Cosmic energy equation and clustering of non-point mass system of galaxies

Cosmic energy equation is an important equation for studying the gravitational galaxy clustering in the expanding universe. We derive the distribution function for fluctuations in particle number by using the cosmic energy equation for extended structures (galaxies with halos). From spatial distribution function, containing particle fluctuations, we derive the velocity distribution function to understand the influence of particle fluctuations on the velocities of galaxies.With the help of cosmic energy equation we try to find out the physical constraints for the application of quasi-equilibrium approximation.     

Clustering of non-point mass system of galaxies in the expanding Universe

We derive the cosmic energy equation for the non-point mass system of galaxies (galaxies with halos) by using the adiabatic approximation for the growth of gravitational clustering of galaxies in the expanding Universe. The cosmic energy equation so derived represents the general form of conservation of energy for the expanding volume. Using the derived form of cosmic energy equation we try to study the evolution of correlation potential energy of the system. We also try to explore the condition under which the approximation of extensivity may be applied to the infinite gravitating non-point mass system of galaxies.     

Gravitational clustering of galaxies in an expanding universe

We inquire the phenomena of clustering of galaxies in an expanding universe from a theoretical point of view on the basis of thermodynamics and correlation functions. The partial differential equation is developed both for the point mass and extended mass structures of a two-point correlation function by using thermodynamic equations in combination with the equation of state taking gravitational interaction between particles into consideration. The unique solution physically satisfies a set of boundary conditions for correlated systems and provides a new insight into the gravitational clustering problem.     

Seeable universe and its accelerated expansion: an observational test

From the equivalence principle, one gets the strength of the gravitational effect of a mass M on the metric at position r from it. It is proportional to the dimensionless parameter β ²=2GM/rc ², which normally is ?1. Here G is the gravitational constant, M the mass of the gravitating body, r the position of the metric from the gravitating body and c the speed of light. The seeable universe is the sphere, with center at the observer, having a size such that it shall contain all light emitted within it. For this to occur one can impose that the gravitational effect on the velocity of light at r is zero for the radial component, and non zero for the tangential one. Light is then trapped. The condition is given by the equality R _g =2GM/c ², where R _g represents the radius of the seeable universe. It is the gravitational radius of the mass M. The result has been presented elsewhere as the condition for the universe to be treated as a black hole. According to present observations, for the case of our universe taken as flat (k=0), and the equation of state as p=?ρc ², we prove here from the Einstein’s cosmological equations that the universe is expanding in an accelerated way as t ², a constant acceleration as has been observed. This implies that the gravitational radius of the universe (at the event horizon) expands as t ². Taking c as constant, observing the galaxies deep in space this means deep in time as ct, linear. Then, far away galaxies from the observer that we see today will disappear in time as they get out of the distance ct that is <R _g . The accelerated expanding vacuum will drag them out of sight. This may be a valid test for the present ideas in cosmology. Previous calculations are here halved by our results.     

The Spins of Astrophysical Systems and Extended Gravitational Theory

Recent data on the Tully–Fisher relation for spiral galaxies are compatible with the traditional correlation for astrophysical systems, where the angular momentum varies as the square of the mass. Such a correlation is consistent with standard gravitational theory, but is not explained by it. We here show that the noted relation follows from currently popular accounts of extended or higher-dimensional gravitational theory. The latter also predicts that the spins of spirals should decay as the universe expands, which can be tested by extending the Tully–Fisher data to higher redshifts.     

Evolution of the universe in inverse and lnf(R) gravity

Evolution of the universe is discussed in the framework of f(R) theory of gravity. The deceleration parameter is used to interpret various phases of the universe. We investigate the future evolution of the flat FRW universe by using observationally viable f(R) models. A numerical technique is applied to solve the evolution equation in terms of Hubble parameter which is used to explore late time acceleration of the universe. Some novel and interesting results based on the choice of coupling parameters in gravitational action are obtained. We can conclude that the considered f(R) models imply unification of matter dominated epoch with present accelerating phase of the universe.     

