Curvature Of Universe Research Articles

Constrain spatial curvature and dark energy with strong lenses and complementary probes: a forecast for next-generation surveys

Abstract Inferring spatial curvature of the Universe with high-fidelity is a longstanding interest in cosmology. However, the strong degeneracy between dark energy equation-of-state parameter w and curvature density parameter ΩK has always been a hurdle for precision measurements of curvature from late-universe probes. With the imminent commissioning of Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST), we demonstrate for the first time, using simulations of stage-IV surveys, the crucial role of time-delay distances from strong gravitational lenses in breaking this degeneracy. Our findings suggest that in non-flat owCDM model, while strong lensing data alone only yield a ΩK constraint at $\sim \mathcal {O}(10^{-1})$ level, the integration with SNe Ia and BAO data breaks the w-ΩK degeneracy and refines the ΩK constraint to $\sim \mathcal {O}(10^{-2})$. This surpasses the constraints typically derived from SNe Ia Hubble diagrams and BAO data and is comparable to the constraints obtained from Planck Primary CMB data. Additionally, we present a non-parametric approach using Gaussian Process to avoid parameter-dependency of the expansion history H(z) and achieve similar $\mathcal {O}(10^{-2})$ level constraint on ΩK. This study demonstrates the significant potential of strong gravitational lenses and Stage-IV surveys like LSST to achieve high-fidelity, independent constraints on ΩK, contributing to our understanding of the Universe’s geometry and the dynamics of dark energy.

Jiawang Liu.

"I am waiting for the day when someone will discover the edge of the universe… Young professors / group leaders / principal investigators are not prepared for the challenges of balancing family life with scientific research…" Find out more about Jiawang Liu in his Introducing… Profile.

Expansion, Topology and Entropy

Object of this work is, to determine, if objects observed more distant are moving away faster than less distant ones. The escape velocity Hr is defined by the HUBBLE-Parameter H, locally H0, which is proportional to the reciprocal of the age T. The calculations are based on a model of Cornelius LANCZOS, outlined at a lecture on the occasion of the Einstein-Symposium 1965 in Berlin [1] and [2]. The model defines the expansion of the universe as a consequence of the existence of a metric wave field. That field also should be the reason for all relativistic effects, both SR and GR. In the context of this work the propagation function of that wave field is determined. Its phase rate is equal to the reciprocal of PLANCK's smallest increment r0. Even the other PLANCK-units set up the basis of the model being functions of space and time.With it, the model leads to a quantization of the universe into single lineelements with the size of r0. Thus, a kind of finite-element-method becomes possible, at which point the single elements are explicitly defined by the wave function. As per definition, objects in the free fall, aren't moving either with respect to the metrics and are carried-with during expansion. With the help of the propagation function it's possible to calculate the HUBBLE-Parameter H even for greater distances. Furthermore the entropy of the universe as a whole is determined considering the special topology of the universe

A polycrystal plasticity-cellular automaton integrated modeling method for continuous dynamic recrystallization and its application to AA2196 alloy

Continuous dynamic recrystallization usually dominates the microstructural evolution in hot working of aluminum alloys, in which the high-angle grain boundaries of new grains mainly originate from the gradual increase in subgrain misorientation angles. In this work, an integrated computational method is proposed to simulate continuous dynamic recrystallization process of aluminum alloys by coupling three-dimensional cellular automaton and visco-plastic self-consistent models. The stress response, dislocation accumulation and recovery, and evolution of crystal orientations are computed in the context of polycrystal plasticity; the formation and rotation of subgrains, followed by stored energy and curvature-driven boundary migration, are captured and visualized by cellular automaton. The non-octahedral slip mode {110}<110> is additionally introduced to capture the 〈001〉 texture during hot compression. A universal cell topology deformation method is adopted to achieve an effective track of grain morphology evolution during plastic deformation. The proposed simulation framework is validated through simulating the isothermal uniaxial compression process of AA2196 alloy under different temperatures and strain rates. The orientation dependence of CDRX during compression is numerically reproduced by correlating the subgrain formation and rotation process with the activation state of slip systems. The simulated macroscopic flow stress, 3D microstructure and inherent microstructural characteristics such as subgrain size, subgrain boundaries and textures are in good agreement with the experimental results. The proposed method provides an effective and efficient tool for multi-scale simulation of hot forming process of aluminum alloys.

