Curvature Inspired Cosmological Scenario

Using modified gravity with non-linear terms of curvature, R ² and R ^(2+r) (with r being a positive real number and R being the scalar curvature), cosmological scenario, beginning at the Planck scale, is obtained. Here a unified picture of cosmology is obtained from f(R)-gravity. In this scenario, universe begins with power-law inflation followed by deceleration and acceleration in the late universe as well as possible collapse of the universe in future. It is different from f(R)-dark energy models with non-linear curvature terms assumed as dark energy. Here, dark energy terms are induced by linear as well as non-linear terms of curvature in Friedmann equation being derived from modified gravity. It is also interesting to see that, in this model, dark radiation and dark matter terms emerge spontaneously from the gravitational sector. It is found that dark energy, obtained here, behaves as quintessence in the early universe and phantom in the late universe. Moreover, analogous to brane-tension in brane-gravity inspired Friedmann equation, a tension term λ arises here being called as cosmic tension, It is found that, in the late universe, Friedmann equation (obtained here) contains a term −ρ ²/2λ (ρ being the phantom energy density) analogous to a similar term in Friedmann equation with loop quantum effects, if λ>0 and brane-gravity correction when λ<0.     

Higher Dimensional Unified Description of Early Universe with Variable <Emphasis Type="Italic">G</Emphasis> and Λ

A homogeneous and isotropic Friedmann-Robertson-Walker (FRW) model with varying gravitational and cosmological constant is studied in the context of higher dimensional space time. Exact solution of the field equations are obtained by using the “gamma law” equation of state p=(γ−1)ρ, where γ is adiabatic parameter varies continuously as the universe expands. The functional form γ which is assumed to be the function of scale factor R as proposed by Carvalho (1996) is used to analyse the behavior of scale factor R, cosmological constant Λ and the gravitational constant G for two different phases: inflation and radiation. The various physical aspects of the early cosmological models has also been discussed in the framework of higher dimensional space time.     

The Decay of Massive Scalar Field in Non-Static Gödel Type Universe with Viscous Fluid and Heat Flow

In this study, we have investigated the dynamics of non-static Gödel type rotating universe with massive scalar field, viscous fluid and heat flow in the presence of cosmological constant. For various cosmic matter forms, the behavior of the cosmological constant (Λ), shear (η) and bulk (ξ) viscosity coefficients and other kinematic quantities have studied in the early universe. We have showed the decay of massive scalar field in the non-static rotating Gödel type universe and we have obtained constant scalar field with and without source density. Also, we have investigated the effects of massive scalar field on the matter density and pressure. From solutions of the field equations, we have a cosmological model with non-zero expansion, shear, heat flux and rotation. Also some physical and geometrical aspects of the model discussed.     

Energy Distributions of the Szekeres Universes in Teleparallel Gravity

In order to evaluate the energy distribution (due to matter and fields including gravitation) associated with a space-time model of Szekeres class I and II metrics, we consider the Einstein, Bergmann–Thomson and Landau–Lifshitz energy definitions in the teleparallel gravity (the tetrad theory of gravitation (TG)). We have found that Einstein and Bergmann–Thomson energy distributions give the same results, Landau–Lifshitz distribution is disagree in TG with these definitions. These results are the same as a previous works of Aygün et al., they investigated the same problem by using Einstein, Bergmann–Thomson, Landau–Lifshitz (LL) and Møller energy-momentum complexes in GR. However, both GR and TG are equivalent theories that is the energy densities are the same using different energy-momentum complexes in both theories. Also, our results are support the Cooperstock’s hypothesis.     

Investigation of Homogeneity and Matter Distribution on Large Scales Using Large Quasar Groups

