Constrained Dynamics of Holographic Dark Energy in Modified f (R) Gravity

In this paper, author studied homogeneous and anisotropic Bianchi type-V universe filled with matter and holographic dark energy (DE) components. The exact solutions to the corresponding Einstein’s field equations are obtained for exponential and power-law volumetric expansion. The holographic dark energy (DE) EoS parameter behaves like constant, i.e. ωΛ=−1, which is mathematically equivalent to cosmological constant (Λ) for exponential expansion of the model, whereas the holographic dark energy (DE) EoS parameter behaves like quintessence for power-law expansion of the model. A correspondence between the holographic dark energy (DE) models with the quintessence dark energy (DE) is also established. Quintessence potential and dynamics of the quintessence scalar field are reconstructed, which describe accelerated expansion of the universe. The statefinder diagnostic pair {r,s} is adopted to characterize different phases of the universe.

In this work, we explore the accelerated expansion of the Universe through a non-linear interaction of newly proposed dark energy models (namely Tsallis holographic dark energy (HDE), Renyi HDE, Sharma Mittal HDE, Tsallis new agegraphic dark energy (NADE), Renyi NADE and Sharma-Mittal NADE) with cold dark matter in the background of flat D -dimensional fractal Universe. The effect of IR cutoffs including the Hubble radius and Granda-Oliveros (GO) on the properties of the considered dark energy models have been investigated in this context. The cosmological parameters such as equation of state (EoS) parameter, squared speed of sound and $ \omega_{d}$ - $ \omega^{\prime}_{d}$ cosmological plane during the cosmic evolution have been calculated. Analyzing the behavior of such cosmological parameters graphically, it is found that the considered HDE and NADE models can lead to the late time accelerated expansion in the presence of interaction between two dark sectors of the Universe in more general space-time. This result is similar to the standard interacting HDE model with Hubble cutoff in FRW Universe.

In this paper, we study the Rényi holographic dark energy (HDE) model in the context of the Chern–Simons (CS) model of modified gravity theory. Different cosmological parameters, such as energy density, deceleration parameter, equation of state, square of sound speed and cosmological plane, are discussed using the Friedmann–Lemaître–Robertson–Walker spacetime background. Two separate solutions of CS field equations arise. The Rényi HDE model shows the transition from deceleration to acceleration phase which is fully consistent with the observational data while the second case represents a decelerated phase of expansion only. Our results, based on the results of the equation of state obtained, predict that the universe is under the influence of dark energy, and therefore, in an accelerated expansion phase. On the other hand, the second-case solution shows the influence of [Formula: see text]CDM. In both cases, [Formula: see text] indicated that the Rényi HDE model is in the freezing region and cosmic expansion is more accelerating in the context of CS modified gravity. It is also observed that the value of the squared sound speed, [Formula: see text], is positive [Formula: see text], a sufficient condition for the stability of the system. Hence, it is concluded that the Rényi HDE model is supported by the results of general relativity in the framework of CS modified gravity.

This paper considers the only sectors to constitute the present universe as the dark matter and dark energy. The proposed new agegraphic dark energy model studies the gradual transition from matter to dark energy in sequential order, including the current dominance of the matter sector by dark energy. The model utilizes concepts of Tsallis entropy and the Karolyhazy relation with conformal time [Formula: see text] as the time scale. Various evolutionary aspects of the universe are characterized by Tsallis parameter [Formula: see text] and the model constant [Formula: see text]. Expressions for dynamic behavior of dark energy, as a differential equation, equation of state and deceleration parameters are obtained to describe the thermal history of universe evolution. Also, the stability of the model is analyzed through squared sound speed parameter. The analysis is made by considering an interaction as well as independence among the constituent sectors of the universe.

We have considered a cosmological model of holographic dark energy interacting with dark matter and another unknown component of dark energy of the universe. We have assumed two interaction terms Q and Q′ in order to include the scenario in which the mutual interaction between the two principal components (i.e., holographic dark energy and dark matter) of the universe leads to some loss in other forms of cosmic constituents. Our model is valid for any sign of Q and Q′. If Q<Q′, then part of the dark energy density decays into dark matter and the rest in the other unknown energy density component. But if Q>Q′, then dark matter energy receives from dark energy and from the unknown component of dark energy. Observation suggests that dark energy decays into dark matter. Here we have presented a general prescription of a cosmological model of dark energy which imposes mutual interaction between holographic dark energy, dark matter and another fluid. We have obtained the equation of state for the holographic dark energy density which is interacting with dark matter and other unknown component of dark energy. Using first law of thermodynamics, we have obtained the entropies for holographic dark energy, dark matter and other component of dark energy, when holographic dark energy interacting with two fluids (i.e., dark matter and other component of dark energy). Also we have found the entropy at the horizon when the radius (L) of the event horizon measured on the sphere of the horizon. We have investigated the GSL of thermodynamics at the present time for the universe enveloped by this horizon. Finally, it has been obtained validity of GSL which implies some bounds on deceleration parameter q.

