Narrow Results

In this paper we investigate the possibility to obtain constraints on the kinematics of the Universe in a flat Friedmann–Robertson–Walker cosmology, through the use of the so-called Cosmography. The basic idea lies directly on fitting the H(z) series, by adopting a more recent dataset of H(z), in the range z≼1.8, obtaining the limits of the kinematical quantities under exam. The advantage that we propose here is that this fitting procedure is model independent and it does not need any assumption given a priori on the cosmology of the Universe, but only its geometry and flatness. Moreover, as an example, we relate the measured cosmographic set to the free parameter of ΛCDM, being the matter density Ω_m. In fact, by inverting Ω_m in terms of the cosmographic set, it would be possible to infer limits on it. We find results in agreement with other kind of cosmological constraints.

In this paper, we demonstrate that the variation of acceleration, namely the jerk parameter j, could give hints for determining the dark energy equation of state (EoS). In particular, it is possible to show that a viable cosmological model is compatible with a constant jerk, here conventionally rewritten as j = 1+ϵ, with ϵ > 0 representing a departure from the ΛCDM model. This suggests that the cosmological constant could be seen as a limiting case of a more general dark energy model. We use the most recent union 2.1 compilation of supernovae Ia, showing at 1σ confidence level, that j is compatible with the condition j ≥ 1. In doing so, we infer a corresponding cosmological model, viable with a negative acceleration parameter, in the observed range -1 < q₀ < 0.

This work analyzes a power law solution under $f(R,T)$ gravity for an isotropic and homogeneous universe. To construct $f(R,T)$ gravity model, we consider the functional form of $f(R,T)$ as the sum of two independent functions of the Ricci scalar R and the trace of the energy–momentum tensor T, i.e. $f(R,T)=R+\xi RT$, with $\xi$ being a positive constant where we study the cosmological model under the following two cases: (i) $f_1(R)=f_2(R)=R$ and (ii) $f_3(T)=\xi T$. In the framework of $f(R,T)$ gravity with homogeneous and isotropic spacetime, the constructed model yields several features on application of the scale factor $a=\alpha t^{\beta }$. We employed the Markov Chain Monte Carlo (MCMC) approach to get model parameters $\alpha$, $\beta$ and $H_0$ over a redshift range of $0\le z\le 1.965$. The model parameter’s restricted values are listed below: $H_0=67.098_{-1.792}^{+2.148}$ km ${\text{s}}^{-1}$Mpc${}^{-1}$, $H_0=67.588_{-2.170}^{+2.229}$km${\text{s}}^{-1}$ Mpc${}^{-1}$, $H_0=66.270_{-2.181}^{+2.215}$kms${}^{-1}$ Mpc${}^{-1}$, $H_0=65.960_{-1.834}^{+2.380}$kms${}^{-1}$Mpc${}^{-1}$, $H_0=66.274_{-1.864}^{+2.015}$kms${}^{-1}$Mpc${}^{-1}$. The model was constrained using the Hubble parameter ($H(z)$) dataset, Baryon Acoustic Oscillations (BAO) dataset, Pantheon dataset, joint $H(z)$ + Pantheon dataset and collective $H(z)$ + BAO + Pantheon dataset. The results from the Planck collaboration group are consistent with these calculated Ho observed values. In order to study and analyze the model, we first look at how the energy circumstances affected our power law assumption. The validity of the model has also been evaluated using the $Om$ diagnostic and the jerk parameter, which are state finding diagnostic tools. We find that the model under investigation agrees with the observed fingerprints within a certain range of constraints.

