Non-flat Universe Research Articles

Non-singular non-flat universes

The quest to understand better the nature of the initial cosmological singularity is with us since the discovery of the expanding universe. Here, we propose several non-flat models, among them the standard cosmological scenario with a critical cosmological constant, the Einstein–Cartan cosmology, the Milne–McCrea universe with quantum corrections and a non-flat universe with bulk viscosity. Within these models, we probe into the initial singularity by using different techniques. Several nonsingular universes emerge, one of the possibilities being a static non-expanding and stable Einstein universe.

Barrow holographic dark energy in a nonflat universe

We construct Barrow holographic dark energy in the case of nonflat universe. In particular, considering closed and open spatial geometry we extract the differential equations that determine the evolution of the dark-energy density parameter, and we provide the analytical expression for the corresponding dark energy equation-of-state parameter. We show that the scenario can describe the thermal history of the universe, with the sequence of matter and dark energy epochs. Comparing to the flat case, where the phantom regime is obtained for relative large Barrow exponents, the incorporation of positive curvature leads the universe into the phantom regime for significantly smaller values. Additionally, in the case of negative curvature we find a reversed behavior, namely for increased Barrow exponent we acquire algebraically higher dark-energy equation-of-state parameters. Furthermore, we confront the scenario with Hubble parameter measurements and supernova type Ia data. Hence, the incorporation of slightly non-flat spatial geometry to Barrow holographic dark energy improves the phenomenology while keeping the new Barrow exponent to smaller values.

Global Dynamics of the Hořava–Lifshitz Cosmological Model in a Non-Flat Universe with Non-Zero Cosmological Constant

When the cosmological constant is non-zero, the dynamics of the cosmological model based on Hořava–Lifshitz gravity in a non-flat universe are characterized by using the qualitative theory of differential equations.

Testing the consistency between cosmological data: the impact of spatial curvature and the dark energy EoS

The results of joint analyses of available cosmological data have motivated an important debate about a possible detection of a non-zero spatial curvature. If confirmed, such a result would imply a change in our present understanding of cosmic evolution with important theoretical and observational consequences. In this paper we discuss the legitimacy of carrying out joint analyses with the currently available data sets and explore their implications for a non-flat universe and extensions of the standard cosmological model. We use a robust tension estimator to perform a quantitative analysis of the physical consistency between the latest data of Cosmic Microwave Background, type Ia supernovae, Baryonic Acoustic Oscillations and Cosmic Chronometers. We consider the flat and non-flat cases of the ΛCDM cosmology and of two dark energy models with a constant and varying dark energy EoS parameter. The present study allows us to better understand if possible inconsistencies between these data sets are significant enough to make the results of their joint analyses misleading, as well as the actual dependence of such results with the spatial curvature and dark energy parameterizations. According to our results, we conclude that a joint analysis in the context of a non-flat universe including the CMB data is only possible if the CMB Lens is taken into account, otherwise, it potentially leads to misleading conclusions.

Constraints on Non-Flat Starobinsky f(R) Dark Energy Model.

We study the viable Starobinsky dark energy model in spatially non-flat FLRW backgrounds, where with and representing the characteristic curvature scale and model parameter, respectively. We modify CAMB and CosmoMC packages with the recent observational data to constrain Starobinsky gravity and the density parameter of curvature . In particular, we find the model and density parameters to be at 68% C.L. and at 95% C.L., respectively. The best fitting result shows that , indicating that the viable gravity model is consistent with CDM when is set as a free parameter. We also evaluate the values of AIC, BIC and DIC for the best fitting results of and CDM models in the non-flat universe.

Barrow HDE model for Statefinder diagnostic in non-flat FRW universe

In this work, we study a non-flat Friedmann–Robertson–Walker universe filled with a pressure-less dark matter (DM) and Barrow holographic dark energy (BHDE) whose IR cutoff is the apparent horizon. Among various DE models, (BHDE) model shows the dynamical enthusiasm to discuss transition phase of the universe. According to the new research, the universe transitioned smoothly from a decelerating to an accelerating phase of expansion in the recent past. We exhibit that the development of q relies upon the type of spatial curvature. Here we study the equation of state (EoS) parameter for the BHDE model to determine the cosmological evolution for the non-flat universe. The (EoS) parameter and the deceleration parameter (DP) show the satisfactory behaviour and it does not cross the phantom line. We also plot the statefinder diagram to characterize the properties of the BHDE model by taking distinct values of the barrow exponent △. Moreover, we likewise noticed the BHDE model in the (ωD−ωD′) plane, which can furnish us with a valuable, powerful finding to the mathematical determination of the statefinder. In the statefinder trajectory, this model was found to be able to reach the ΛCDM fixed point.

