Abstract:
Considering the inflation model based on a $f(R)$ gravity theory, we obtain several important constraints from the large angular scale CMBR observations. First, the ordinary slow-roll assumption during the inflation together with Harrison-Zel'dovich spectral conditions chooses $R^2$ gravity as a unique candidate. Second, the $R^2$ gravity leads to specific near scale-invariant Harrison-Zel'dovich spectra both for the scalar and the tensor perturbations. Third, using the COBE-DMR data we derive the strong constraints on the coupling constant and the energy scale during the inflation. Also, our result shows the gravitational wave contribution to the CMBR anisotropy is negligible. So, the future observation can provide the strong constraints on the inflation model based on $R^2$ gravity. This is a summary of a talk presented in COSMO-01, and the more completed published version can be found in astro-ph/0102423.

Abstract:
We extend the fully non-linear and exact cosmological perturbation equations in a Friedmann background universe to include the background curvature. The perturbation equations are presented in a gauge ready form, so any temporal gauge condition can be adopted freely depending on the problem to be solved. %The background curvature term explicitly appears only in the energy and momentum constraint equations. We consider the scalar, and vector perturbations without anisotropic stress. As an application, we analyze the equations in the special case of irrotational zero-pressure fluid in the comoving gauge condition. We also present the fully nonlinear formulation for a minimally coupled scalar field.

Abstract:
A new class of static plane symmetric solution of Einstein field equation, which is judged as the source of Taub solution, was presented in our previous work. In this letter the properties of geodesics of this solution are explored. It is found that this solution can be an appropriate simulation to the field of a uniformly accelerated observer in Newton mechanics. The essence of the source is investigated. A phantom with dust and photon is suggested as the substance of the source matter.

Abstract:
A new class of plane symmetric solution sourced by a perfect fluid is found in our recent work. An n-dimensional ($n\geq 4$) global plane symmetric solution of Einstein field equation generated by a perfect fluid source is investigated, which is the direct generalization of our previous 4-dimensional solution. One time-like Killing vector and $(n-2)(n-1)/2$ space-like Killing vectors, which span a Euclidean group $G_{(n-2)(n-1)/2}$, are permitted in this solution. The regions of the parameters constrained by weak, strong and dominant energy conditions for the source are studied. The boundary condition to match to n-dimensional Taub metric and Minkowski metric are analyzed respectively.

Abstract:
A new braneworld in the sourced-Taub background is proposed. The gravity field equations in the internal source region and external vacuum region are investigated, respectively. We find that the equation of state for the effective dark energy of a dust brane in the source region can cross the phantom divide $w=-1$. Furthermore, there is a drop on $H(z)$ diagram, which presents a possible mechanism for the recent direct data of $H(z)$.

Abstract:
Here we generally prove that the axion as a coherently oscillating scalar field acts as a cold dark matter in nearly all cosmologically relevant scales. The proof is made in the linear perturbation order. Compared with our previous proof based on solutions, here we compare the equations in the axion with the ones in the cold dark matter, thus expanding the valid range of the proof. Deviation from purely pressureless medium appears in very small scale where axion reveals a peculiar equation of state. Our analysis is made in the presence of the cosmological constant, and our conclusions are valid in the presence of other fluid and field components.

Abstract:
A modified Chaplygin gas model (MCG), $\rho_{MCG}/\rho_{MCG0}=[B_{s}+(1-B_{s})a^{-3(1+B)(1+\alpha)}]^{1/(1+\alpha)}$, as a unified dark matter model and dark energy model is constrained by using current available cosmic observational data points which include type Ia supernovae, baryon acoustic oscillation and the seventh year full WMAP data points. As a contrast to the consideration in the literatures, we {\it do not} separate the MCG into two components, i.e. dark mater and dark energy component, but we take it as a whole energy component-a unified dark sector. By using Markov Chain Monte Carlo method, a tight constraint is obtained: $\alpha= 0.000727_{- 0.00140- 0.00234}^{+ 0.00142+ 0.00391}$, $B=0.000777_{- 0.000302- 0.000697}^{+ 0.000201+ 0.000915}$ and $B_s= 0.782_{- 0.0162- 0.0329}^{+ 0.0163+ 0.0307}$ .}

Abstract:
We present the general relativistic pressure correction terms in Newtonian hydrodynamic equations to the nonlinear order: these are equations (\ref{mass-conservation-Mink})-(\ref{Poisson-eq-Mink}). The derivation is made in the zero-shear gauge based on the fully nonlinear formulation of cosmological perturbation in Einstein's gravity. The correction terms {\it differ} from many of the previously suggested forms in the literature based on hand-waving manners. We confirm our results by comparing with (i) the nonlinear perturbation theory, (ii) the first order post-Newtonian approximation, and (iii) the special relativistic limit, and by checking (iv) the consistency with full Einstein's equation.

Abstract:
We compare the cosmological first-order post-Newtonian (1PN) approximation with the relativistic cosmological linear perturbation theory in a zero-pressure medium with the cosmological constant. We compare equations and solutions in several different gauge conditions available in both methods. In the PN method we have perturbation equations for density, velocity and gravitational potential independently of the gauge condition to 1PN order. However, correspondences with these 1PN equations are available only in certain gauge conditions in the perturbation theory. Equations of perturbed velocity and the perturbed gravitational potential in the zero-shear gauge exactly coincide with the Newtonian equations which remain valid even to 1PN order (the same is true for perturbed velocity in the comoving gauge), and equations of perturbed density in the zero-shear gauge and the uniform-expansion gauge coincide to 1PN order. We identify other correspondences available in different gauge conditions of the perturbation theory.

Abstract:
In this paper, a decay vacuum model $\bar{\rho}_\Lambda=3\sigma M_p^2H_0 H$ is revisited by detailed analysis of background evolution and perturbation equations. We show the imprints on CMB temperature and matter power spectrum from the effective coupling terms between dark sectors by comparing to the standard cosmological constant model and observational data points (WMAP7 and SDSS DR7). We find that the decay vacuum model can describe the expansion rate at late times as well as the standard cosmological constant model but it fails to simultaneously reproduce the observed CMB and matter power spectrum. Its generalization $\bar{\rho}_\Lambda=3M_p^2(\xi_1 H_0 H+\xi_2 H^2)$ is also discussed. Detailed analysis of the background evolution shows that the dimensionless parameter $\xi_{2}$ would be zero to avoid the unnatural 'fine tuning' and to keep the positivity of energy density of dark matter and dark energy in the early epoch.