Narrow Results

This study focuses on a spacetime admitting quasi-constant curvature tensor. Several properties of this spacetime are found. Also, such a spacetime satisfying a critical point equation is analyzed. Considering some special situations of this spacetime, some novel properties of this spacetime are examined. Some remarkable results about these subjects are obtained.

In this work, the cosmic solutions, particularly the well-known $\mathrm{\Lambda }$CDM model, are investigated in the framework of the Gauss–Bonnet (GB) gravity, where the gravitational action incorporates the GB invariant function. We utilize a specialized formulation of the deceleration parameter in terms of the Hubble parameter $H$, given by $q=-1-\frac{Ḣ}{H^2}$, to solve the field equations. To identify the appropriate model parameters, we align them to the most recent observational datasets, which include 31 data points from the Cosmic Chronometers, Pantheon+, and BAO datasets. The physical characteristics of the cosmographic parameters, such as pressure and energy density, that correlate to the limited values of the model parameters, are examined. The evolution of the deceleration parameter suggests a transition from a decelerated to an accelerated phase of the universe. Additionally, we examine the stability of the assumed model and provide an explanation for late-time acceleration using the energy conditions. The behavior of the equation of state parameter has been analyzed through dynamical variables by constraining various parameters in light of the recent observational data. This study has resulted in a quintessence-like evolution.

In this paper, we use a set of observational H(z) data (OHD) to constrain the ΛCDM cosmology. This data set can be derived from the differential ages of the passively evolving galaxies. Meanwhile, the -parameter, which describes the Baryonic Acoustic Oscillation (BAO) peak, and the newly measured value of the Cosmic Microwave Background (CMB) shift parameter are used to present combinational constraints on the same cosmology. The combinational constraints favor an accelerating flat universe while the flat ΛCDM cosmology is also analyzed in the same way. We obtain a result compatible with that by many other independent cosmological observations. We find that the observational H(z) data set is a complementarity to other cosmological probes.

The Hubble parameter is a critical measurement in cosmology, which contains the most direct information of the cosmic expansion history. Since discrepancy is found between low redshift and high redshift estimations of Hubble constant, we are interested in whether that tension indicates dynamical dark energy. In this paper, we emphasize that the observed Hubble parameters at various redshifts, along with observed Hubble constant, can help us in probing the evolutional behavior of the mysterious dark energy. Null hypothesis tests are carried out with two diagnostic approaches. We find out that, according to the present measurements of Hubble parameters, rejection of constant dark energy is captured at 1σ level from null tests with and without the observed value of Hubble constant.

We turn our attention on evaluating the most recent Hubble parameter data measured via the differential evolution of cosmic-chronometers from a deep learning perspective. To achieve this goal, we start our investigation by introducing the selected theoretical setup and compiling the most recent statistical data obtained in cosmology experiments. Then we implement a tuned version of the long-short term memory (LSTM) architecture and run it to predict possible values of the Cosmic Hubble parameter for different red-shift states. Since we observe a good correlation between the observed and predicted datasets of the Hubble parameter, we conclude that the machine learning approaches can play important roles in the future cosmology investigations.

We consider the brane universe in the bulk background of the topological Reissner–Nordström de Sitter black holes. We show that the thermodynamic quantities (including entropy) of the dual CFT take usual special forms expressed in terms of Hubble parameter and its time derivative at the moment, when the brane crosses the black hole horizon or the cosmological horizon. We obtain the generalized Cardy–Verlinde formula for the CFT with a charge and cosmological constant, for any values of the curvature parameter k in the Friedmann equations.

We study spatially homogeneous and anisotropic Bianchi-V perfect fluid cosmological model with variable G and Λ. Exact solutions to the field equations in the case of particle creation and in the absence of particle creation are obtained by assuming a constant deceleration parameter. The model has a big-bang-type singularity at the initial time t = 0. We find that a constant value of deceleration parameter is reasonable for a description of the present day universe. We also observe that the variable G does not necessarily imply particle creation. The behavior of observationally important parameters such as the expansion scalar, mean anisotropic parameter and shear scalar are discussed. It is observed that the solutions are compatible with the results of recent observations.

