Homogeneous Universe Research Articles

Symmetric teleparallel cosmology with boundary corrections

We investigate the geometrodynamical effects of introducing the boundary term in symmetric teleparallel gravity. Specifically, we consider a homogeneous and isotropic universe in fQ,B, where Q is the non-metricity scalar, and B is the boundary term that relates the non-metricity and Ricci scalars. For the connection in the coincidence gauge, we find that the field equations are of fourth-order, and the fluid components introduced by the boundary are attributed to a scalar field. In the coincidence gauge, the cosmological field equations are equivalent to those of teleparallelism with a boundary term. Nevertheless, for the connection defined in the non-coincidence gauge, the geometrodynamical fluid consists of three scalar fields. We focus on the special case of fQ,B=Q+FB theory, and we determine a new analytic cosmological solution that can explain the late-time acceleration of the universe and provide a geometric mechanism for the unification of dark energy with dark matter.

Spatially homogeneous universes with late-time anisotropy

The cosmological principle asserts that on sufficiently large scales the Universe is homogeneous and isotropic on spatial slices. To deviate from this principle requires a departure from the FLRW ansatz. In this paper we analyze the cosmological evolution of two spatially homogeneous but anisotropic universes, namely the spatially closed Kantowski–Sachs Universe and the open axisymmetric Bianchi type III Universe. These models are characterized by two scale factors and we study their evolution in universes with radiation, matter and a cosmological constant. In all cases, the two scale factors evolve differently and this anisotropy leads to a lensing effect in the propagation of light. We derive explicit formulae for computing redshifts, angular diameter distances and luminosity distances and discuss the predictions of these models in relation to observations for type Ia supernovae and the CMB. We comment on the possibility of explaining the observed luminosity distance plot for type Ia supernovae within the context of cosmologies featuring late-time anisotropy and a vanishing cosmological constant.

Geodesic deviation equation in generalized hybrid metric-Palatini gravity

In the context of general relativity, the geodesic deviation equation (GDE) relates the Riemann curvature tensor to the relative acceleration of two neighboring geodesics. In this paper, we consider the GDE for the generalized hybrid metric-Palatini gravity and apply it in this model to investigate the structure of time-like, space-like, and null geodesics in the homogeneous and isotropic universe. We propose a particular case f(R,R)=R+R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(R,{{\\mathcal {R}}})=R+{{\\mathcal {R}}}$$\\end{document} to study the numerical behavior of the deviation vector η(z)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta (z)$$\\end{document} and the observer area–distance r0(z)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{0}(z)$$\\end{document} with respect to redshift z. Also, we consider the GDE in the framework of the scalar–tensor representation of the generalized hybrid metric-Palatini gravity, i.e., f(R,R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(R, {{\\mathcal {R}}} )$$\\end{document}, in which the model can be considered as dynamically equivalent to a gravitational theory with two scalar fields. Finally, we extend our calculations to obtain the modification of the Mattig relation in this model.

Generalization of instanton-induced inflation and dynamical compactification

It was shown that Yang-Mills instantons on an internal space can trigger the expansion of our four-dimensional universe as well as the dynamical compactification of the internal space. We generalize the instanton-induced inflation and dynamical compactification to general Einstein manifolds with positive curvature and also to the FLRW metric with spatial curvature. We explicitly construct Yang-Mills instantons on all Einstein manifolds under consideration and find that the homogeneous and isotropic universe is allowed only if the internal space is homogeneous. We then consider the FLRW metric with spatial curvature as a solution of the eight-dimensional Einstein-Yang-Mills theory. We find that open universe (k = −1) admits bouncing solutions unlike the other cases (k = 0, +1).