Cosmic topology. Part IVa. Classification of manifolds using machine learning: a case study with small toroidal universes

Non-trivial spatial topology of the Universe may give rise to potentially measurable signatures in the cosmic microwave background. We explore different machine learning approaches to classify harmonic-space realizations of the microwave background in the test case of Euclidean E 1 topology (the 3-torus) with a cubic fundamental domain of a size scale significantly smaller than the diameter of the last scattering surface. This is the first step toward developing a machine learning approach to classification of cosmic topology and likelihood-free inference of topological parameters. Different machine learning approaches are capable of classifying the harmonic-space realizations with accuracy greater than 99% if the topology scale is half of the diameter of the last-scattering surface and orientation of the topology is known. For distinguishing random rotations of these sky realizations from realizations of the covering space, the extreme gradient boosting classifier algorithm performs best with an accuracy of 88%. Slightly lower accuracies of 83% to 87% are obtained with the random forest classifier along with one- and two-dimensional convolutional neural networks. The techniques presented here can also accurately classify non-rotated cubic E 1 topology realizations with a topology scale slightly larger than the diameter of the last-scattering surface, if enough training data are provided. While information compressing methods like most machine learning approaches cannot exceed the statistical power of a likelihood-based approach that captures all available information, they potentially offer a computationally cheaper alternative. A principle challenge appears to be accounting for arbitrary orientations of a given topology, although this is also a significant hurdle for likelihood-based approaches.

Improving constraints on inflation with CMB delensing

The delensing of cosmic microwave background (CMB) maps will be increasingly valuable for extracting as much information as possible from future CMB surveys. Delensing provides many general benefits, including sharpening of the acoustic peaks, more accurate recovery of the damping tail, and reduction of lensing-induced B-mode power. In this paper we present several applications of delensing focused on testing theories of early-universe inflation with observations of the CMB. We find that delensing the CMB results in improved parameter constraints for reconstructing the spectrum of primordial curvature fluctuations, probing oscillatory features in the primordial curvature spectrum, measuring the spatial curvature of the universe, and constraining several different models of isocurvature perturbations. In some cases we find that delensing can recover almost all of the constraining power contained in unlensed spectra, and it will be a particularly valuable analysis technique to achieve further improvements in constraints for model parameters whose measurements are not expected to improve significantly when utilizing only lensed CMB maps from next-generation CMB surveys. We also quantify the prospects of testing the single-field inflation tensor consistency condition using delensed CMB data; we find it to be out of reach of current and proposed experimental technology and advocate for alternative detection methods.

The Shell of the Cosmos

The Big Bang theory, widely accepted by cosmologists, explains the origin, expansion, and eventual fate of the universe. It was further developed by inflation theory, which solves issues like the horizon and flatness problems. This theory states that the Cosmic Microwave Background (CMB), a remnant of the Big Bang, permeates the entire universe. Cosmologists believe these photons were emitted during the recombination epoch, approximately 380,000 years after the Big Bang when the cosmos had a temperature of around 3,000 Kelvin. Additionally, the Lambda-Cold Dark Matter (ΛCDM) model addresses questions arising from observations of the cosmos, such as the existence of light elements like hydrogen, helium, lithium, and the anisotropy in the CMB, and eventually, the continuous expansion of space. In this model, dark energy, represented as the cosmological constant lambda (Λ), exerts negative pressure on empty space, counteracting the effects of gravity with a repulsive force. While the Standard Model of Particle Physics (SMPP) posits that the universe's matter originated from fundamental particles (quarks and leptons), it cannot explain the origin of these particles and how they came into existence, because general relativity and the SMPP cannot be integrated to explain matter production at the singularity point. T-Consciousness Cosmology introduces the ‘Spherical Cosmos Model’ (SCM) to answer questions about the cause of the explosion, expansion, and shape of the universe, the nature of ordinary matter and energy, dark matter and energy, the fate of the universe, the reason for the high density of objects in the depths of space, etc. In this model, the spherical cosmos has a shell called the ‘Shell of the Cosmos,’ made of Taheri Absolute Matter (TAM) that not only isolates it but also produces dark matter and dark energy, ordinary matter and ordinary energy, and finally space mesh from the inner surface to the inside of the cosmos since the birth of the universe. The Shell of this isolated sphere is currently expanding at a speed faster than the speed of light. In this perspective, dark matter and energy are the same space mesh that have been compressed to varying degrees. Dark energy, which is constantly being released from the Shell into the cosmos, unlike the standard model of cosmology, is one of the factors in the expansion of the isolated cosmos by creating positive pressure in it. Also in this model, the recombination epoch will always be located spherically at a certain distance from the Shell until the ultimate stage of Rebound. In other words, not only is the origin of the CMB not related to the past of the cosmos, but it also exists now, and given the vastness of the sphere and the position of the Earth within this sphere, we detect it in the microwave wavelength with a delay of several billion years. Therefore, the observed distant galaxies that have been attributed to the early epochs of the cosmos in the Big Bang model are currently being created by the Shell according to the Spherical Cosmos Model, and we are surrounded by particles and objects that are constantly being produced.