In the $\mathrm{\Lambda }$CDM model, dark energy is viewed as a constant vacuum energy density, the cosmological constant in the Einstein–Hilbert action. This assumption can be relaxed in various models that introduce a dynamical dark energy. In this paper, we argue that the mixing between infrared (IR) and ultraviolet (UV) degrees of freedom in quantum gravity leads to infinite statistics, the unique statistics consistent with Lorentz invariance in the presence of nonlocality, and yields a fine structure for dark energy. Introducing IR and UV cutoffs into the quantum gravity action, we deduce the form of $\mathrm{\Lambda }$ as a function of redshift and translate this to the behavior of the Hubble parameter.

Constraints on the Hubble parameter, H₀, via X-ray surface brightness and Sunyaev–Zel'dovich effect (SZE) observations of the galaxy clusters depend on the validity of the cosmic distance duality relation (DD relation), η = D_L(z)(1+z)^-2/D_A(z) = 1, where D_L and D_A are the luminosity distance and angular diameter distance (ADD), respectively. In this work, we argue that if the DD relation does not hold, the X-ray plus SZE technique furnishes a . We use 25 ADD of galaxy clusters to obtain simultaneous constraints on H₀ and possible violation of the DD relation in a flat ΛCDM model. Such a violation is parametrized by two functions: η(z) = 1 + η₀z and η(z) = 1 + η₀z/(1+z), where η₀ is a constant parameter quantifying possible departures from the strict validity. Finally, by marginalizing on the η₀ in both parametrizations, we obtain constraints on H₀ regardless of the validity of the DD relation. For the linear and nonlinear η(z) functions, we obtain km/s/Mpc and km/s/Mpc, respectively (without systematic errors). Our results support recent H₀ measurements by using X-ray and SZE observations of galaxy clusters which have taken the distance duality as valid.

We address some recent erroneous claim that H₀ observations are difficult to accommodate with LTB cosmological models, showing how to construct solutions in agreement with an arbitrary value of H₀ by rewriting the exact solution in terms of dimensionless parameters and functions. This approach can be applied to fully exploit LTB solutions in designing models alternative to dark energy without making any restrictive or implicit assumption about the inhomogeneity profile. The same solution can also be used to study structure formation in the regime in which perturbation theory is not enough and an exact solution of the Einstein's equation is required, or to estimate the effects of a local inhomogeneities on the apparent equation of state of dark energy.

Using comoving distance $d_c$ and angular diameter distance $d_A$, we recalculate parameters describing kinematical state of the universe, still combining the kinematical model of universe but not relying on dynamical equations for gravity. Comoving distance $d_c$ comes from Hubble data $H(z)$ and is more reliable. Angular diameter distance $d_A$ comes from SZE (Sunyaev–Zel’dovich Effect) and X-ray data, and needs calibration. In low redshift case, we use expansion of relation between luminosity distance and redshift about redshift $z$; in high redshift case, we take variable substitution $y=1/(1+z)$, and expand the relation between luminosity distance and redshift about variable $y$ in order to reduce computational errors. Finally, we get the more precise value of Hubble parameter $H_0=69.13\pm 0.24$ km ⋅ s${}^{-1}\cdot {\mathrm{\text{Mpc}}}^{-1}$, corresponding to $0.4\%$ uncertainty in $68.3\%$ confidence region, also deceleration factor $q_0=-0.57\pm 0.04$ and acceleration rate $j_0=1.28\pm 0.33$, and their statistical values and probability graph. We compare the values of $H_0$, $q_0$ and $j_0$ with those obtained from other observation data and model.

