CMBR constraints on R2R^2 gravity

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.Comment: summary of a talk presented in "COSMO-01 Particle physics and the early universe

Fully nonlinear and exact perturbations of the Friedmann world model: Non-flat background

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.Comment: 13 pages, no figur

Newtonian limit of fully nonlinear cosmological perturbations in Einstein's gravity

We prove that in the infinite speed-of-light limit (i.e., non-relativistic and subhorizon limits), the relativistic fully nonlinear cosmological perturbation equations in two gauge conditions, the zero-shear gauge and the uniform-expansion gauge, exactly reproduce the Newtonian hydrodynamic perturbation equations in the cosmological background; as a consequence, in the same two gauge conditions, the Newtonian hydrodynamic equations are exactly recovered in the Minkowsky background.Comment: 12 Pages, appeared in JCA

Newtonian, post-Newtonian and Relativistic Cosmological Perturbation Theory

Newtonian cosmological perturbation equations valid to full nonlinear order are well known in the literature. Assuming the absence of the transverse-tracefree part of the metric, we present the general relativistic counterpart valid to full nonlinear order. The relativistic equations are presented without taking the slicing (temporal gauge) condition. The equations do have the proper Newtonian and first post-Newtonian limits. We also present the relativistic pressure correction terms in the Newtonian hydrodynamic equations.Comment: 7 pages, published in Nuclear Physics B (Proc. Suppl.

Axion as a Cold Dark Matter candidate

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.Comment: 4 pages, no figur

Cosmological post-Newtonian equations from nonlinear perturbation theory

We derive the basic equations of the cosmological first-order post-Newtonian approximation from the recently formulated fully nonlinear and exact cosmological perturbation theory in Einstein's gravity. Apparently the latter, being exact, should include the former, and here we use this fact as a new derivation of the former. The complete sets of equations in both approaches are presented without fixing the temporal gauge conditions so that we can use the gauge choice as an advantage. Comparisons between the two approaches are made. Both are potentially important in handling relativistic aspects of nonlinear processes occurring in cosmological structure formation. We consider an ideal fluid and include the cosmological constant.Comment: 16 pages, no figur

Newtonian Hydrodynamics with General Relativistic Pressure

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.Comment: JCAP in press, 11 page

Unified Dark Fluid with Constant Adiabatic Sound Speed and Cosmic Constraints

As is known above 90% of the energy content in Universe is made of unknown dark component. Usually this dark fluid is separated into two parts: dark matter and dark energy. However, it may be a mixture of these two energy components, or just one exotic unknown fluid. This property is dubbed as dark degeneracy. With this motivation, in this paper, a unified dark fluid having constant adiabatic sound speed $c_s^2=\alpha$, which is in the range $[0,1]$, is studied. At first, via the energy conservation equation, its energy density, $\rho_d/\rho_{d0}=(1-B_s)+B_s a^{-3(1+\alpha)}$ where $B_s$ is related to integration constant from energy conservation equation as another model parameter, is presented. Then by using Markov Chain Monte Carlo method with currently available cosmic observational data sets which include type Ia supernova Union 2, baryon acoustic oscillation and WMAP 7-year data of cosmic background radiation, we show that small values of $\alpha$ are favored in this unified dark fluid model. Furthermore, we show that smaller values of $\alpha<10^{-5}$ are required to match matter (baryon) power spectrum from SDSS DR7.Comment: 9 pages, 5 figure

Cosmological nonlinear density and velocity power spectra including nonlinear vector and tensor modes

We present the leading order non-linear density and velocity power spectra in the complete form; previous studies have omitted the vector- and tensor-type perturbations simultaneously excited by the scalar-type perturbation in nonlinear order. These additional contributions are comparable to the scalar-type purely relativistic perturbations, and thus negligible in the current paradigm of concordance cosmology: i.e., concerning density and velocity perturbations of the pressureless matter in perturbation regime well inside of matter-dominated epoch, we show that pure Einstein's gravity contributions appearing from the third order are entirely negligible (five orders of magnitude smaller than the Newtonian contributions) in all scales. We thus prove that Newtonian perturbation theory is quite reliable in calculating the amplitude of matter fluctuations even in the precision era of cosmology. Therefore, besides the ones imprinted as the initial condition generated in the earlier phase, the other relativistic effect relevant for interpreting observational data must be the projection effect that occurs when mapping galaxies on to the observed coordinate.Comment: 13 pages, 2 figures, the version accepted to be published in MNRA

Gauge dependence of gravitational waves generated from scalar perturbations

A tensor-type cosmological perturbation, defined as a transverse and traceless spatial fluctuation, is often interpreted as the gravitational waves. While decoupled from the scalar-type perturbations in linear order, the tensor perturbations can be sourced from the scalar-type in the nonlinear order. The tensor perturbations generated by the quadratic combination of linear scalar-type cosmological perturbation are widely studied in the literature, but all previous studies are based on zero-shear gauge without proper justification. Here, we show that, being second order in perturbation, such an induced tensor perturbation is generically gauge dependent. In particular, the gravitational wave power spectrum depends on the hypersurface (temporal gauge) condition taken for the linear scalar perturbation. We further show that, during the matter-dominated era, the induced tensor modes dominate over the linearly evolved primordial gravitational waves amplitude for $k\gtrsim10^{-2}~[h/{\rm Mpc}]$ even for the gauge that gives lowest induced tensor modes with the optimistic choice of primordial gravitational waves ($r=0.1$). The induced tensor modes, therefore, must be modeled correctly specific to the observational strategy for the measurement of primordial gravitational waves from large-scale structure via, for example, parity-odd mode of weak gravitational lensing, or clustering fossils.Comment: 13 pages, 1 figure (4 files), submitted to Ap