We use three infrared (IR) cutoffs, including the future event horizon, the Hubble and Granda–Oliveros (GO) cutoffs, to construct three holographic models of dark energy (DE). Additionally, we consider a Friedmann–Robertson–Walker (FRW) universe filled by a dark matter (DM) and a DE that interact with each other through a mutual sign-changeable interaction with positive coupling constant. Thereinafter, we address the evolution of the some cosmological parameters, such as the equation of state (EoS) and dimensionless density parameters of DE as well as the deceleration parameter, during the cosmic evolution from the matter-dominated era until the late-time acceleration. We observe that a holographic dark energy (HDE) model with Hubble cutoff interacting with DM cannot be in line with the current universe. Our study shows that models with the future event horizon as the IR cutoff or the GO cutoff are in good agreement with the observational data. In fact, we find out that these two recent models can predict the universe transition from a deceleration phase to the acceleration one in a compatible way with observations. The three obtained models may also allow the EoS parameter to cross the phantom line, a result which depends on the values of the system’s constants such as the value of the interaction coupling constant.

The main motivation of our study is to explore Rényi holographic dark energy, Sharma–Mittal holographic dark energy, Rényi new agegraphic dark energy, and Sharma–Mittal new agegraphic dark energy in the context of generalized Rastall gravity with the two-fluid system, dark energy, and dark matter. In this regard, we have considered the scale factors into two distinct categories, one of which corresponds to the future singularity, whereas the other represents initial singularity. By employing future event horizon as infrared (IR)-cutoff, different cosmological quantities like deceleration parameter, equation of state (EoS) parameter are evaluated, and their ramifications have been described graphically. Analyzing the squared speed of sound, we have seen classically stable and unstable behavior for each of the considered models. Finally, we study [Formula: see text]–[Formula: see text] plane and find the thawing/freezing regions.

The cosmic expansion phenomenon is being studied through the interaction of newly proposed dark energy models (Tsallis, Rényi and Sharma-Mittal holographic dark energy (HDE) models) with cold dark matter in the framework of loop quantum cosmology. We investigate different cosmic implications such as equation of state parameter, squared sound speed and cosmological plane (ω d - ω d ′ , ω d and ω d ′ represent the equation of state (EoS) parameter and its evolution, respectively). It is found that EoS parameter exhibits quintom like behavior of the universe for all three models of HDE. The squared speed of sound represents the stable behavior of Rényi HDE and Sharma-Mittal HDE at the latter epoch while unstable behavior for Tsallis HDE. Moreover, ω d - ω d ′ plane lies in the thawing region for all three HDE models.

Cosmic analysis through dark energy models in fractal universe with non-linear interaction term

In this paper, we reconsider the concept of holographic dark energy in the framework of Brans–Dicke theory in the formalism of the flat Friedmann–Lemaitre–Robertson–Walker metric. Firstly, we demonstrate how the assumption phi propto a^n, where phi and a stand for the Brans–Dicke scalar field and scale factor, respectively, naturally leads to a constant deceleration parameter, irrespective of the energy content of the universe. Secondly, we consider interacting holographic dark energy with Hubble horizon as IR cut-off, and find the value of the Hubble parameter and corresponding value of the scale factor. Further, we find the value of the Brans–Dicke scalar field phi for the obtained value of the Hubble parameter and holographic dark energy. We obtain the corresponding value of the deceleration parameter and show that it can explain the phase transition of the universe. Moreover, statefinder diagnostics has been applied to compare the model with existing models. On the other hand, we consider the viscous behavior of holographic dark energy and show that the viscous holographic dark energy can play the role of interacting holographic dark energy as it is able to explain the phase transition of the universe. Further, we find the value of the Brans–Dicke scalar field phi for this viscous holographic dark energy. In this model also, we apply the statefinder diagnostic.