Percolation of ‘civilisation’ in a homogeneous isotropic universe

In this work, we consider the spread of a ‘civilisation’ in an idealised homogeneous isotropic universe where all the planets of interest are habitable. Following a framework that goes beyond the usual idea of percolation in common undergraduate computational physics textbooks, we investigate the behaviour of the number of colonised planets with time, and the total colonisation time for three types of universes. These include static, dark energy-dominated, and matter-dominated universes. For all these types of universes, we find a remarkable fit with the Logistic Growth Function for the number of colonised planets with time. This is in spite of the fact that for the matter- and dark-energy dominated universes, the space itself is expanding. For the total colonisation time, T, the case for a dark energy-dominated universe is marked with divergence beyond the linear regime characterised by small values of the Hubble parameter, H. Not all planets in a spherical section of this universe can be ‘colonised’ due to the presence of a shrinking Hubble sphere. In other words, the recession speeds of other planets go beyond the speed of light making them impossible to reach. On the other hand, for a matter-dominated universe, while there is an apparent horizon, the Hubble sphere is growing instead of shrinking. This leads to a finite total colonisation time that depends on the Hubble parameter characterising the Universe; in particular, we find T ∼ H for small H and T ∼ H 2 for large H.

Cosmic Evolution of Five‐dimensional Einstein Chern‐Simons Gravity Through Dark Energy Model

AbstractIn this paper, the cosmic evolution in the context of five‐dimensional Einstein Chern‐Simons gravity theory by using flat homogeneous and isotropic universe model is studied. The interaction is taken into account between dark sector of the evolving universe along with holographic dark energy model with Hubble horizon. Our study with well‐known models EChS ‐β5 and EChS ‐ for Einstein Chern‐Simons gravity theory in five dimensions are carried. Some cosmological parameters through graphical representations such as coincidence parameter u, equation of state parameter , deceleration parameter q and squared speed of sound parameter is analyzed. It is found that these cosmological parameters show consistent behavior with current cosmic scenario. Also, the behavior of generalized second law of thermodynamics in the underlying gravity theory with Bekenstein‐Hawking entropy and its validity for some fixed values of constants appearing in each model are explored.

From Homogeneous and Isotropic Universes to Braneworlds with Dynamical Tension Strings

Cosmological solutions are studied in the context of the modified measure formulation of string theory, then the string tension is a dynamical variable and the string the tension is an additional dynamical degree of freedom and its value is dynamically generated. These tensions are then not universal, rather each string generates its own tension which can have a different value for each of the string world sheets and in an ensemble of strings the values of the tensions can have a certain dispersion. We consider a new background field that can couple to these strings, the “tension scalar” which is capable of changing locally along the world sheet and then the value of the tension of the string changes accordingly. When many types of strings probing the same region of space are considered this tension scalar is constrained by the requirement of quantum conformal invariance. For the case of two types of strings probing the same region of space with different dynamically generated tensions, there are two different metrics, associated to the different strings. Each of these metrics have to satisfy vacuum Einstein’s equations and the consistency of these two Einstein’s equations determine the tension scalar. The universal metric, common to both strings generically does not satisfy Einstein’s equation. The two string dependent metrics considered here are flat space in Minkowski space and Minkowski space after a special conformal transformation. The limit where the two string tensions are the same is studied, it leads to a well defined solution. If the string tension difference between the two types of strings is very small but finite, the approximately homogeneous and isotropic cosmological solution lasts for a long time, inversely proportional to the string tension difference and then the homogeneity and isotropy of the cosmology disappears and the solution turns into an expanding Braneworld where the strings are confined between two expanding bubbles separated by a very small distance at large times.

Impact of dark energy on the equation of state in light of the latest cosmological data

Abstract We reconstruct the effective equation of state (EoS) within the framework of the general theory of relativity in a homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker universe, which is assumed to be composed of matter and dark energy (DE). Our analysis employs a dataset consisting of 31 cosmic chronometer data points, six data points of baryon acoustic oscillations, and 1048 type Ia supernovae from the Pantheon sample, and we determine the best-fitting values of the model parameters through Markov chain Monte Carlo simulation. We then use these parameter values to calculate various cosmological parameters, such as the DE EoS parameter, the energy density, the deceleration parameter, the state-finder parameters, and the Om(z) diagnostic. All the analyzed cosmological parameters show behavior consistent with the accelerated universe scenario.