The recent analysis of low-redshift supernovae (SN) has increased the apparent tension between the value of $H_0$ estimated from low and high redshift observations such as the cosmic microwave background (CMB) radiation. At the same time other observations have provided evidence of the existence of local radial inhomogeneities extending in different directions up to a redshift of about $0.07$. About $40\%$ of the Cepheids used for SN calibration are directly affected because they are located along the directions of these inhomogeneities. We compute with different methods the effects of these inhomogeneities on the low-redshift luminosity and angular diameter distance using an exact solution of the Einstein’s equations, linear perturbation theory and a low-redshift expansion. We confirm that at low redshift the dominant effect is the nonrelativistic Doppler redshift correction, which is proportional to the volume averaged density contrast and to the comoving distance from the center. We derive a new simple formula relating directly the luminosity distance to the monopole of the density contrast, which does not involve any metric perturbation. We then use it to develop a new inversion method to reconstruct the monopole of the density field from the deviations of the redshift uncorrected observed luminosity distance respect to the $\mathrm{\Lambda }$CDM prediction based on cosmological parameters obtained from large scale observations. The inversion method confirms the existence of inhomogeneities whose effects were not previously taken into account because the $2M++$ [G. Lavaux and M. J. Hudson, Mon. Not. R. Astron. Soc.416 (2011) 2840] density field maps used to obtain the peculiar velocity [J. Carrick et al., Mon. Not. R. Astron. Soc.450 (2015) 317] for redshift correction were for $z\le 0.06$, which is not a sufficiently large scale to detect the presence of inhomogeneities extending up to $z=0.07$. The inhomogeneity does not affect the high redshift luminosity distance because the volume averaged density contrast tends to zero asymptotically, making the value of $H_0^{\mathrm{\text{CMB}}}$ obtained from CMB observations insensitive to any local structure. The inversion method can provide a unique tool to reconstruct the density field at high redshift where only SN data is available, and in particular to normalize correctly the density field respect to the average large scale density of the Universe.

A modified and generalised Chaplygin gas (MCG, $B\ne 0.0$ and GCG, $B=0.0$) has been separately chosen here as a constituent of the universe. Concept of state finder and Om diagnostics are introduced to track the dark energy in the models. Here, observed Hubble data (OHD) and binned Pantheon data of supernovae are used to determine the best-fit equation-of-state (EoS) parameters of these models and these are compared with the $\mathrm{\Lambda }$CDM model. The best-fit value and expected values of cosmological jerk parameter $j$, snap parameter $s$ are determined, which are close to each other. A plot of $j,s$ with red-shift, with themselves, as well as with deceleration parameter $q$, shows the evolution of the universe and its possible future. Variations of $q$ and EoS parameter $\omega$ with red-shift show acceleration–deceleration phase transition in the recent past. Lastly, the state finder pair $(j,s)$ and Om diagnostic have been utilized to discriminate the models.

In this work, Friedmann–Robertson–Walker model is investigated in $f(R,T)=R+\alpha T+\beta T^2$ gravity for a perfect fluid by a numerical analysis. In order to solve the modified field equations, we use a new solution method based on to propose the functional forms of the energy density and the pressure. In this context, in keeping with the recent indications of the observed universe, we consider two different propositions. We show for both propositions that the behaviors of the Hubble and the deceleration parameters are consistent with astrophysical observations and the model depicts de Sitter universe. It is also shown that the model incorporates the initial radiation-dominated era, and it is dominated by a quintessence like fluid at late era for both the propositions.

In this work, we have proposed a simple parametrization for the pressure component $p(z)$ of the dark energy model and have studied the cosmological implications of this model in the framework of $f(Q)$ modified gravity theory, aka, the symmetric teleparallel gravity theory, where Q is known as the nonmetricity scalar. By considering a particular parametric form of $p(z)$, we obtained the Hubble solution for the $f(Q)$ modified gravity model. In order to see whether this model is consistent with or challenges the $\mathrm{\Lambda }$CDM limits, we tried to put constraints on the model parameters using the recent observational datasets like Hubble data, Cosmic Chronometer data, Type Ia Supernovae (SNIa) data, baryonic acoustic oscillations (BAO) data. We have employed the ${\chi }^2$ minimization technique and have carried out the Markov Chain Monte Carlo (MCMC) analysis using emcee package. We have found that the deceleration parameter shows a smooth transition from positive to negative value in recent past which is essential for the structure formation of the Universe. It has been found that the parametric form of the dark energy pressure parameter is consistent with current cosmological scenario.

In this paper, we propose a simple parametrization of the Hubble parameter (HP) $H$ in order to explain the late-time cosmic acceleration. We show that our proposal covers many models obtained in different schemes of parametrization under one umbrella. We demonstrate that a simple modification in the functional form of HP can give rise to interesting cosmological phenomena such as big rip singularity, bounce and others. We have also constrained the model parameters using the latest 28 points of $H(z)$ data for three cases which admit transition from deceleration to acceleration.