Tachyon model of Tsallis holographic dark energy

In this paper, we consider the correspondence between the tachyon dark energy model and the Tsallis holographic dark energy scenario in an FRW universe.We demonstrate the Tsallis holographic description of tachyon dark energy in an FRW universe and reconstruct the potential and basic results of the dynamics of the scalar field which describe the tachyon cosmology. In a flat universe, in the tachyon model of Tsallis holographic dark energy, independent of the existence of interaction between dark energy and matter or not, \dot{T}^2 must always be zero. Therefore, the equation of state {\omega}_D is always -1 in such a flat universe. For a non-flat universe, \dot{T}^2 cannot be zero so that {\omega}_D=-1 which cannot be used to explain the origin of the cosmological constant. \dot{T}^2 monotonically decreases with the increase in \cos(R_h/a) and \cosh(R_h/a) for different {\delta}'s. In particular, for an open universe, \dot{T}^2 is always larger than zero, while for a closed universe, \dot{T}^2 is always smaller than zerowhich is physically invalid. In addition, we conclude that with the increase in \cos(R_h/a) and \cosh(R_h/a), \dot{T}^2 always decreases monotonically irrespective of the value of b^2.

Gravitational waves for some dark energy models in FRW Universe

We study the gravitational waves phenomena for generalized Chaplygin gas, variable modified Chaplygin gas and some parametrizations of dark energy models. Motivated by their works, here we consider the Friedmann–Robertson–Walker (FRW) model of the non-flat Universe in the presence of dark matter with dark energy and we investigate the gravitational waves phenomena for some other candidates of dark energy like tachyonic field, generalized cosmic Chaplygin gas, new variable modified Chaplygin gas and Van der Waals fluid. By considering the individual conservation laws of dark matter and the dark energy components, we obtain the solutions of energy densities of the dark matter and dark energy components separately in terms of redshift. Next, we get the evolution equation for gravitational waves in FRW Universe. Then we analyze the natures of wave curves and their power spectrums for tachyonic field, generalized cosmic Chaplygin gas, new variable modified Chaplygin gas, and Van der Waals fluid.

Cosmological bound on neutrino masses in the light of H0 tension

Although cosmic microwave background (CMB) is a critical component of cosmological probes of neutrino masses, it has trouble with local direct measurements of ${H}_{0}$, and this is called the ${H}_{0}$ tension. Since neutrino masses are correlated with ${H}_{0}$ in CMB, one can expect the cosmological bound on neutrino masses would be much affected by the ${H}_{0}$ tension. We investigate what impact this tension brings to the cosmological bound on neutrino masses by assuming a model with early recombination in the framework allowing a nonflat Universe which has been shown to resolve the tension. We argue that constraints on neutrino masses become significantly weaker in models where the ${H}_{0}$ tension can be resolved.

Interacting Rényi Holographic Dark Energy in the Brans-Dicke Theory

In this work, we construct an interacting model of the Rényi holographic dark energy in the Brans-Dicke theory of gravity using Rényi entropy in a spatially flat Friedmann-Lemaître-Robertson-Walker Universe considering the infrared cut-off as the Hubble horizon. In this setup, we then study the evolutionary history of some important cosmological parameters, in particular, deceleration parameter, Hubble parameter, equation of state parameter, and Rényi holographic dark energy density parameter in both nonflat Universe and flat Universe scenarios and also observe satisfactory behaviors of these parameters in the model. We find that during the evolution, the present model can give rise to a late-time accelerated expansion phase for the Universe preceded by a decelerated expansion phase for both flat and nonflat cases. Moreover, we obtain ω D → − 1 as z → − 1 , which indicates that this model behaves like the cosmological constant at the future. The stability analysis for the distinct estimations of the Rényi parameter δ and coupling coefficient b 2 has been analyzed. The results indicate that the model is stable at the late time.

