Abstract:
observations on the anisotropies of the cosmic microwave background have become a fundamental tool in cosmology. we present a brief description of the mathematical formulae that is necessary to understand the evolution of the anisotropies, and how their power spectrum gives us information about the evolution and composition of the universe.

Abstract:
Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity – such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans–Dicke theory and Gauss–Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.

Abstract:
Cosmological Models frequently suggest the existence of physical, quantities, e.g. dark energy, we cannot yet observe and measure directly. Their values are obtained indirectly setting them equal to values and accuracy of the associated model parameters which best fit model and observation. Apparently results are so accurate that some researchers speak of precision cosmology. The accuracy attributed to these indirect values of the physical quantities however does not include the uncertainty of the model used to get them. We suggest a Confidence Level Estimator to be attached to these indirect measurements and apply it to current cosmological models.

Abstract:
The Bianchi type- III and Kantowski-Sachs (KS) Universes filled with dark energy from a wet dark fluid has been considered. A new equation of state for the dark energy component of the universe has been used. It is modeled on the equation of state ρ=γ(ρ -ρ _{*}) , which can describe a liquid, for example water. The exact solutions to the corresponding field equations are obtained in quadrature form. The solution for constant deceleration parameter have been studied in detail for power-law and exponential forms both. The case γ = 0,γ =1,and γ =1/3have been also analysed.

Abstract:
In this paper, we have studied the generalized chaplygin gas of interacting dark energy to ob-tain the equation of state for the generalized chaplygin gas energy density in anisotropic Bianchi type-I cosmological model. For negative value of B in equation of state of generalized chaplygin gas, we see that γ ^{eff}_{Λ}<-1 , that corresponds to a universe dominated by phantom dark energy.

Abstract:
The Bianchi type- VIo universe filled with dark energy from a wet dark fluid has been considered. A new equation of state for the dark energy component of the universe has been used. It is modeled on the equation of state p=γ(ρ-ρ_{﹡}) which can describe a liquid, for example water. The exact solutions to the corresponding field equations are obtained in quadrature form. The solution for constant deceleration parameter have been studied in detail for power-law and exponential forms both. The case γ=0, γ=1, and γ=1/3 have been also analysed.

A closed model of the universe was constructed according to the assumption that very minor fraction of the dark energy transfers so slowly to matter and radiation. The cosmological parameter is no longer fixed but represents so slowly decreasing function with time. In this model the universe expands to maximum limit at t_{me} = 26.81253 Gyr, then it will contract to a big crunch at t_{bc} = 53.6251 Gyr. Observational tests to the closed cosmic model were illustrated. Distributions of the universe expansion and contraction speed established in this model which indicated that the expansion speed in the early universe is appreciably high, then it will decrease rapidly until it vanishes at t_{me}. However, the contraction speed of the universe increases continuously until the time just before t_{be}. Distributions of the universe expansion and contraction acceleration were performed empirically which confirmed the previous result were performed empirically. In the closed cosmic model the universe history can be categorized into six main stages, these are the first radiation epoch, the first matter epoch, the first dark energy epoch, the last dark energy epoch, the last matter epoch and the last radiation epoch. Distributions of the density parameters of the radiation, matter, dark energy and the total density as well as the distributions of temperature of the radiation and non-relativistic matter were all investigated in this model at all epochs of the universe.

The cosmological constant problem is reanalyzed by imposing the limitation of the number of degrees of freedom (d.o.f.) due to entropy bounds directly in the calculation of the energy density of a field theory. It is shown that if a quantum field theory has to be consistent with gravity and holography, i.e. with an upper limit of storing information in a given area, the ultraviolet momentum cut-off is not the Planck mass, M_{p}, as naively expected, but where N_{u}is the number of d.o.f. of the universe. The energy density evaluation turns out completely consistent with Bousso’s bound on the cosmological constant value. The scale , that in the “fat graviton” theory corresponds to the graviton size, originates by a self-similar rearrangement of the elementary d.o.f. at different scales that can be seen as an infrared-ultraviolet connection.

Abstract:
The author presents how to make a link between the low temperature and low entropy of pre big bang state of cosmology as given by Carroll and Chen in 2005, to the quantum cosmology conditions predicted by Weinberg when the temperature reaches 10^{32} degrees Kelvin. We do this bridge building in our model construction as a way to get about the fact that cosmological CMB is limited by a red shift about z = 1100, so in order to get our suppositions consistent with observations, we also examine what happens in our model when we introduce quantization via a shift in values of the Hartle-Hawking wave function from a lower value of nearly zero to one which is set via an upper bound of the Planck’s constant of the order of 360 times the square of the Planck’s mass.

Abstract:
If a non-zero graviton mass exists, the question arises if a release of gravitons, possibly as a “Graviton gas” at the onset of inflation could be an initial vacuum state. Pros and cons to this idea are raised, in part based upon Bose gases. The analysis starts with Volovik’s condensed matter treatment of GR, and ends with consequences, which the author sees, if the supposition is true.