bianchi I model. This way, the expression of the critical energy density that includes the anisotropic energylike contribution is obtained, demonstrating that in this set of variables the big bounce has a universal nature (i.e. its critical energy density has a maximum value fixed by fundamental constants and the Immirzi parameter). Finally, a proposal is made to recover the equivalence between the dynamics in the Ashtekar set and in the anisotropic volumelike one, showing that this request is satisfied when a polymer parameter depending on the configurational coordinates is considered. Then, we apply the Arnowitt-Deser-Misner reduction of the variational principle and we quantize the system. We study the resulting Schr\"odinger-like dynamics only in the Ashtekar variables and in the proper volume ones, stressing that the behavior of the Universe wave packet over time singles out common features with the semiclassical trajectories. However, we show that the standard deviation for the Universe volume operator grows with time. This is a signal of the spreading of the Bianchi I wave packet and hence of the importance of the quantum fluctuations in order to properly study the big bounce picture.

Optimizing femur symmetry judgment using three-dimensional data correction scheme in fractures of the proximal femur

BackgroundThe application of the 3D printing mirror image model is based on the symmetry of the limbs. Different from image fusion to judge the similarity, based on the commonality of the limb morphology of the same organism and the isotropic of the long bone cross-section, the symmetry of the femur has been determined by calculating the dimension difference of the corresponding cross-section of the non-fractured area. However, the previous version used equidistant cross-sections for measurement and two-dimensional data correction, and there were problems with insufficient reliability and data failure. The purpose of this study is to achieve a more accurate and universal symmetry verification scheme for bilateral tubular bones through an improved method. MethodsForty-five imaging data of proximal femoral fracture and osteopathy were selected from October 2015 to September 2017. 10%, 30%, and 50% of the full-length of the bilateral femur is sliced to judge the similarity between paired femurs. Long and short axes of the bilateral femoral cross-sections on the two-dimensional slices were measured and compared. A stylized trigonometric were used to correct the measured axes lengths such that they more closely match with measurements taken from slices perpendicular to femoral shaft axis. Results540 valid data items from the long axis and short axis of the bilateral side of the distal femur were obtained, and 192 of these were corrected. There were no significant differences between the left and right of the long and short axis of each cross-section in paired cases (P>0.05). ConclusionsThis study have demonstrated symmetricity of the left and right femurs. The availability of CT data at any position of the patient's lower limbs is realized through replacing the previous “two-dimensional data correction” with “three-dimensional data correction”.

An introduction to the relativistic kinetic theory on curved spacetimes

This article provides a self-contained pedagogical introduction to the relativistic kinetic theory of a dilute gas propagating on a curved spacetime manifold (M,g) of arbitrary dimension. Special emphasis is made on geometric aspects of the theory in order to achieve a formulation which is manifestly covariant on the relativistic phase space. Whereas most previous work has focussed on the tangent bundle formulation, here we work on the cotangent bundle associated with (M,g) which is more naturally adapted to the Hamiltonian framework of the theory. In the first part of this work we discuss the relevant geometric structures of the cotangent bundle T*M, starting with the natural symplectic form on T*M, the one-particle Hamiltonian and the Liouville vector field, defined as the corresponding Hamiltonian vector field. Next, we discuss the Sasaki metric on T*M and its most important properties, including the role it plays for the physical interpretation of the one-particle distribution function. In the second part of this work we describe the general relativistic theory of a collisionless gas, starting with the derivation of the collisionless Boltzmann equation for a neutral simple gas. Subsequently, the description is generalized to a charged gas consisting of several species of particles and the general relativistic Vlasov-Maxwell equations are derived for this system. The last part of this work is devoted to a transparent derivation of the collision term, leading to the general relativistic Boltzmann equation on (M,g). The meaning of global and local equilibrium and the stringent restrictions for the existence of the former on a curved spacetime are discussed. We close this article with an application of our formalism to the expansion of a homogeneous and isotropic universe filled with a collisional simple gas and its behavior in the early and late epochs. [abbreviated version]

Clocks and Trajectories in Quantum Cosmology

We consider a simple cosmological model consisting of an empty Bianchi I Universe, whose Hamiltonian we deparametrise to provide a natural clock variable. The model thus effectively describes an isotropic universe with an induced clock given by the shear. By quantising this model, we obtain various different possible bouncing trajectories (semiquantum expectation values on coherent states or obtained by the de Broglie–Bohm formulation) and explicit their clock dependence, specifically emphasising the question of symmetry across the bounce.