For the use of gamma-ray bursts (GRBs) to probe cosmology in a cosmology-independent way, a new method has been proposed to obtain luminosity distances of GRBs by interpolating directly from the Hubble diagram of SNe Ia, and then calibrating GRB relations at high redshift. In this paper, following the basic assumption in the interpolation method that objects at the same redshift should have the same luminosity distance, we propose another approach to calibrate GRB luminosity relations with cosmographic fitting directly from SN Ia data. In cosmography, there is a well-known fitting formula which can reflect the Hubble relation between luminosity distance and redshift with cosmographic parameters which can be fitted from observation data. Using the Cosmographic fitting results from the Union set of SNe Ia, we calibrate five GRB relations using GRB sample at z ≤ 1.4 and deduce distance moduli of GRBs at 1.4 < z ≤ 6.6 by generalizing above calibrated relations at high redshift. Finally, we constrain the dark energy parameterization models of the Chevallier–Polarski–Linder (CPL) model, the Jassal–Bagla–Padmanabhan (JBP) model and the Alam model with GRB data at high redshift, as well as with the cosmic microwave background radiation (CMB) and the baryonic acoustic oscillation (BAO) observations, and we find the ΛCDM model is consistent with the current data in 1-σ confidence region.

We show that the dark energy (DE) effects can be modeled by using an Ising perfect fluid with network interactions, whose low redshift equation of state (EoS), i.e. ω₀, becomes ω₀ = -1 as in the ΛCDM model. In our picture, DE is characterized by a barotropic fluid on a lattice in the equilibrium configuration. Thus, mimicking the spin interaction by replacing the spin variable with an occupational number, the pressure naturally becomes negative. We find that the corresponding EoS mimics the effects of a variable DE term, whose limiting case reduces to the cosmological constant Λ. This permits us to avoid the introduction of a vacuum energy as DE source by hand, alleviating the coincidence and fine tuning problems. We find fairly good cosmological constraints, by performing three tests with supernovae Ia (SNeIa), baryonic acoustic oscillation (BAO) and cosmic microwave background (CMB) measurements. Finally, we perform the Akaike information criterion (AIC) and Bayesian information criterion (BIC) selection criteria, showing that our model is statistically favored with respect to the Chevallier–Polarsky–Linder (CPL) parametrization.

The present work deals with a detailed study of interacting holographic dark energy model for three common choices of the interaction term. Also, two standard choices of IR cut-off, namely, Ricci length scale and radius of the event horizon are considered here. Finally, the cosmographic parameters are presented both analytically and graphically.

In the last dozen years, a wide and variegated mass of observational data revealed that the universe is now expanding at an accelerated rate. In the absence of a well-based theory to interpret the observations, cosmography provides information about the evolution of the universe from measured distances, only assuming that the geometry can be described by the Friedmann–Lemaitre–Robertson–Walker metric. In this paper, we perform a high-redshift analysis which allows us to put constraints on the cosmographic parameters up to the fifth-order, thus inducing indirect constraints on any gravity theory. Here, we are interested in the so-called teleparallel gravity theory, $f(T)$. Actually, we use the analytical expressions of the present day values of $f(T)$ and its derivatives as functions of the cosmographic parameters to map the cosmography region of confidences into confidence ranges for $f(T)$ and its derivative. Moreover, we show how these can be used to test some teleparallel gravity models without solving the dynamical equations. Our analysis is based on the Union2 Type Ia supernovae (SNIa) data set, a set of 28 measurements of the Hubble parameter, the Hubble diagram constructed from some gamma ray bursts (GRB) luminosity distance indicators and Gaussian priors on the distance from the baryon acoustic oscillations (BAOs) and the Hubble constant $h$. To perform our statistical analysis and to explore the probability distributions of the cosmographic parameters, we use the Markov chain Monte Carlo (MCMC) method.

In this paper, in a new approach, we study the stability of the dynamical system (DS) of $R^{1+ϵ}$ in terms of two significant cosmological parameters, deceleration parameter and jerk parameter $\{q,j\}$. Other cosmographic parameters such as $(l,s,\dots )$ have been obtained in terms of these two parameters. We have obtained critical points ($q_e,j_e$), the best fitted current values of cosmographic parameters ($q_0,j_0,l_0,s_0$), best value for model parameter $ϵ$ and best trajectory of dynamics of system in phase space by simultaneously solving the DS and best fitting the parameter by the SNIa data. By defining modified redshift in anisotropic cosmological model as $1+z(t,\widehat{p})=\frac{a(t_{0)}}{a(t)}(1-A(\widehat{n}\cdot \widehat{p}))$ (where $A$ is a magnitude of anisotropy, $\widehat{n}$ is direction of privileged axis and $\widehat{p}$ is the direction of each SNe Ia sample to galactic coordinates), the luminosity distance has been obtained in terms of modified redshift using cosmography method. Using union 2 data, we have found the direction of privileged axis in the galactic coordinate. The results show that the magnitude of anisotropy is about $\left|A\right|\simeq 10^{-3}$ and the direction of privileged axis is $(l,b)=(298_{+34}^{-34},2_{+23}^{-23})$. Also, our results are consistent with other studies in $1-\sigma$ confidence level.