In this paper, we considered the study of Friedmann–Robertson–Walker (FRW) model in the framework of $f(Q,T)$ gravity, an extension of symmetric teleparallel gravity, recently defined by Xu et al. [$f(Q,T)$ gravity, Eur. Phys. J. C 79 (2019) 708]. The nonlinear model $f(Q,T)=-\alpha Q-\beta T^2$, where $\alpha >0$ and $\beta >0$ are constants, is taken into account. The equation of state of perfect fluid is assumed and 31 points of Hubble data are used to constrain the value of model parameter. To explore the evolution of the universe, the numerical solutions of cosmological implications, such as Hubble parameter, deceleration parameter, apparent magnitude and luminosity distance, are determined and the energy conditions are examined. The theoretical results of Hubble parameter are compared with $\mathrm{\Lambda }$CDM model. Further, 57 Supernova data (42 from Supernova cosmology project and 15 from Calán/Tolono supernova survey) are also used to have consistent results of apparent magnitude and luminosity distance.

This work aims to study the bouncing universe under f(G, T) theory of gravity (where G and T are the Gauss–Bonnet invariance and trace of energy–momentum tensor, respectively). We construct modified field equations (MFEs) to analyze the behavior of Hubble parameter (HP) for $f(G,T)=G+\alpha G^n+2\lambda T$ with $\alpha$, $\lambda$ and $(n>0)$ are constant terms. Different constraints are applied, engaging HP to examine the accelerating universe and to test initial singularity. The graphical analysis is made for different values of n to explain bouncing process more precisely with respect to cosmic time that also provides an indication of null energy condition (NEC) violation. Resultantly, all mandatory conditions are fulfilled indicating that our proposed model provides good bouncing solutions.

In this study, we investigate the dynamics of the Universe during the observed late-time acceleration phase within the framework of the Weyl-type $f(Q,T)$ theory. Specifically, we consider a well-motivated model with the functional form $f(Q,T)=\alpha Q+\frac{\beta }{6{\kappa }^2}T$, where $Q$ represents the scalar of non-metricity and $T$ denotes the trace of the energy–momentum tensor. In this context, the non-metricity $Q_{\mu \alpha \beta }$ of the space-time is established by the vector field $w_{\mu }$. The parameters $\alpha$ and $\beta$ govern the gravitational field and its interaction with the matter content of the Universe. By considering the case of dust matter, we obtain exact solutions for the field equations and observe that the Hubble parameter $H(z)$ follows a power-law behavior with respect to redshift $z$. To constrain the model parameters, we analyze various datasets including the Hubble, Pantheon datasets, and their combination. Our results indicate that the Weyl-type $f(Q,T)$ theory offers a viable alternative to explain the observed late-time acceleration of the Universe avoiding the use of dark energy.

The $f(R,T)$ theory of gravity investigated by Harko et al. [T. Harko, F. S. N. Lobo, S. Nojiri and S. D. Odintsov, Phys. Rev. D 84 (2011) 024020; T. Harko, Phys. Rev. D 90(4) (2014) 044067] serves as the inspiration for the homogeneous and isotropic cosmological model presented in generalized $f(R,T^{\varphi })$ theories connected with a scalar field. Assuming that $T^{\varphi }$ is the trace of the energy-momentum tensor, $f(R,T^{\varphi })$ gravity can be understood as $f(R,T)$ gravity with a self-interacting scalar field $\varphi$. To address this, we provide a novel model-independent method for the parametrization of the Hubble parameter, and we apply it to the Friedmann equations in the FLRW Universe. The Markov Chain Monte Carlo (MCMC) approach is then used to estimate the best-fit values of the model parameters using a combination of the updated $H(z)$ dataset, which comprises 57 points, and the Pantheon dataset, which contains 1048 points. The evolution of the deceleration parameter shows a transition from the universe’s deceleration phase to its acceleration phase. We also investigate the behavior of the statefinder and the Om diagnostic parameter. Finally, a thorough discussion of the model’s physical attributes has been carried out.