Cosmological evolution of pilgrim dark energy

We study pilgrim dark energy model by taking IR cut-offs as particle and event horizons as well as conformal age of the universe. We derive evolution equations for fractional energy density and equation of state parameters for pilgrim dark energy. The phantom cosmic evolution is established in these scenarios which is well supported by the cosmological parameters such as deceleration parameter, statefinder parameters and phase space of ω _? and \(\omega'_{\vartheta}\) . We conclude that the consistent value of parameter μ is μ<0 in accordance with the current Planck and WMAP9 results.     

Effective dark energy models and dark energy models with bounce in frames of F(T) gravity

Various cosmological models in frames of F(T) gravity are considered. The general scheme of constructing effective dark energy models with various evolution is presented. It is showed that these models in principle are compatible with ΛCDM model. The dynamics of universe governed by F(T) gravity can mimics ΛCDM evolution in past but declines from it in a future. We also construct some dark energy models with the “real” (non-effective) equation-of-state parameter w such that w≤?1. It is showed that in F(T) gravity the Universe filled phantom field not necessarily ends its existence in singularity. There are two possible mechanisms permitting the final singularity. Firstly due to the nonlinear dependence between energy density and H ² (H is the Hubble parameter) the universe can expands not so fast as in the general relativity and in fact Little Rip regime take place instead Big Rip. We also considered the models with possible bounce in future. In these models the universe expansion can mimics the dynamics with future singularity but due to bounce in future universe begin contracts.     

Interacting holographic dark energy with variable deceleration parameter and tachyon scalar field dark energy model in LRS Bianchi type-II universe

In this work, we have considered the spatially homogeneous and anisotropic Bianchi type-II universe filled with two interacting fluids; dark matter and holographic dark energy components. Assuming the proportionality relation between one of the components of shear scalar and expansion scalar which yields time dependent deceleration parameter, an exact solution to Einstein’s field equations in Bianchi type-II line element is obtained. We have investigated geometric and kinematics properties of the model and the behaviour of the holographic dark energy. It is observed that the mean anisotropic parameter is uniform through the whole evolution of the universe and the coincidence parameter increases with increasing time. The solutions are also found to be in good agreement with the results of recent observations. We have applied the statefinder diagnostics method to study the behaviour of different stages of the universe and to differentiate the proposed dark energy model from the ΛCDM model. We have also established a correspondence between the holographic dark energy model and the tachyon scalar field dark energy model. We have reconstructed the potential and the dynamics of the tachyon scalar field, which describes accelerated expansion of the universe.     

Holographic dark energy with time depend gravitational constant in the non-flat Ho?ava-Lifshitz cosmology

We study the holographic dark energy on the subject of Hořava-Lifshitz gravity with a time dependent gravitational constant G(t), in the non-flat space-time. We obtain the differential equation that specify the evolution of the dark energy density parameter based on varying gravitational constant. We find out a relation for the state parameter of the dark energy equation of state to low red-shifts which containing varying G corrections in the non-flat space-time.     

GOLD’s coating and testing facilities for ISSIS-WSO

The interaction between Ricci scalar curvature and the baryon number current, dynamically breaks CPT in an expanding universe and leads to baryon asymmetry. Using this kind of interaction and study the gravitational baryogenesis in the Bianchi type I universe. We find out the effect of anisotropy of the universe on the baryon asymmetry for the case which the equation of state parameter, ω, varies with time.     

Cosmic Background Bose Condensation (CBBC)

Degeneracy effects for bosons are more important for smaller particle mass, smaller temperature and higher number density. Bose condensation requires that particles be in the same lowest energy quantum state. We propose a cosmic background Bose condensation, present everywhere, with its particles having the lowest quantum energy state, ?c/λ, with λ about the size of the visible universe, and therefore unlocalized. This we identify with the quantum of the self gravitational potential energy of any particle, and with the bit of information of minimum energy. The entropy of the universe (～10¹²² bits) has the highest number density (～10³⁶ bits/cm³) of particles inside the visible universe, the smallest mass, ～10^?66 g, and the smallest temperature, ～10^?29 K. Therefore it is the best candidate for a Cosmic Background Bose Condensation (CBBC), a completely calmed fluid, with no viscosity, in a superfluidity state, and possibly responsible for the expansion of the universe.     