Betti Functionals as Probes for Cosmic Topology

The question of the global topology of the Universe (cosmic topology) is still open. In the ΛCDM concordance model, it is assumed that the space of the Universe possesses the trivial topology of R3, and thus that the Universe has an infinite volume. As an alternative, in this paper, we study one of the simplest non-trivial topologies given by a cubic 3-torus describing a universe with a finite volume. To probe cosmic topology, we analyze certain structure properties in the cosmic microwave background (CMB) using Betti functionals and the Euler characteristic evaluated on excursions sets, which possess a simple geometrical interpretation. Since the CMB temperature fluctuations δT are observed on the sphere S2 surrounding the observer, there are only three Betti functionals βk(ν), k=0,1,2. Here, ν=δT/σ0 denotes the temperature threshold normalized by the standard deviation σ0 of δT. The analytic approximations of the Gaussian expectations for the Betti functionals and an exact formula for the Euler characteristic are given. It is shown that the amplitudes of β0(ν) and β1(ν) decrease with an increasing volume V=L3 of the cubic 3-torus universe. Since the computation of the βk’s from observational sky maps is hindered due to the presence of masks, we suggest a method that yields lower and upper bounds for them and apply it to four Planck 2018 sky maps. It is found that the βk’s of the Planck maps lie between those of the torus universes with side-lengths L=2.0 and L=3.0 in units of the Hubble length and above the infinite ΛCDM case. These results give a further hint that the Universe has a non-trivial topology.

A Historical Review of Research on the Density-Size Correlation of the Observable Universe

This literature review explores the correlation between the density and size of celestial objects - a key subject in understanding their formation, evolution, and the potential existence of higher-order clusters. It draws attention to the two seminal papers - E. F. Carpenter's density-size correlation study and Gerard De Vaucouleurs's study on matter density in groups and clusters. While acknowledging the limitations and outdated nature of Carpenter's body of work, it underscores the need for a more contemporary, comprehensive examination across various scales from neutron stars to galaxy clusters. The review highlights how such a study can clarify questions surrounding the size and shape of the universe, address Olbers' Paradox, and contribute to theories that describe the universe's origins and dynamics.

“So, I trucked out to the border, learned to say ain’t, came to find work”: the sociolinguistics of Firefly

Abstract Firefly is a TV series that aired in 2002 and 2003 in the United States. The series belongs to the space western subgenre, which allies science fiction and western tropes by layering, in this case, a dystopian society, space travel, standoffs in desolate landscapes, and saloon brawls. This juxtaposition of genres is reflected in the language of Firefly’s characters in three ways: world-specific slang, Chinese code-switching, and features evoking Southern American English. This study explores the latter, employing quantitative methods used in variationist sociolinguistics. Using a corpus of all episodes of the series and the film Serenity (2005), we show that features reminiscent of Southern varieties of English, specifically nasal fronting and the use of ain’t, are stratified according to the social realities of the world of Firefly. Nonstandard linguistic variants are used to represent rebel smugglers as opposed to characters representing valued professions. This pattern contributes to world-building in Firefly by indexing divisions between the superpower-controlled territories and the recently settled edge of the universe. The use of realistically constrained Southern linguistic features draws upon present-day notions of linguistic (non)standardness to indicate marginality. Firefly therefore relies on its audience’s linguistic knowledge of the real world to create its fictional one.

Constraining the Spatial Curvature of the Local Universe with Deep Learning

We use the distance sum rule method to constrain the spatial curvature of the Universe with a large sample of 161 strong gravitational lensing systems, whose distances are calibrated from the Pantheon compilation of type Ia supernovae using deep learning. To investigate the possible influence of mass model of the lens galaxy on constraining the curvature parameter Ω k , we consider three different lens models. Results show that a flat Universe is supported in the singular isothermal sphere (SIS) model with the parameter . While in the power-law (PL) model, a closed Universe is preferred at the ∼3σ confidence level, with the parameter . In the extended PL model, the 95% confidence level upper limit of Ω k is <0.011. As for the parameters of the lens models, constraints on the three models indicate that the mass profile of the lens galaxy could not be simply described by the standard SIS model.