At the present paper, Locally Rotationally Symmetric (LRS) Bianchi type-II cosmological model with interacting dark matter (DM) and holographic dark energy (DE) have been discussed. In order to obtain solutions of the field equations, it is assume that the shear scalar (σ) is proportional to expansion scalar (θ). To have a general description of holographic dark energy and dark matter, a phenomenological parameterization of dark energy in terms of its equation of state (EoS) has been taken. Statefinder diagnostic pair i.e.｛r, s｝is adopted to separate other existing dark energy models from this model. Here we discuss two models: when n=1/2, we obtain acyclic universe and the model converges into phantom region whereas when n=3/2, we get a expanding universe and the model converges into quintessence region. Some important geometrical and physical features regarding to this model have also been studied.

The present work discusses the topic of cosmic evolution in an intriguing framework of theory of gravity (with as a non‐metricity (NM) scalar which controls the gravitational interaction) by using some recently proposed holographic dark energy (HDE) models. To achieve this goal, the dynamical equations for locally rotationally symmetric (LRS) Bianchi type‐I (BI) geometry are formulated with matter contents as a mixture of dust and anisotropic fluids. By assuming that the time‐redshift relation follows a Lambert function, the cosmological model is constructed by using Rényi HDE (RHDE), Sharma–Mittal HDE (SMHDE) and Generalized HDE (GHDE) as separate cases where Hubble horizon is taken as an infrared (IR) cutoff. Cosmological characteristics of these models are then examined through graphs of energy densities, skewness parameter , deceleration, and EoS parameters. The evolution of the EoS parameter is also studied, i.e., to discuss the dynamical characteristics of constructed DE models and assess the stability of models via the squared speed of sound parameter. It is found that the plane shows the freezing region for RHDE and GHDE models while the thawing region for the SMHDE case. Also, it is concluded that all constructed models exhibit cosmologically viable and stable behavior.

We investigate the interacting holographic dark energy (HDE) with Granda–Oliveros (GO) infrared (IR)-cutoff in the framework of Brans–Dicke (BD) cosmology. We obtain the equation of state (EoS) parameter of HDE, wD, the effective EoS parameter w eff , the deceleration parameter q and the squared of sound speed [Formula: see text] in a flat Friedmann–Robertson–Walker (FRW) universe. We show that at late-time the cosmic coincidence problem can be alleviated. Also we show that for noninteracting case, HDE can give a unified dark matter–dark energy (DM–DE) profile in BD cosmology, except that it cannot solve the coincidence problem in the future. By studying the EoS parameter, we see that the phantom divide may be crossed. Using the latest observational data, we calculate the best values of the parameters for interacting HDE in BD framework. Computing the deceleration parameter implies that the transition from deceleration to the acceleration phase occurred for redshift z ≥ 0.5. Finally, we investigate the sound stability of the model, and find that HDE with Granda–Oliveros (GO)-cutoff in the framework of BD cosmology can lead to a stable DE-dominated universe favored by observations, provided we take β = 0.44 and b2 &lt; 0.35. This is in contrast to HDE model in Einstein gravity which does not lead to a stable DE-dominated universe.

Modified gravity models are popular among cosmologists, as they can describe the cosmological evolution quite efficiently. Reconstruction of newly introduced [Formula: see text] gravity, with the help of ordinary, power-law entropy corrected and logarithmic entropy-corrected versions of Holographic dark energy (HDE) and Pilgrim dark energy (PDE) models have been studied in this work. For such reconstruction, we have considered the power-law scale factor [Formula: see text]. Further, the classical stabilities (the squared speed of sound method) of such reconstructions and their implications on the nature of the equation of state (EoS) parameters and deceleration parameter with respect to red-shift have also been examined. Finally, we have computed the age of the universe for reconstructed models.

Here we briefly discuss the Galileon gravity theory and modified Friedmann equations. By considering new holographic dark energy (NHDE) in the framework of Galileon gravity, we found the energy density, pressure, equation of state and the deceleration parameter in terms of the scale factor. Subsequently, we study the correspondence between the NHDE in the framework of Galileon gravity with other dark energies like quintessence, k-essence, tachyon, dilaton, hessence and DBI-essence dark energies and construct the scalar field and corresponding scalar potentials which describe the dynamics of the scalar fields graphically. All the dark energy models, the scalar field and the potential decrease due to the evolution of the universe.