Bianchi type I two-fluid cosmological models with a variable G and Λ

This paper presents anisotropic, homogeneous two-fluid cosmological models in a Bianchi type I space–time with a variable gravitational constant G and cosmological constant Λ. In the two-fluid model, one fluid represents the matter content of the universe and another fluid is chosen to model the CMB radiation. We find a variety of solutions in which the cosmological parameter varies inversely with time t. We also discuss in detail the behavior of associated fluid parameters and kinematical parameters. This paper pictures cosmic history when the radiation and matter content of the universe are in an interactive phase. Here, Ω is closing to 1 throughout the cosmic evolution.      

G-corrected holographic dark energy model

Here we investigate the holographic dark energy model in the framework of FRW cosmology where the Newtonian gravitational constant, G, is varying with cosmic time. Using the complementary astronomical data which support the time dependency of G, the evolutionary treatment of EoS parameter and energy density of dark energy model are calculated in the presence of time variation of G. It has been shown that in this case, the phantom regime can be achieved at the present time. We also calculate the evolution of G-corrected deceleration parameter for holographic dark energy model and show that the dependency of G on the comic time can influence on the transition epoch from decelerated expansion to the accelerated phase. Finally we perform the statefinder analysis for G-corrected holographic model and show that this model has a shorter distance from the observational point in s–r plane compare with original holographic dark energy model.     

Dark energy constraints on masses and sizes of large scale cosmic structures

The requirement that their gravitational binding self-energy density must at least equal the background repulsive dark energy density for large scale cosmic structures implies a mass-radius relation of \({M} / {R^{2}} \approx 1~\mbox{g}/{\mbox{cm}^{2}}\), as pointed out earlier. This relation seems to hold true for primeval galaxies as well as those at present epoch. This could set constraints on the nature and evolution of dark energy. Besides, we also set constraints on the size of galaxy clusters and superclusters due to the repulsive cosmological dark energy. This could indicate as to why large scale cosmic structures much larger than ～200 Mpc are not seen.     

Statefinder diagnosis and the interacting ghost model of dark energy

A new model of dark energy namely “ghost dark energy model” has recently been suggested to interpret the positive acceleration of cosmic expansion. The energy density of ghost dark energy is proportional to the hubble parameter. In this paper we perform the statefinder diagnostic tool for this model both in flat and non-flat universe. We discuss the dependency of the evolutionary trajectories in s–r and q–r planes on the interaction parameter between dark matter and dark energy as well as the spatial curvature parameter of the universe. Eventually, in the light of SNe+BAO+OHD+CMB observational data, we plot the evolutionary trajectories in s–r and q–r planes for the best fit values of the cosmological parameters and compare the interacting ghost model with other dynamical dark energy models. We show that the evolutionary trajectory of ghost dark energy in statefinder diagram is similar to holographic dark energy model. Finally, it has been shown that from the viewpoint of statefinder analysis, the ghost dark energy model has a better agreement with observations compare with holographic and new holographic dark energy models.     

Fluctuations of non-point mass galaxy distribution

We examine cosmic energy equation for extended galaxy structures on the basis of different models of universe. We also extend the power spectrum and density fluctuations for extended structure by introducing softening parameter both for linear and non-linear regimes. The results are compared with earlier results of point mass structures. It is found that softening parameters introduced in the theory influence the thermodynamic fluctuation theory. Results obtained with spectrum analysis are also compared with Riemannian geometric approach (Ruppeiner in Rev. Mod. Phys. 67:605, 1995) to the galaxy clustering. The singular solutions of thermodynamic fluctuation results can be interpreted on the basis of power spectrum analysis in terms of power index law of two point correlation function.     

The study of Gödel type solutions in f(R, ϕ) gravity

The aim of this paper is to study the Gödel type universe in modified f(R, ϕ) theory of gravity, where R stands for Ricci scalar and ϕ be the scalar potential. We investigate the modified field equations by using anisotropic and perfect fluid distributions. In particular, we consider two proposed models with some fixed values of parameters and investigate the exact solutions. The behaviour of energy conditions can be seen by a detailed graphical analysis. Furthermore, Tolman-Oppenheimer-Volkoff equation has been studied for both models in this theory. We have also discussed some exact solutions using perfect fluid. It is concluded that f(R, ϕ) theory of gravity support the phenomenon of cosmic expansion of the universe through Gödel type universe for both models.