Galaxy rotation curve in hyperconical universes: a natural relativistic MOND

Abstract Modified Newtonian dynamics (MOND) and similar proposals can (at least partially) explain the excess rotation of galaxies or the equivalent mass-discrepancy acceleration, without (or by reducing) the requirement of dark matter halos. This paper develops a modified gravity model to obtain local limit to the general relativity (GR) compatible with a cosmological metric different to the standard Friedmann–Lemaître–Robertson–Walker metric. Specifically, the paper uses a distorted stereographic projection of hyperconical universes, which are 4D hypersurfaces embedded into 5D Minkowski spacetime. This embedding is a key in the MOND effects found in galactic scales. To adequately describe the mass-discrepancy acceleration relation, centrifugal force would present a small time-like contribution at large-scale dynamics due to curvature of the Universe. Therefore, the Lagrangian density is very similar to the GR but with subtracting the background curvature (or vacuum energy density) of the perturbed hyperconical metric. Results showed that the proposed model adjusts well to 123 galaxy rotation curves obtained from the Spitzer Photometry and Accurate Rotation Curves database, using only a free parameter.

Cosmological constraints in covariant f(Q) gravity with different connections

Recently it has been shown that the cosmological dynamics of covariant f(Q) gravity depend on different affine connections. In this paper, two specific f(Q) models are investigated with SNe+CC+BAO+QSO observational data, and the spatial curvature of the universe is studied in covariant f(Q) gravity. It is found that the parameters {mathcal {X}}_0 and {mathcal {X}}'_0 characterizing affine connections significantly affect the behavior of the effective equation of state w_Q and may drive it across the phantom divide line. These results imply some inertial effects of the universe change the cosmic dynamics. However based on the Bayesian evidence, the zero inertial effect is more favored in the flat universe. Moreover, a closed universe is favored not only in the Lambda CDM model but also in covariant f(Q) gravity. The f(Q) models have less support evidence than the Lambda CDM model in the non-flat universe.

Super Structure Fault-Tolerance Assessment of the Generalized Hypercube

Abstract Fault-tolerant performance of a network is the prerequisite and guarantee for the normal operation of a network, which is often characterized by connectivity. Let $H$ denote a connected subgraph of $G$ and $H^{*}$ denote the union of the set of all connected subgraphs of $H$ and the set of the trivial graph. Super $H$-connectivity (resp. super $H^{*}$-connectivity) satisfies the conditions of both super connectivity and $H$-structure connectivity (resp. $H$-substructure connectivity). These two kinds of new connectivity provide a new metric to measure the fault-tolerance of the network, that is, the super structure fault-tolerance. The generalized hypercube $G(m_{r}, m_{r-1},..., m_{1})$ is a universal topology of interconnection networks that contains other commonly used topologies and it has been applied in many data center networks because of its excellent qualities. In this paper, we research the super structure fault-tolerance of $G(m_{r}, m_{r-1},..., m_{1})$ by studying super $H$-connectivity $\kappa ^{\prime}(G|H)$ and super $H^{*}$-connectivity $\kappa ^{\prime}(G|H^{*})$ for $H\in \{K_{1,M},\ C_{3},\ C_{4},\ K_{4}\}$.

Causal structure and the geodesics in the hairy extension of the Bertotti-Robinson spacetime

A hairy extension of the Bertotti-Robinson regular spacetime has been recently introduced in the context of the Einstein-Maxwell-Scaler theory that surprisingly is a singular black hole formed in the S 3 background spatial topology [CQG39(2022)167001]. In this research, we first clarify the topology of the spacetime based on the coordinate transformations as well as the energy-momentum configuration and the causal structure of the black hole. Furthermore, we investigate the geodesics of the null and timelike particles in this spacetime. It is shown that in the radial motion on the equatorial plane, while photons may collapse to the singularity or escape to the edge of the Universe, a massive particle always collapses to the singularity. The general geodesics of null and massive particles reveal that all particles except the outgoing light ray, eventually fall into the black hole.