A Study of Evolution of Cosmological Parameters Based on a Dark Energy Model in the Framework of Brans-Dicke Gravity

The objective of the present study is to find the characteristics of evolution of a homogeneous and isotropic universe in the framework of Brans-Dicke (BD) theory of gravity. FLRW space-time, with zero spatial curvature, has been used to obtain BD field equations. Scale factor and Hubble parameter have been obtained from an ansatz for the deceleration parameter, assumed on the basis of its property of signature flip indicating a change of phase from deceleration to acceleration. Validation of the model has been achieved by a suitable parametrization of that ansatz. Expressions for energy density, pressure, equation of state (EoS) parameter, cosmological constant, gravitational constant have been derived and depicted graphically. The gravitational constant is found to decrease with time at a gradually decreasing rate. The Hubble parameter, deceleration parameter and energy density decrease with time, which is in agreement with many other studies. The value of the EoS parameter at the present epoch is negative, and it becomes more negative with time. The cosmological constant increases very rapidly in the early universe from negative to smaller negative values, becoming positive finally, with a much slower change thereafter. A cosmographic and a geometrical analysis have been carried out. It is observed that a gradual transition takes place from a regime of quintessence to phantom dark energy. An important finding of this study is that the signature flip of the deceleration parameter takes place almost simultaneously with the signature flip of the cosmological constant, implying a connection between accelerated expansion and dark energy, which is represented here by the cosmological constant. Unlike the common practice of using arbitrary units, proper SI units for all measurable quantities have been used. This theoretical investigation provides the reader with a simple method to formulate models in the framework of BD theory.

Renyi Holographic Dark Energy Model in f(R) Gravity with Hubble's IR Cut-Off

In the present study, a homogeneous and anisotropic LRS Bianchi type-I universe model is considered with an interacting dark matter and Renyi holographic dark energy model (RHDE) in f(R) gravity. The deceleration parameter (DP) shows a signature flipping for a universe which was decelerating in past and accelerating at present epoch. Therefore, the DP is a most physically justified parameter to analyze the solution of cosmological model. In order to find an exact solution of the field equations of the model, the shear scalar is considered to be proportional to the expansion scalar. We have considered f(R) = b Rn, the depiction model of f(R) which is the function of Ricci scalar R. The physical and geometrical characteristics of the universe model have been studied.

Isotropization of symmetric teleparallel gravity with observational constraints

In this paper, we examine the homogeneous and isotropic flat Universe in the frame of symmetric teleparallel gravity say [Formula: see text] gravity (where [Formula: see text] is the nonmetricity scalar). In this work, we parametrized the field equations with the help of Hubble’s parameter defined as [Formula: see text], where [Formula: see text] and [Formula: see text] are model/free parameters which are constrained with updated 57 data points of the Hubble data set within the redshift range [Formula: see text]. For this, we have used a Markov Chain Monte Carlo Technique (MCMCT). Some physical parameters of the model are discussed. In addition, we analyze the jerk parameter and the statefinder parameters and we also study the energy conditions to assess the compatibility of our model with dark energy models; we determine that the Strong Energy Condition (SEC) is violated due to the fact that the Universe is currently accelerating.

GWSim: Python package for creating mock GW samples for different astrophysical populations and cosmological models of binary black holes

Precision cosmology with gravitational wave (GW) sources requires a deeper understanding of the interplay between GW source population and cosmological parameters governing the dynamics of the Universe. With the swift increase in GW detections, it is necessary to develop a tool for exploring many aspects of cosmology and fundamental physics; this tools allows to simulate GW mock samples for several populations and cosmological models. We have developed a new code called GWSim, which allows us to make a large sample of GW mock events from a broad range of configurations, while varying the cosmology, the merger rate, and the GW source parameters (i.e. mass and spin distributions in particular) for a given network of GW detectors. A large sample of simulated mock GW events will be useful for improving our understanding of the statistical properties of the distribution of GW sources, as long as it is detectable for a given detector noise and an astrophysical and cosmological model. It will also be useful to compare simulated samples with the observed distribution of the GW sources from data and infer the underlying population of the GW source parameters and cosmology. We restricted the cosmology to spatially flat universes, including models with varying dark energy equation of state. The GWSim code provides each mock event with a position in the sky and a redshift; these values can be those of random host galaxies coming from an isotropic and homogeneous simulated Universe or a user-supplied galaxy catalog. We used realistic detector configurations of the LIGO and Virgo network of detectors to demonstrate the performance of this code for the latest observation runs and the upcoming observation run.

