New method to constrain the relativistic free-streaming gas in the Universe

We discuss a method to constrain the fraction density f of the relativistic gas in the radiation-dominant stage, by their impacts on a relic gravitational waves and the cosmic microwave background (CMB) B-polarization power spectrum. We find that the uncertainty of f   strongly depends on the noise power spectra of the CMB experiments and the amplitude of the gravitational waves. Taking into account of the CMBPol instrumental noises, an uncertainty Δf=0.046$\mathrm{\Delta }f=0.046$ is obtained for the model with tensor-to-scalar ratio r=0.1$r=0.1$. For an ideal experiment with only the reduced cosmic lensing as the contamination of B  -polarization, Δf=0.008$\mathrm{\Delta }f=0.008$ is obtained for the model with r=0.1$r=0.1$. So the precise observation of the CMB B-polarization provides a great opportunity to study the relativistic components in the early Universe.     

Cosmic microwave background fluctuations from gravitational waves: An analytic approach

We develop an analytic approach to calculation of the temperature and polarisation power spectra of the cosmic microwave background due to inflationary gravitational waves. This approach complements the more precise numerical results by providing insight into the physical origins of the features in the power spectra. We explore the use of analytic approximations for the gravitational-wave evolution, making use of the WKB approach to handle the radiation-matter transition. In the process, we describe scaling relations for the temperature and polarisation power spectra. We illustrate the dependence of the amplitude, shape, and peak locations on the details of recombination, the gravitational-wave power spectrum, and the cosmological parameters, and explain the origin of the peak locations in the temperature and polarisation power spectra. The decline in power on small scales in the polarisation power spectra is discussed in terms of phase-damping. In an appendix we detail numerical techniques for integrating the gravitational-wave evolution in the presence of anisotropic stress from free-streaming neutrinos.     

Gaussian wave packet states of relic gravitons

In this contribution, we investigate quantum effects of relic gravitons in a Friedmann–Robertson–Walker (FRW) cosmological background. We reduce the problem to that of a generalized time-dependent harmonic oscillator and find the corresponding exact Schrödinger states with the help of linear invariants and of the dynamical invariant method. Afterwards, we construct Gaussian wave packet states and calculate the quantum dispersions as well as the quantum correlations for each mode of the quantized field.     

Weak gravitational lensing of the CMB

Weak gravitational lensing has several important effects on the cosmic microwave background (CMB): it changes the CMB power spectra, induces non-Gaussianities, and generates a B-mode polarization signal that is an important source of confusion for the signal from primordial gravitational waves. The lensing signal can also be used to help constrain cosmological parameters and lensing mass distributions. We review the origin and calculation of these effects. Topics include: lensing in General Relativity, the lensing potential, lensed temperature and polarization power spectra, implications for constraining inflation, non-Gaussian structure, reconstruction of the lensing potential, delensing, sky curvature corrections, simulations, cosmological parameter estimation, cluster mass reconstruction, and moving lenses/dipole lensing.     

Energy-Momentum Pseudo-Tensor of Relic Gravitational Wave of Both the Polarized States

Unlike usual celestial gravitational waves, the relic gravitational waves （RGWs） form random signals in curved spacetime background. We calculate the energy-momentum pseudo-tensor of a certain component of the RGWs propagating along arbitrary directions in Cartesian coordinates. It is found that the energy density of RGWs is positive definitely, and the momentum density components have reasonable behaviour. Such results may provide a theoretical basis for the detection of RGWs.     

Evolution of high-frequency gravitational waves in some cosmological models

We investigate Isaacson’s high-frequency gravitational waves which propagate in some relevant cosmological models, in particular the FRW spacetimes. Their time evolution in Fourier space is explicitly obtained for various metric forms of (anti-)de Sitter universe. Behaviour of high-frequency waves in the anisotropic Kasner spacetime is also described.     

An Inflationary Solution of Scalar Field in Finsler Universe

Using the energy-dependent rainbow metric, we investigate the rainbow universe metric as a Finsler metric, and obtain an inflationary solution of the universe. The theoretical results are in agreement with the astronomical observations.     

Phase and Polarization State of High-Frequency Relic Gravitational Waves

The displaying condition of strength, phase and polarization states of high-frequency relic gravitational waves （HFRGWs） in electromagnetic （EM） detecting systems is studied. It is shown that the displaying condition depends not only on the sensitivity of EM detecting systems and the amplitudes of HFRGWs, but also on the phase, the polarization states of HFRGWs and their matching to the EM detecting systems. In order to display simultaneously the strength, phase and polarization states of the resonant ＂monochromatic component＂ of HFRGWs, an important necessary condition is the utilization of two or more different EM detectors.     

Dimensionally regulated graviton 1-point function in de Sitter

We use dimensional regularization to compute the 1PI 1-point function of quantum gravity at one loop order in a locally de Sitter background. As with other computations, the result is a finite constant at this order. It corresponds to a small positive renormalization of the cosmological constant.     