Nonlocal extension of causal thermodynamics of the isotropic cosmic fluid

We establish the nonlocal generalization of the Israel-Stewart model for the relativistic causal thermodynamics of the cosmic fluid, which evolves in the homogeneous isotropic Universe. Based on the second law of thermodynamics we derive the integro-differential master equation for the nonequilibrium pressure scalar and reduce it to the differential equation of the second order in time derivatives. We show that this master equation can be considered as the relativistic analog of the Burgers equation, which is known in the classical theory of viscoelasticity. We obtain the nonlinear key equation, which contains the energy density scalar only, and analyze two exact solutions of the model. The effective temperature is considered to be associated with the barotropic equation of state of the cosmic fluid.

Vacuum Energy in Saez-Ballester Theory and Stabilization of Extra Dimensions

In this work, we study a spherically symmetric metric in 5D within the framework of Saez-Ballester Theory, where minimal dark energy-matter interaction occurs. We predict that the expanding isotropic universe will be progressively DE dominated. We estimate few values of the deceleration parameter, very close to the recently predicted values. We obtain the value of the DE EoS parameter as ω=−1. Additionally, we measure the value of the overall density parameter as Ω=0.97(≈1), in line with the notion of a close to or nearly (not exactly) flat universe. We predict that the model universe starts with the Big-Bang and ends at the Big Freeze singularity. In general, we cannot find conditions for stabilization of extra dimensions in general relativity, and all dimensions want to be dynamical. Here, we present two possible conditions to solve this stabilization problem in general relativity.

Hubble Tension

The results of measurements of the Hubble constant H0, which characterizes the expansion rate of the universe, show that the values of H0 vary significantly depending on Methodology. The disagreement in the values of H0 obtained by the various teams far exceeds the standard uncertainties provided with the values. This discrepancy is called the Hubble Tension. In this paper, we discuss Macrostructures of the World (Superclusters and Galaxies); explain their Origin and Evolution in frames of the developed Hypersphere World-Universe Model (WUM), which is an alternative to the prevailing Big Bang Model (BBM) [1]; and provide the explanation of the Hubble Tension. The main difference between WUM and BBM is: Instead of the Infinite Homogeneous and Isotropic Universe around the Initial Singularity in BBM, in WUM, the 3D Finite Boundless World (a Hypersphere) presents a Patchwork Quilt of different Luminous Superclusters (103), which emerged in various places of the World at different Cosmological times. In WUM, the Medium of the World is Homogeneous and Isotropic. The distribution of Macroobjects in the World is spatially Inhomogeneous and Anisotropic and temporally Non-simultaneous.

The Origin of Power and Acceleration of High-Redshift Galaxies in the Unicentric Model of the Universe

Recently, a unicentric model of our observable universe was proposed. Accordingly, the big bang was neither a singular event nor invoked by external forces, but rather a frequent event in cosmic life cycles that occur sequentially or in parallel at the same and/or in different locations of our infinitely large, flat, homogeneous, and isotropic parent universe. The progenitor of our big bang is predicted to have been of a measurable size and happened to be in our neighbourhood. Based on theoretical arguments and general relativistic numerical calculations, it is argued that: 1) The surface of the progenitor is most appropriate for the hadron flash to run away; 2) The structure of the progenitor is immune to self-collapse into a hyper-massive black hole; and 3) The power and acceleration of high-redshift galaxies may be connected to the BB-explosion. We conclude that the currently observed high-redshift galaxies must have been old and inactive in older times, but turned into life through matter and momentum transfer from the fireball and the collision of the locally curved spacetime embedding the galaxy with the expanding one embedding the fireball. With the present scenario, the origin of the monstrous black hole candidates with MBH ≥109Me , that are believed to have resided at the centre of galaxies when the observable universe was 400 Myr old, could be straightforwardly explained. This implies that QSOs with ever higher redshifts should exist, though their detection becomes increasingly harder.

The effects of lensing by local structures on the dipole of radio source counts

ABSTRACT Our peculiar motion in a homogeneous and isotropic universe imprints a dipole in the cosmic microwave background (CMB) temperature field and similarly imprints a dipole in the distribution of extragalactic radio sources on the sky. Each of these effects have been measured; however, each of these measurements give different results for the velocity of our motion through the Universe: the radio dipole measurements finds the speed of our motion to be around three times larger than that of the CMB. Here we show the effects of the previously unconstrained lensing dipole, whereby necessarily local structures (required for large angular lensing scales) will distort the distribution of radio sources on the sky. We find that the inclusion of these effects does not reduce the tension between the CMB and radio source dipole measurements; however, without their inclusion future extragalactic number counts could lead to incorrect inferences of our peculiar motion. In addition we can constrain the size of the lensing dipole to be κ < 3 · 10−2 at the 2σ level.