In this work, we use cosmography to alleviate the degeneracy among cosmological models, proposing a way to parametrize matter and dark energy in terms of cosmokinematics quantities. The recipe of using cosmography allows to expand observable quantities in Taylor series and to directly compare those expansions with data. The strategy involves the expansions of $q$ and $j$, up to the second-order around $a(t)=1$. This includes additional cosmographic parameters which are fixed by current values of $q_0$ and $j_0$. We therefore propose a fully self-consistent parametrization of the total energy density driving the late-time universe speed up. This stratagem does not remove all the degeneracy but enables one to pass from the model-dependent couple of coefficients, ${\omega }_0$ and ${\mathrm{\Omega }}_{m,0}$, to model-independent quantities determined from cosmography. Afterwards, we describe a feasible cosmographic dark energy model, in which matter is fixed whereas dark energy evolves by means of the cosmographic series. Our technique provides robust constraints on cosmokinematic parameters, permitting one to separately bound matter from dark energy densities. Our cosmographic dark energy model turns out to be one parameter only, but differently from the lambda cold dark matter ($\mathrm{\Lambda }$CDM) paradigm, it does not contain ansatz on the dark energy form. In addition, we even determine the free parameter of our model in suitable $1\sigma$ intervals through Monte Carlo analyses based on the Metropolis algorithm. We compare our results with the standard concordance model and we find that our treatment seems to indicate that dark energy slightly evolves in time, reducing to a pure cosmological constant only as $z\to 0$.

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.

Cosmography can be considered as a sort of a model-independent approach to tackle the dark energy/modified gravity problem. In this review, the success and the shortcomings of the $\mathrm{\Lambda }$CDM model, based on General Relativity (GR) and standard model of particles, are discussed in view of the most recent observational constraints. The motivations for considering extensions and modifications of GR are taken into account, with particular attention to $f(R)$ and $f(T)$ theories of gravity where dynamics is represented by curvature or torsion field, respectively. The features of $f(R)$ models are explored in metric and Palatini formalisms. We discuss the connection between $f(R)$ gravity and scalar–tensor theories highlighting the role of conformal transformations in the Einstein and Jordan frames. Cosmological dynamics of $f(R)$ models is investigated through the corresponding viability criteria. Afterwards, the equivalent formulation of GR (Teleparallel Equivalent General Relativity (TEGR)) in terms of torsion and its extension to $f(T)$ gravity is considered. Finally, the cosmographic method is adopted to break the degeneracy among dark energy models. A novel approach, built upon rational Padé and Chebyshev polynomials, is proposed to overcome limits of standard cosmography based on Taylor expansion. The approach provides accurate model-independent approximations of the Hubble flow. Numerical analyses, based on Monte Carlo Markov Chain integration of cosmic data, are presented to bound coefficients of the cosmographic series. These techniques are thus applied to reconstruct $f(R)$ and $f(T)$ functions and to frame the late-time expansion history of the universe with no a priori assumptions on its equation-of-state. A comparison between the $\mathrm{\Lambda }$CDM cosmological model with $f(R)$ and $f(T)$ models is reported.

Constraining the dark energy equation of state, $w_x(z)$, is one of the main issues of current and future cosmological surveys. In practice, this requires making assumptions about the evolution of $w_x$ with redshift $z$, which can be manifested in a choice of a specific parametric form where the number of cosmological parameters play an important role in the observed cosmic acceleration. Since any attempt to constrain the EoS requires some prior fixing in one form or the other, settling a method to constrain cosmological parameters is of great importance. In this paper, we provide a straightforward approach to show how cosmological tests can be improved via a parametric methodology based on cosmography. Using Supernovae Type IA samplers, we show how by performing a statistical analysis of a specific dark energy parametrization can give directly the cosmographic parameters values.