Gravitational radiation from binary systems in f(R) gravity: A semi-classical approach

The rate of energy loss and orbital period decay of quasi- stable compact binary systems are derived in f(R) theory of gravity using the method of a single vertex graviton emission process from a classical source. After linearising the f(R) action written in an equivalent scalar-tensor format in the Einstein frame, we identify the appropriate interaction terms between the massless spin-2 tensor mode, massive scalar mode, and the energy momentum tensor. The definition of the scalar field is related to the f(R) models. Then using the interaction vertex we compute the rate of energy loss due to spin-2 quadrupole radiation, which comes out to be the same as the Peter-Mathews formula with a multiplication factor, and also the energy loss due to the scalar dipole radiation. The total energy loss is the sum of these two contributions. Our derivation is most general as it is applicable for both arbitrary eccentricity of the binary orbits and arbitrary mass of the scalar field. Using the derived theoretical formula for the period decay of the binary systems, we compare the predictions of f(R) gravity and general relativity for the observations of four binary systems, i.e. Hulse-Taylor Binary, PSR J1141-6545, PSR J1738+0333, and PSR J0348+0432. Thus we put bound on three well-known f(R) dark energy models, namely the Hu-Sawicki, the Starobinsky, and the Tsujikawa model. We get the best constraint on f'(R 0)-1 (where R 0 is the scalar curvature of the Universe at the present epoch) from the Tsujikawa model, i.e |f'(R 0)-1| < 2.09 × 10-4. This bound is stronger than those from most of the astrophysical observations and even some cosmological observations.

Unity Formulas for the Coupling Constants and the Dimensionless Physical Constants

In this paper in an elegant way will be presented the unity formulas for the coupling constants and the dimensionless physical constants. We reached the conclusion of the simple unification of the fundamental interactions. We will find the formulas for the Gravitational constant. It will be presented that the gravitational fine-structure constant is a simple analogy between atomic physics and cosmology. We will find the expression that connects the gravitational fine-structure constant with the four coupling constants. Perhaps the gravitational fine-structure constant is the coupling constant for the fifth force. Also will be presented the simple unification of atomic physics and cosmology. We will find the formulas for the cosmological constant and we will propose a possible solution for the cosmological parameters. Perhaps the shape of the universe is Poincare dodecahedral space. This article will be followed by the energy wave theory and the fractal space-time theory.

A Model of Accelerated Expansion of the Universe Based on the Idea about a Hypothetical 4-Dimensial Substance with an Inverse Population of Energy Levels

Based on the idea of hypothetical 4-dimensial substance with an inverse population of energy levels, a model of accelerated expansion of the Universe has been developed, which describes Hubble diagrams with great accuracy for type Ia supernovae, quasars and gamma-ray burst sources at the Hubble parameter value of 67.7 km/s/Mpc, coinciding with the value obtained from analysis of inhomogeneities of relic radiation. Calculations at the Hubble parameter value of 73.5 km/s/Mpc, obtained using the ΛCDM model based on the analysis of data on type Ia supernovae and cepheids, differ markedly from the observed data. An explanation of the two values of the Hubble constant is proposed. It is shown that in this model, the magnitude of 13.8 billion years characterizes not the age of the Universe, but the time of propagation of light from those galaxes whose acceleration of removal has a minimal value. Based on the recently discovered curvature of the Universe, estimates are given of the lower limits of its size and lifetime, which turned out to be at least 270 billon years. The probability of transition from the excited state to the underlying energy levels of a hypothetical 4-dimensial substance, as well as the low of increasing energy density as a result of transitions to the underlying levels of this substance, is determined.

Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searches

The Einstein field equations of general relativity constrain the local curvature at every point in spacetime, but say nothing about the global topology of the Universe. Cosmic microwave background anisotropies have proven to be the most powerful probe of non-trivial topology since, within ΛCDM, these anisotropies have well-characterized statistical properties, the signal is principally from a thin spherical shell centered on the observer (the last scattering surface), and space-based observations nearly cover the full sky. The most generic signature of cosmic topology in the microwave background is pairs of circles with matching temperature and polarization patterns. No such circle pairs have been seen above noise in the WMAP or Planck temperature data, implying that the shortest non-contractible loop around the Universe through our location is longer than 98.5% of the comoving diameter of the last scattering surface. We translate this generic constraint into limits on the parameters that characterize manifolds with each of the nine possible non-trivial orientable Euclidean topologies, and provide a code which computes these constraints. In all but the simplest cases, the shortest non-contractible loop in the space can avoid us, and be shorter than the diameter of the last scattering surface by a factor ranging from 2 to at least 6. This result implies that a broader range of manifolds is observationally allowed than widely appreciated. Probing these manifolds will require more subtle statistical signatures than matched circles, such as off-diagonal correlations of harmonic coefficients.

Relativistic particles in curved space with a static metric using the Dunkl derivative in the Dirac operator

In this paper, we introduce matrix operator algebra involving a universal curvature constant and using the Dunkl derivative. Consequently, the Dirac equation can be written without spin connections. Iterating the Dirac equation gives the Klein–Gordon equation in its canonical form without first-order Dunkl derivatives. This leads to a new form for the static metric based on the Dunkl operator in curved space.