黎曼函数与宇宙能量密度

通常由查表得相对论性粒子的能量密度,但这对黎曼ζ函数并无深入了解,本文浅述由黎曼ζ函数推导能量密度的过程.

宇宙能量密度与黎曼ζ函数

宇宙之演化由宇宙能量密度来决定 ,当我们在计算相对论性粒子之能量密度时 ,总会伴随着出现黎曼 ζ函数。本文试图由黎曼 ζ函数推导出宇宙能量密度。

Holography,UV/IR Relation,Causal Entropy Bound,and Dark Energy

The constraint on the total energy in a given spatial region is given from holography by the mass of a black hole that just fits in that region, which leads to an UV/IR relation： the maximal energy density in that region is proportional to Mp^2/L^2, where Mp is the Planck mass and L is the spatial scale of that region under consideration. Assuming the maximal black hole in the universe is formed through gravitational collapse of perturbations in the universe, then the ＂Jeans＂ scale of the perturbations gives a causal connection scale RCC. For gravitational perturbations, RCC^-2= Max （H＋ 2H^2, -H） for a fiat universe. We study the cosmological dynamics of the corresponding vacuum energy density by choosing the causal connection scale as the IR cutoff in the UV/IR relation, in the cases of the vacuum energy density as an independently conserved energy component and an effective dynamical cosmological constant, respectively. It turns out that only the case with the choice RCC^-2 = H＋ 2H^2, could be consistent with the current cosmological observations when the vacuum density appears as an independently conserved energy component. In this case, the model is called holographic Ricci scalar dark energy model in the literature.

Anisotropic Bianchi Type-I Magnetized String Cosmological Models with Decaying Vacuum Energy Density A(t)

The present study deals with a spatially homogeneous and anisotropic Bianehi-I cosmological models representing massive strings with magnetic field and decaying vacuum energy density A. The energy-momentum tensor, as formulated by Letelier （1983）, has been used to construct massive string cosmological models for which we assume the expansion scalar in the models is proportional to one of the components of shear tensor. The Einstein＇s field equations have been solved by applying a variation law for generalized Hubble＇s parameter in Bianchi-I space-time. The variation law for Hubble＇s parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential form. Using these two forms, Einstein＇s field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. We have made a comparative study of accelerating and decelerating models in the presence of string scenario. The study reveals that massive strings dominate in the decelerating universe whereas strings dominate in the accelerating universe. The strings eventually disappear from the universe for sufficiently large times, which is in agreement with current astronomical observations. The cosmological constant A is found to be a positive decreasing function of time which is corroborated by results from recent supernovae Ia observations. The physical and geometric properties of the models have been also discussed in detail.

Cosmological Model Based on Gauge Theory of Gravity

A cosmological model based on gauge theory of gravity is proposed in thispaper. Combining cosmological principle and field equation of gravitational gauge field, dynamicalequations of the scale factor R(t) of our universe can be obtained. This set of equations has threedifferent solutions. A prediction of the present model is that, if the energy density of theuniverse is not zero and the universe is expanding, the universe must be space-fiat, the totalenergy density must be the critical density ρ_c of the universe. For space-Bat case, this modelgives the same solution as that of the Friedmann model. In other words, though they have differentdynamics of gravitational interactions, general relativity and gauge theory of gravity give the samecosmological model.

Modified Holographic Ricci Dark Energy in Chameleon Brans–Dicke Cosmology and Its Thermodynamic Consequence

The objective of this paper is to discuss the Chameleon Brans–Dicke gravity with non-minimally matter coupling of scalar field. We take modified Holographic Ricci dark energy model in this gravity with its energy density in interaction with energy density of cold dark matter. We assume power-law ansatz for scale factor and scalar field to discuss potential as well as coupling functions in the evolving universe. These reconstructed functions are plotted versus scalar field and time for different values of power component of scale factor n. We observe that potential and coupling functions represent increasing behavior, in particular, consistent results for a specific value of n. Finally, we have examined validity of the generalized second law of thermodynamics and we have observed its validity for all values of n.

Comparing the VGCG model as the unification of dark sectors with observations

Current observations indicate that 95% of the energy density in the universe is the unknown dark component.The dark component is considered composed of two fluids:dark matter and dark energy.Or it is a mixture of these two dark components,i.e.,one can consider it an exotic unknown dark fluid.With this consideration,the variable generalized Chaplygin gas(VGCG)model is studied with not dividing the unknown fluid into dark matter and dark energy parts in this paper.By using the Markov Chain Monte Carlo method,the VGCG model as the unification of dark sectors is constrained,and the constraint results on the VGCG model parameters are,n=0.00057+0.0001+0.0009-0.0006-0.0006,α=0.0015+0.0003+0.0017-0.0015-0.0015and B s=0.778+0.016+0.030-0.016-0.035,obtained by the cosmic microwave background data from the 7-year WMAP full data points,the baryon acoustic oscillation data from Sloan Digital Sky Survey(SDSS)and 2-degree Field Galaxy Redshift(2dFGRS)survey,and the Union2 type Ia supernova data with systematic errors.At last,according to the evolution of deceleration parameter it is shown that an expanded universe from deceleration to acceleration can be obtained in VGCG cosmology.