In this paper, we have investigated a very natural question regarding the dynamics of the universe, namely, the possibility of its decelerating phase immediately after the present accelerating phase. To begin with, we have focused on the matter creation theory which is considered to be a viable alternative to dark energy and modified gravity models. Moreover, we have introduced the cosmographic approach which allows us to express the free parameters of a cosmological model in terms of the known cosmographic parameters. Assuming a generalized matter creation rate, we have discussed the theoretical bounds on the model parameters allowing the future deceleration of the universe. Moreover, using the observational bounds on the cosmographic parameters obtained from the low redshifts observational probes, we have also examined the chance of a decelerating phase of the universe. Finally, considering a variety of known cosmological models and parametrizations, we have tested the same possibility. Our analysis shows that the chance of a future decelerating expansion of the universe is highly dependent on the choice of the cosmological models and parametrizations and also on the observational data. Even though the future decelerating expansion is allowed in some cosmological frameworks, but we do not see any strong evidence in favor of this. Perhaps, the future cosmological surveys could offer some more information regarding the fate of the universe.

We examine the cosmic scenario of interacting Kaniadakis holographic dark energy in dynamical Chern–Simons modified gravity and the fractal universe. For this purpose, the Hubble, deceleration, coincidence, equation-of-state and jerk parameters have been evaluated in view of the redshift parameter. It is observed that deceleration parameter $(q)$ evaluates the accelerated expansion of the universe in both gravities. The coincidence parameter $(u)$ exhibits the transition of behavior from dark matter to dark energy era of the universe. The behavior of the equation-of-state parameter $({\omega }_{\theta })$ describes the quintessence and vacuum regions of the universe in both gravities for maximum choices of the interacting parameters. The jerk parameter shows the correspondence of the given model with $\mathrm{\Lambda }$CDM model and other standard models in both gravities. All the parameters exhibit consistent behavior with the Planck 2018 data. We also analyze the dynamical stability in both frameworks by formulating dynamical models in the form of a system of differential equations and evaluating their corresponding critical points. Critical points of both models are stable and phase plots indicate attractor behavior that implies stability of the models. Further, stability conditions of both models signify the accelerating expansion of the universe. In addition, we discuss the thermodynamics of this model with the generalized second law and find its validity in both frameworks.

Cosmography represents an important branch of cosmology which aims to describe the universe without the need of postulating a priori any particular cosmological model. All quantities of interest are expanded as a Taylor series around here and now, providing in principle, a way of directly matching with cosmological data. In this way, cosmography can be regarded a model-independent technique, able to fix cosmic bounds, although several issues limit its use in various model reconstructions. The main purpose of this review is to focus on the key features of cosmography, emphasizing both the strategy for obtaining the observable cosmographic series and pointing out any drawbacks which might plague the standard cosmographic treatment. In doing so, we relate cosmography to the most relevant cosmological quantities and to several dark energy models. We also investigate whether cosmography is able to provide information about the form of the cosmological expansion history, discussing how to reproduce the dark fluid from the cosmographic sound speed. Following this, we discuss limits on cosmographic priors and focus on how to experimentally treat cosmographic expansions. Finally, we present some of the latest developments of the cosmographic method, reviewing the use of rational approximations, based on cosmographic Padé polynomials. Future prospects leading to more accurate cosmographic results, able to better reproduce the expansion history of the universe, are also discussed in detail.

In this work, we focus on the gravitationally influenced adiabatic particle creation process, a mechanism that does not need any dark energy or modified gravity models to explain the current accelerating phase of the universe. Introducing some particle creation models that generalize some previous models in the literature, we constrain the cosmological scenarios using the latest compilation of the Type Ia Supernovae data only, the first indicator of the accelerating universe. Aside from the observational constraints on the models, we examine the models using two model independent diagnoses, namely the cosmography and $Om$. Further, we establish the general conditions to test the thermodynamic viabilities of any particle creation model. Our analysis shows that at late-time, the models have close resemblance to that of the $\mathrm{\Lambda }$CDM cosmology, and the models always satisfy the generalized second law of thermodynamics under certain conditions.