Comparative Analysis of Standard ΛCDM and ΛCS Models

We draw a comparison of time-dependent cosmological parameters calculated in the standard ΛCDM model with those of the model of a homogeneous and isotropic Universe with non-zero cosmological constant filled with a perfect gas of low-velocity cosmic strings (ΛCS model). It is shown that pressure-free matter can obtain the properties of a gas of low-velocity cosmic strings in the epoch, when the global geometry and the total amount of matter in the Universe as a whole obey an additional constraint. This constraint follows from the quantum geometrodynamical approach in the semiclassical approximation. In terms of general relativity, its effective contribution to the field equations can be linked to the time evolution of the equation of state of matter caused by the processes of redistribution of the energy between matter components. In the present article, the exact solutions of the Einstein equations for the ΛCS model are found. It is demonstrated that this model is equivalent to the open de Sitter model. After the scale transformation of the time variable of the ΛCS model, the standard ΛCDM and ΛCS models provide the equivalent descriptions of cosmological parameters as functions of time at equal values of the cosmological constant. The exception is the behavior of the deceleration parameter in the early Universe.

Viscous cosmology in the Weyl-type f(Q,\xa0T) gravity

Bulk viscosity is the only viscous influence that can change the background dynamics in a homogeneous and isotropic universe. In the present work, we analyze the bulk viscous cosmological model with the bulk viscosity coefficient of the form zeta =zeta _0+zeta _1H+zeta _2left( frac{dot{H}}{H}+Hright) where, zeta _0, zeta _1 and zeta _2 are bulk viscous parameters, and H is the Hubble parameter. We investigate the impact of the bulk viscous parameter on dynamics of the universe in the recently proposed Weyl-type f(Q, T) gravity, where Q is the non-metricity, and T is the trace of the matter energy–momentum tensor. The exact solutions to the corresponding field equations are obtained with the viscous fluid and the linear model of the form f(Q, T)=alpha Q+frac{beta }{6kappa ^2}T, where alpha and beta are model parameters. Further, we constrain the model parameters using the 57 points Hubble dataset the recently released 1048 points Pantheon sample and the combination Hz + BAO + Pantheon, which shows our model is good congeniality with observations. We study the possible scenarios and the evolution of the universe through the deceleration parameter, the equation of state (EoS) parameter, the statefinder diagnostics, and the Om diagnostics. It is observed that the universe exhibits a transition from a decelerated to an accelerated phase of the universe under certain constraints of model parameters.

A Fibonacci-like universe expansion on time-scale

The time scale Fibonacci sequences satisfy the Friedmann–Lemaître–Robertson–Walker (FLRW) dynamic equation on time scale, which are an exact solution of Einstein’s field equations of general relativity for an expanding homogeneous and isotropic universe. We show that the equations of motion correspond to the one-dimensional motion of a particle of position F(t) in an inverted harmonic potential. For the dynamic equations on time scale describing the Fibonacci numbers F(t), we present the Lagrangian and Hamiltonian formalism. Identifying these with the equations that describe factor scales, we conclude that for a certain granulation, for both the continuous and the discrete universe, we have the same dynamics.

Bouncing cosmology in the limiting curvature theory of gravity

In this paper we discuss models satisfying the limiting curvature condition. For this purpose we modify the Einstein-Hilbert action by adding a term which restricts the growth of curvature. We analyze cosmological solutions in such models. Namely, we consider a closed contracting homogeneous isotropic universe filled with thermal radiation. We demonstrate that for properly chosen curvature constraints such a universe has a bounce. As a result its evolution is nonsingular and contains a "de Sitter-type" supercritical stage connecting contracting and expanding phases. Possible generalizations of these results are briefly discussed.

Finite action principle and Hořava-Lifshitz gravity: Early universe, black holes, and wormholes

The destructive interference of the neighbouring field configurations with infinite classical action in the gravitational path integral approach serves as a dynamical mechanism resolving the black hole singularity problem. It also provides an isotropic and homogeneous early universe without the need of inflation. In this work, we elaborate on the finite action in the framework of Horava-Lifshitz gravity -- a ghost-free QFT. Assuming the mixmaster chaotic solutions in the projectable H-L theory, we show that the beginning of the universe is homogeneous and isotropic. Furthermore, we show that the H-L gravity action selects only the regular black-hole spacetimes. We also comment on possibility of traversable wormholes in theories with higher curvature invariants.