Eppur è piatto? The Cosmic Chronometers Take on Spatial Curvature and Cosmic Concordance

Abstract The question of whether cosmic microwave background (CMB) temperature and polarization data from Planck favor a spatially closed universe with curvature parameter Ω K < 0 has been the subject of recent intense discussions. Attempts to break the geometrical degeneracy combining Planck data with external data sets such as baryon acoustic oscillation (BAO) measurements all point toward a spatially flat universe at the cost of significant tensions with Planck, which makes the resulting data set combination problematic. Settling this issue requires identifying a data set that can break the geometrical degeneracy while avoiding these tensions. We argue that cosmic chronometers (CCs), measurements of the expansion rate H(z) from the relative ages of massive early-type passively evolving galaxies, are the data set we are after. Furthermore, CCs come with the additional advantage of being virtually free of cosmological model assumptions. Combining Planck 2018 CMB temperature and polarization data with the latest CCs, we break the geometrical degeneracy and find Ω K = −0.0054 ± 0.0055, consistent with a spatially flat universe and competitive with the Planck+BAO constraint. Our results are stable against minimal parameter space extensions and CC systematics, and we find no substantial tension between Planck and CC data within a nonflat universe, making the resulting combination reliable. Our results allow us to assert with confidence that the universe is spatially flat to the level, a finding that might possibly settle the ongoing spatial curvature debate and lends even more support to the already very successful inflationary paradigm.

The growth factor parametrization versus numerical solutions in flat and non-flat dark energy models

In the present investigation we use observational data of f sigma _ {8} to determine observational constraints in the plane (Omega _{m0},sigma _{8}) using two different methods: the growth factor parametrization and the numerical solutions method for density contrast, delta _{m}. We verified the correspondence between both methods for three models of accelerated expansion: the Lambda CDM model, the w_{0}w_{a} CDM model and the running cosmological constant RCC model. In all case we consider also the curvature as free parameter. The study of this correspondence is important because the growth factor parametrization method is frequently used to discriminate between competitive models. Our results we allow us to determine that there is a good correspondence between the observational constrains using both methods. We also test the power of the fsigma _ {8} data to constraints the curvature parameter within the Lambda CDM model. For this we use a non-parametric reconstruction using Gaussian processes. Our results show that the fsigma _ {8} data with the current precision level does not allow to distinguish between a flat and non-flat universe.

Rényi holographic dark energy in the Brans–Dicke cosmology

In this paper, we construct a holographic dark energy (HDE) model considering the IR cut-off as Hubble horizon, holographic hypothesis, and using the generalized Rényi entropy, and investigate its cosmological outcomes in Brans–Dicke gravity without interaction. We observe the suitable behavior for the cosmological parameters, involving the deceleration parameter, the equation of state (EoS) parameter, and the density parameter in both flat and non-flat Universes. It is also concluded by the stability analysis that the Rényi holographic dark energy (RHDE) model is classically stable at present and future for the Rényi parameter [Formula: see text] in both flat and non-flat Universe.

Running vacuum model in a non-flat universe * * Supported in part by National Center for Theoretical Sciences, MoST (MoST-107-2119-M-007-013-MY3), National Natural Science Foundation of China (11505004, 11447104) and the Anhui Provincial Natural Science Foundation of China (1508085QA17)

We investigate observational constraints on the running vacuum model (RVM) of in a spatially curved universe, where is the model parameter, corresponds to the spatial curvature constant, represents the scalar factor, and is a constant defined by the boundary conditions. We study the CMB power spectra with several sets of and in the RVM. By fitting the cosmological data, we find that the best fitted value for RVM is slightly smaller than that of CDM in the non-flat universe, along with the constraints of (68% C.L.) and (95% C.L.). In particular, our results favor the open universe in both CDM and RVM. In addition, we show that the cosmological constraints of (RVM) and ( CDM) at 95% C.L. for the neutrino mass sum are relaxed in both models in the spatially curved universe.

Dark energy–dark matter interactive model with time-varying lambda in Kaluza–Klein metric

The dark energy (DE)–dark matter (DM) interaction in cosmology is modeled considering Kaluza–Klein metric (five-dimensional FRW (Friedman–Robertson–Walker) metric) with time-varying cosmological constant (Λ). Λ is considered inversely proportional to square of the scalar factor (R−2). An interaction term (Q) introduced between DE and DM is proportional to dark matter density (ρm) and Hubble’s constant H, which facilitates analysis of energy transfer from DE to DM. Other physical parameters are also obtained and studied for flat and non-flat universe. The ratio of dark energy to dark matter density being a constant enables to deal with the cosmological coincidence problem. Phantom cross-behavior is also studied with this model.