In this paper, we consider the extension of the Hilbert–Einstein action to analyze several interesting features of the theory. More specifically, the Lagrangian $f(R)$ is replaced by $f(R,L_m)$ in action, where $R$ is the Ricci scalar, and $L_m$ is the matter Lagrangian. We derive the motion equations for a test particle in the Friedmann–Lemaître–Robertson–Walker (FLRW) flat and homogeneous spacetime. We also derive the energy conditions in this framework. Then, we use the cosmographic parameter such as Hubble, deceleration, jerk and snap parameters to constraint the model parameters. As a result, we observe that with the constraint range of model parameters, our model shows the current accelerated expansion of the universe.

This paper is devoted to explore bouncing cosmology in $f(T,{𝒯})$ modified gravity. In the background of $f(T,{𝒯})$ modified theory with $T$ being Torsion scalar and ${𝒯}$ being the trace of energy–momentum tensor, the Hubble parameter is considered for the isotropic, flat, and homogenous universe. The standard bouncing scale factor has employed the exponential term to unify bounce with late-time acceleration. Phase portrait analysis reveals us that Minkowskian origin transfers to de Sitter origin in $(H,Ḣ)$-plane and as past infinite time $t\to -\infty$$\Rightarrow$$a(t)\to 0$ and $(H,Ḣ)\to$ constant which corresponds to some physical cosmological scenarios. Since field equations of $f(T,{𝒯})$ gravity are of second order, a one-dimensional autonomous system has been extracted. Finally, outcomes have been plotted graphically, and any type of singular behavior has not been experienced. The study of the equation of state parameter against cosmic time reveals that phantom phase is quite significant for both models. The inertial force in terms of Hubble parameter and cosmic time gives rise to pseudo Rip. The study of cosmographic parameters tells us that the present model corresponds to $\mathrm{\Lambda }$CDM at a large value of cosmic time.

The concept of dark energy (DE) emerged as a result of confirming the accelerated expansion of the universe. Since then, numerous models have been developed to explore the origin and nature of DE. In this study, we investigate several recent cosmological models (Models 1–9) based on the parametrization of the DE equation of state. Our analysis focuses on a homogeneous, isotropic flat universe comprising DE, dark matter (DM), and radiation. We assume the separate conservation of the dark components (DE and DM) and radiation. By employing various parametrizations of ${\omega }_D(z)$, we derive the corresponding Hubble function $E(z)$. To understand the cosmic expansion history of the universe in a model-independent manner, we employ cosmography as an approach. We express important cosmographic parameters such as deceleration, jerk, snap, and lerk parameters in terms of the Hubble rate $E(z)$ and its derivative up to the fourth order. Additionally, we examine the statefinder parameter and $O_m$ diagnostics to distinguish between different types of DE models. Finally, we compare the physical interpretations of these diagnostic parameters with the standard $\mathrm{\Lambda }$CDM model to assess the viability of each model.

In this paper, we study the cosmic dynamics of varying vacuum models where the dark matter interacts with the vacuum energy. We consider the homogeneous and isotropic spacetime with spatial curvature and apply the dynamical system technique to the varying vacuum models by specifying the form of energy exchange rate $(Q)$ between the dark energy and dark matter. Further, we utilize the cosmographic parameters and statefinder parameters in the terms of dynamical variables of the cosmological dynamical system to explore the cosmic dynamics of the universe. The Milne universe solution exists as a consequence of spatially curved geometry in the model. The models also yield radiation- matter- and dark energy-dominated phases in order and thus explain the late-time accelerated expansion of the universe. The strength of interaction terms will affect the existence of cosmological phases in the model but there will always be an attractor corresponding to the accelerating universe. We numerically solve the system to illustrate the evolution of cosmological quantities and dynamical variables in the models. The role of curvature is visible during the transition from the decelerated phase into the accelerating phase. The numerical solutions affirm that the cosmological parameters in the models are consistent with their corresponding observational values.