Homogeneous and anisotropic universe models with bouncing deceleration parameter in $f(R,T)$ theory

In this study, we have investigated the cloud of string with perfect fluid (CSPF) matter distribution for the homogeneous and anisotropic (Bianchi I, III, and Kantowski-Sachs) universe models in the $f(R,T)$ theory. We have used the\, bouncing\, deceleration parameter, anisotropy parameter, and equation of state to obtain the exact solutions of field equations. The obtained physical and kinematic quantities were analyzed with the help of graphics. If the anisotropy parameter is zero, then our model becomes an isotropic model of the universe and the string tension vanishes in LRS Bianchi I metric. Finally, we discuss the need for further research.

Modified cosmology from quantum deformed entropy

Jalalzadeh (2022), established that the thermodynamical entropy of a quantum-deformed black hole with horizon area A can be written as Sq=πsinA8GN/sinπ2N, where N=Lq2/LP2, LP being the Planck length and Lq denoting, generically, the q-deformed cosmic event horizon distance Lq. Motivated by this, we now extend the framework constructed in Jalalzadeh (2022) towards the Friedmann and Raychaudhuri equations describing spatially homogeneous and isotropic universe dynamics. Our procedure in this paper involves a twofold assumption. On the one hand, we take the entropy associated with the apparent horizon of the Robertson–Walker universe in the form of the aforementioned expression. On the other hand, we assume that the unified first law of thermodynamics, dE=TdS+WdV, holds on the apparent horizon. Subsequently, we find a novel modified cosmological scenario characterized by quantum-deformed (q-deformed) Friedmann and Raychaudhuri equations containing additional components that generate an effective dark energy sector. Our results indicate an effective dark energy component, which can explain the Universe’s late-time acceleration. Moreover, the Universe follows the standard thermal history, with a transition redshift from deceleration to acceleration at ztran=0.5. More precisely, according to our model, at a redshift of z=0.377, the effective dark energy dominates with a de Sitter universe in the long run. We include the evolution of luminosity distance, μ, the Hubble parameter, H(z), and the deceleration parameter, q(z), versus redshift. Finally, we have conducted a comparative analysis of our proposed model with others involving non-extensive entropies.

Introduction to Hamiltonian formulation of general relativity and homogeneous cosmologies

We give a pedagogical introduction to the Hamiltonian formalism of general relativity at an advanced undergraduate and graduate levels. After covering the mathematical pre-requisites as well as the 3+1-decomposition of spacetime, we proceed to discuss the Arnowitt-Deser-Misner (ADM) formalism (a Hamiltonian approach) of general relativity. Then we proceed to give a brief but self-contained introduction to homogeneous (but not necessarily isotropic) universes and discuss the associated Bianchi classification. We first study their dynamics in the Lagrangian formulation, followed by the Hamiltonian formulation to show the equivalence of both approaches. We present a variety of examples to illustrate the ADM formalism: (i) free & massless scalar field coupled to homogeneous (in particular, Bianchi IX) universe, (ii) scalar field with a potential term coupled to Bianchi IX universe, (iii) electromagnetic field coupled to gravity in general, and (iv) electromagnetic field coupled to Bianchi IX universe.

Dynamic dark energy from the local limit of nonlocal gravity

Nonlocal gravity (NLG), a classical extension of Einstein’s theory of gravitation, has been studied mainly in linearized form. In particular, nonlinearities have thus far prevented the treatment of cosmological models in NLG. In this essay, we discuss the local limit of NLG and apply this limit to the expanding homogenous and isotropic universe. The theory only allows spatially flat cosmological models; furthermore, de Sitter spacetime is forbidden. The components of the model will have different dynamics with respect to cosmic time as compared to the standard [Formula: see text]CDM model; specifically, instead of the cosmological constant, the modified flat model of cosmology involves a dynamic dark energy component in order to account for the accelerated phase of the expansion of the universe.