Coincidence problem in YM field dark energy model

The coincidence problem is studied in the effective Yang–Mills condensate dark energy model. As the effective YM Lagrangian is completely determined by quantum field theory, there is no adjustable parameter in this model except the energy scale, and the cosmic evolution only depends on the initial conditions. For generic initial conditions with the YM condensate subdominant to the radiation and matter, the model always has a tracking solution, the Universe transits from matter-dominated into the dark energy dominated stage only recently z∼0.3$z\sim 0.3$, and evolve to the present state with Ωy∼0.73${\Omega }_y\sim 0.73$ and Ωm∼0.27${\Omega }_m\sim 0.27$.     

Stabilization of the extra dimensions in brane gas cosmology with bulk flux

We consider the anisotropic evolution of spatial dimensions and the stabilization of internal dimensions in the framework of brane gas cosmology. We observe that the bulk RR field can give an effective potential which prevents the internal subvolume from collapsing. For a combination of (D−3)$(D-3)$-brane gas wrapping the extra dimensions and 4-form RR flux in the unwrapped dimensions, it is possible that the wrapped subvolume has an oscillating solution around the minimum of the effective potential while the unwrapped subvolume expands monotonically. The flux gives a logarithmic bounce to the effective potential of the internal dimensions.     

Circular Loop Equation of a Cosmic String in Gauss--Bonnet--de

We perform the analysis of evolution of cosmic string loops in the background of Gauss-Bonnet-de Sitter. The equation of motion of cosmic string loops in this spacetime is derived. Having solved the equation numerically, we investigate the dependence of the loop evolution on the values of a, related to the Gauss-Bonnet coupling. In the Gauss-Bonnet-de Sitter spacetimes with different dimensionality there exists a special parameter αm. In the environment with α 〉 αm, all the cosmic string loops will collapse to form black holes. Within the region 0 〈 α 〈 αm, the stronger Gauss-Bonnet effect will lead more cosmic string loops, including smaller ones, to form black holes. The larger the value of a is, the smaller the special values that exist, and only the cosmic string loops with initial radius larger than the special values can expand and evolve instead of becoming black holes.     

Dark energy from quantum wave function collapse of dark matter

Dynamical wave function collapse models entail the continuous liberation of a specified rate of energy arising from the interaction of a fluctuating scalar field with the matter wave function. We consider the wave function collapse process for the constituents of dark matter in our universe. Beginning from a particular early era of the universe chosen from physical considerations, the rate of the associated energy liberation is integrated to yield the requisite magnitude of dark energy around the era of galaxy formation. Further, the equation of state for the liberated energy approaches w→−1$w\to -1$ asymptotically, providing a mechanism to generate the present acceleration of the universe.     

Signature of the interaction between dark energy and dark matter in galaxy clusters

We investigate the influence of an interaction between dark energy and dark matter upon the dynamics of galaxy clusters. We obtain the general Layser–Irvine equation in the presence of interactions, and find how, in that case, the virial theorem stands corrected. Using optical, X-ray and weak lensing data from 33 relaxed galaxy clusters, we put constraints on the strength of the coupling between the dark sectors. Available data suggests that this coupling is small but positive, indicating that dark energy might be decaying into dark matter. Systematic effects between the several mass estimates, however, should be better known, before definitive conclusions on the magnitude and significance of this coupling could be established.     

Stability of the curvature perturbation in dark sectors' mutual interacting models

We consider perturbations in a cosmological model with a small coupling between dark energy and dark matter. We prove that the stability of the curvature perturbation depends on the type of coupling between dark sectors. When the dark energy is of quintessence type, if the coupling is proportional to the dark matter energy density, it will drive the instability in the curvature perturbations; however if the coupling is proportional to the energy density of dark energy, there is room for the stability in the curvature perturbations. When the dark energy is of phantom type, the perturbations are always stable, no matter whether the coupling is proportional to the one or the other energy density.     

Wave function of the Universe in the early stage of its evolution

In quantum cosmological models, constructed in the framework of Friedmann–Robertson–Walker metrics, a nucleation of the Universe with its further expansion is described as a tunneling transition through an effective barrier between regions with small and large values of the scale factor a at non-zero (or zero) energy. The approach for describing this tunneling consists of constructing a wave function satisfying an appropriate boundary condition. There are various ways for defining the boundary condition that lead to different estimates of the barrier penetrability and the tunneling time. In order to describe the escape from the tunneling region as accurately as possible and to construct the total wave function on the basis of its two partial solutions unambiguously, we use the tunneling boundary condition that the total wave function must represent only the outgoing wave at the point of escape from the barrier, where the following definition for the wave is introduced: the wave is represented by the wave function whose modulus changes minimally under a variation of the scale factor a. We construct a new method for a direct non-semiclassical calculation of the total stationary wave function of the Universe, analyze the behavior of this wave function in the tunneling region, near the escape point and in the asymptotic region, and estimate the barrier penetrability. We observe oscillations of the modulus of the wave function in the external region starting from the turning point which decrease with increasing of a and which are not shown in semiclassical calculations. The period of such an oscillation decreases uniformly with increasing a and can be used as a fully quantum dynamical characteristic of the expansion of the Universe.