Determining Model-independent H0 and Consistency Tests

Abstract We determine the Hubble constant H 0 precisely (2.3% uncertainty) in a manner independent of the cosmological model through Gaussian process regression, using strong lensing and supernova data. Strong gravitational lensing of a variable source can provide a time-delay distance D Δt and angular diameter distance to the lens D d. These absolute distances can anchor Type Ia supernovae, which give an excellent constraint on the shape of the distance–redshift relation. Updating our previous results to use the H0LiCOW program’s milestone data set consisting of six lenses, four of which have both D Δt and D d measurements, we obtain for a flat universe and for a non-flat universe. We carry out several consistency checks on the data and find no statistically significant tensions, though a noticeable redshift dependence persists in a particular systematic manner that we investigate. Speculating on the possibility that this trend of derived Hubble constant with lens distance is physical, we show how this can arise through modified gravity light propagation, which would also impact the weak lensing σ 8 tension.

Supernova Magnitude Evolution and PAge Approximation

Abstract The evidence of environmental dependence of SN Ia luminosity has inspired recent discussion about whether the late-universe cosmic acceleration is still supported by supernova data. We adopt the ΔHR/Δage parameter, which describes the dependence of supernova absolute magnitude on the age of supernova progenitor, as an additional nuisance parameter. Using the Pantheon supernova data, a lower bound ≥12 Gyr on the cosmic age, and a Gaussian prior on the Hubble constant, we reconstruct the cosmic expansion history. Within the flat Λ cold dark matter framework, we still find a 5.6σ detection of cosmic acceleration. This is because a matter-dominated decelerating universe would be too young to accommodate observed old stars with age ≳12 Gyr. A decelerating but non-flat universe is marginally consistent with the data, however, only in the presence of a negative spatial curvature ∼2 orders of magnitude beyond the current constraint from cosmic microwave background data. Finally, we propose a more general parameterization based on the cosmic age (PAge), which is not directly tied to the dark energy concept and hence is ideal for a null test of the cosmic acceleration. We find that, for a magnitude evolution rate ΔHR/Δage ≲ 0.3 mag/5.3 Gyr, a spatially flat and decelerating PAge universe is fully consistent with the supernova data and the cosmic age bound, and has no tension with the geometric constraint from the observed cosmic microwave background acoustic angular scales.

Statefinder hierarchy for Tsallis holographic dark energy

We apply the cosmological statefinder hierarchy to diagnose Tsallis holographic dark energy (THDE) models, which has been suggested by Tavayef et al. (2018), a new class of holographic dark energy (HDE) models in the non-flat universe. The IR cut off for the Tsallis holographic dark energy is taken as the apparent horizon. The evolutionary trajectories of statefinder hierarchy S31 and S41 against redshift z has been plotted. We observe from the evolutionary trajectories of S31 and S41, the statefinder hierarchy parameter S31 and S41 performs almost the same behavior and corresponds to the ΛCDM model in the future for all the three cases i.e flat, open and closed Universes.

Dynamics of dark energy and scalar field models in non-flat universe

This Paper is devoted to study the effects of different scalar field models under the influence of interacting generalized ghost pilgrim dark energy model in the framework of non-flat FRW universe. For this purpose, we examine the behavior of equation of state and Hubble parameters for two different values of interaction term. Moreover, we consider Lagrangian density of quintessence, tachyon, k-essence and dilaton models to check the consistency of dark energy model with scalar field models. We also evaluate their corresponding potentials and discuss the behavior of kinetic as well as potential energies graphically. We also check the consistency of fractional density of matter and dark energy with Planks 2018.

Diagnosing interacting Tsallis holographic dark energy in the non-flat universe

This paper explores the interacting Tsallis holographic dark energy (THDE) model in a non-flat universe following an infrared cutoff as the apparent horizon. The equation of state (EoS) and the deceleration parameter of THDE model are determined to understand the cosmological evolution for interacting THDE model in the non-flat universe. By applying the statefinder [Formula: see text] parameter-pairs diagnostic and [Formula: see text] pair dynamical analysis for the derived THDE model, we plot the evolutionary trajectories for different cases of Tsallis parameter [Formula: see text] and interaction term [Formula: see text] and also, for spatial curvature [Formula: see text], [Formula: see text] and [Formula: see text] corresponding to flat, open and closed universes, respectively, in the framework of Planck 2018 base cosmology results VI-LCDM observational data.