Comparison of energy conditions in general relativity and modified theories of gravity

To make a comparison of energy conditions in the theory of general relativity and in the modified theories, we have considered [Formula: see text], [Formula: see text] and [Formula: see text] theories (where [Formula: see text] and [Formula: see text] are the Ricci scalar and trace of the energy–momentum tensor, respectively, while [Formula: see text]) to test the validity of all the four energy conditions. These energy conditions had been derived to check the viability of cosmological as well as astrophysical models. In this paper, we consider the standard Friedmann–Robertson–Walker spacetime representing the homogeneous and isotropic universe, and investigate the available literature on testing energy conditions as well as calculate these conditions ourselves. In order to provide the comparative results, we test these conditions analytically as well as graphically and present how energy bounds in modified theories depend on the values of the involved parameters and its validity within certain limits. We discuss here, that which of the modified theories comply with certain energy conditions, and hence provide a supporting argument on the existence of modified theories.

Dark energy–matter equivalence by the evolution of cosmic equation of state

We consider a model-independent approach to constrain the equivalence redshift, zeq, at which dark energy and the total matter (cold dark matter and baryonic) equate their magnitudes. To this aim, in the context of a homogeneous and isotropic universe, we first consider a generic model where the dark energy contribution is provided by an unknown function of barotropic fluids. Afterwards, we compute the deceleration and jerk parameters, evaluating at our epoch, namely z=0, and at z=zeq. Thus, by Taylor expanding around current time the Hubble rate, luminosity and angular distances, we substitute the theoretical expressions obtained from the aforementioned generic dark energy model, defining a correspondence between quantities evaluated at z=0 and z=zeq. In so doing, we directly fit these quantities by means of current data sets, involving the most recent Pantheon type Ia supernovae, baryonic acoustic oscillation and Hubble rate points. We consider two hierarchies in our fitting procedures and compare our findings in the spatially-flat universe first and including spatial curvature, later. We assess constraints on the overall equation of state of the universe and its first derivative. We compare our results with those predicted by the standard ΛCDM paradigm. Specifically, our findings are in agreement at the 2σ confidence level, assuming a constant dark energy term. However, our analysis does not rule out the possibility of a slight evolution of dark energy, indicating a small deviation from the scenario of a pure cosmological constant. In particular, the possible departures appear consistent with a phenomenological ωCDM model, rather than more complicated dark energy parameterizations.

A non-singular early-time viscous cosmological model

In this paper, we study the thermodynamical and mathematical consistencies for a non-singular early-time viscous cosmological model known as soft-Big Bang, which was previously found in [N. Cruz, E. González and J. Jovel, Phys. Rev. D 105, 024047 (2022)]. This model represents a flat homogeneous and isotropic universe filled with a dissipative radiation fluid and a cosmological constant [Formula: see text], which is small but not negligible, in the framework of Eckart’s theory. In particular, we discuss the capability of the solution in the fulfillment of the three following conditions: (i) the near equilibrium condition, which is assumed in Eckart’s theory of non-perfect fluids, (ii) the mathematical stability of the solution under small perturbations, and (iii) the positiveness of the entropy production. We have found that this viscous model can describe the radiation domination era of the [Formula: see text]CDM model and, at the same time, fulfill the three conditions mentioned by the fulfillment of a single constraint on the bulk viscous coefficient [Formula: see text], finding also that this non-singular model has a positive energy density in the infinity past which is infinity hotter with a constant entropy.

The Big Bang could be anisotropic. The case of Bianchi I model

We consider an evolution of anisotropic cosmological model on the example of the Bianchi type I homogeneous Universe. It is filled by the mixture of matter and dark energy with an arbitrary barotropic equation of state (EoS). The general solution for this case is found and analyzed. A complete list of possible future singularities for this model is given. Some new solution were obtained for a particular EoSs, e.g. for the Bianchi type I ΛCDM homogeneous model. It is shown that all special cases corresponding to different EoSs have common properties, provided that now or at another moment of time the Universe is expanding, and the density of the mixture is positive. Then the evolution always begins with an anisotropic ‘Big Bang’ which happened a finite time ago. After that the Universe is constantly expanding and in all cases, with rare exceptions, becomes more isotropic. A particularly strong isotropization is associated with the epoch of inflation. After its completion, the expansion of the Universe becomes almost isotropic, and this case cannot be distinguished from isotropic by astronomical observations. This fact allows us to consider an anisotropic cosmological model as a possible candidate for the description of the observed Universe despite the isotropic pattern of expansion.