We use 20 large quasar group (LQG) samples in Park et al. (2015) to investigate the homogeneity of the 0.3 z 1.6 Universe (z denotes the redshift). For comparison, we also employ the 12 LQGs samples at 0.5 z 2 in Komberg et al. (1996) to do the analysis. We calculate the bias factor b and the two-point correlation function ξ_LQG for such groups for three different density profiles of the LQG dark matter halos, i.e. the isothermal profile, the Navarro-Frenk-White (NFW) profile, and the (gravitational) lensing profile. We consider the CDM (cold dark matter plus a cosmological constant ) underlying matter power spectrum with Ω_m = 0.28, Ω_Λ= 0.72, the Hubble constant H₀ = 100 h·km·s^-1·Mpc^-1 with h = 0.72. Dividing the samples into three redshift bins, we find that the LQGs with higher redshift are more biased and correlated than those with lower redshift. The homogeneity scale RH of the LQG distribution is also deduced from theory. It is defined as the comoving radius of the sphere inside which the number of LQGs N(< r) is proportional to r³ within 1%, or equivalently above which the correlation dimension of the sample D₂ is within 1% of D₂ = 3. For Park et al.'s samples and the NFW dark matter halo profile, the homogeneity scales of the LQG distribution are R_H ～ 247 h^-1·Mpc for 0.2 < z ≤ 0.6, R_H ～ 360 h^-1·Mpc for 0.6 < z ≤ 1.2, and R_H ～ 480 h^-1·Mpc for 1.2 < z 1.6. The maximum extent of the LQG samples are beyond RH in each bin, showing that the LQG samples are not homogeneously distributed on such a scale, i.e. a length range of ～ 500 h^-1·Mpc and a mass scale of ～ 10¹⁴M_⊙. The possibilities of a top-down structure formation process as was predicted by the hot/warm dark matter (WDM) scenarios and the redshift evolution of bias factor b and correlation amplitude ξ_LQG of the LQGs as a consequence of the cosmic expansion are both discussed. Different results were obtained based on the LQG sample in Komberg et al. (1996) and the possible reasons for such differences were discussed.     

First Principles Calculation of the Baryon Asymmetry of the Universe: Generalities and Application

We present a formalism that allows the computation of the lepton asymmetry of the universe from first principles of statistical physics and quantum field theory (this lepton asymmetry is then converted to a baryon asymmetry via sphaleron processes). This formalism includes a thermal bath of Standard Model particles (active neutrinos) coupled to a new sector that is out-of-equilibrium (sterile neutrinos). The key point that allows a first principles computation is that the number of sterile neutrinos produced during the relevant cosmological period remains small (we assume zero sterile neutrinos initially). In such a case, it is possible to expand the formal solution of Liouville's equation perturbatively and obtain a master formula for the lepton asymmetry expressed in terms of non-equilibrium Wightman functions. The master formula neatly separates CP-violating contributions from finite temperature correlation functions and satisfies all three Sakharov conditions. These correlation functions can then be evaluated perturbatively; the validity of the perturbative expansion depends on the parameters of the model considered. Here we choose the νMSM (i.e. a minimal extension of the Standard Model that includes three generations of sterile neutrinos with masses of the order of the electroweak scale) to illustrate the use of the formalism, but it could in principle be applied to other models.     

Statistical Properties of the Burgers Equation with Brownian Initial Velocity

We study the one-dimensional Burgers equation in the inviscid limit for Brownian initial velocity (i.e. the initial velocity is a two-sided Brownian motion that starts from the origin x=0). We obtain the one-point distribution of the velocity field in closed analytical form. In the limit where we are far from the origin, we also obtain the two-point and higher-order distributions. We show how they factorize and recover the statistical invariance through translations for the distributions of velocity increments and Lagrangian increments. We also derive the velocity structure functions and we recover the bifractality of the inverse Lagrangian map. Then, for the case where the initial density is uniform, we obtain the distribution of the density field and its n-point correlations. In the same limit, we derive the n-point distributions of the Lagrangian displacement field and the properties of shocks. We note that both the stable-clustering ansatz and the Press-Schechter mass function, that are widely used in the cosmological context, happen to be exact for this one-dimensional version of the adhesion model.     

Quantum Tunneling from Apparent Horizon of?Rainbow-FRW Universe

The quantum tunneling from the apparent horizon of rainbow-FRW universe is studied in this paper. We apply the semi-classical approximation, which is put forward by Parikh and Wilczek et al., to research on the scalar field particles tunneling from the apparent horizon of the rainbow-FRW universe, and then use the spin 1/2 Fermions tunneling theory, which brought forward by Kerner and Mann firstly, to research on the Fermions Hawking radiation via semi-classical approximation. Finally, we discuss the meanings of the quantum effect via Finsler geometry.