A transitioning universe with time varying G and decaying Λ

We present a model of a universe that transitions from an early deceleration phase to the current acceleration phase under the framework of general relativity, in the presence of gravitational coupling G（t） and cosmological terms A（t）. Einstein＇s field equations have been solved by considering the time dependent deceleration parameter （DP） which renders the scale factor e = （thekt）1/m where m, n and k are positive con- stants. The cosmological term （A （t）） is found to be positive and a decreasing function of time, which supports the result obtained from observations of type Ia supernovae. The geometrical and kinematical features of the model are examined in detail.

Detecting Very-High-Frequency Relic Gravitational Waves by a Waveguide

The polarization vector （PV） of an electromagnetic wave （EW） will experience a rotation in a region of spacetime perturbed by gravitational waves （GWs）. Based on this consideration, Cruise＇s group has built an annular waveguide to detect GWs. We give detailed calculations of the rotations of polarization vector of an EW caused by incident GWs from various directions and in various polarization states, and then analyze the accumulative effects on the polarization vector when the EW passes n cycles along the annular waveguide. We reexamine the feasibility and limitation of this method to detect GWs of high frequency around 100 MHz, in particular the relic gravitational waves （RGWs）. By comparing the spectrum of RGWs in the accelerating universe with the detector sensitivity of the current waveguide, it is found that the amplitude of the RGWs is too low to be detected by the waveguide detectors currently operating. Possible ways of improvements on detection are suggested.

A new interpretation of zero Lyapunov exponents in BKL time for Mixmaster cosmology

A global relationship between cosmological time and Belinskii-Khalatnikov -Lifshitz （BKL） time during the entire evolution of the Mixmaster Bianchi IX universe is used to explain why all the Lyapunov exponents are zero at the BKL time. The actual reason is that the domain of the cosmological time is finite as the BKL time runs from minus infinity to infinity.

Estimation of spectrum and parameters of relic gravitational waves using space-borne interferometers

We present a study of spectrum estimation of relic gravitational waves(RGWs) as a Gaussian stochastic background from output signals of future space-borne interferometers, like LISA and ASTROD.As the target of detection, the analytical spectrum of RGWs generated during inflation is described by three parameters: the tensor-scalar ratio, the spectral index and the running index. The Michelson interferometer is shown to have a better sensitivity than Sagnac and symmetrized Sagnac. For RGW detection, we analyze the auto-correlated signals for a single interferometer, and the cross-correlated, integrated as well as unintegrated signals for a pair of interferometers, and give the signal-to-noise ratio(SNR) for RGW, and obtain lower limits of the RGW parameters that can be detected. By suppressing noise level, a pair has a sensitivity2 orders better than a single for one year observation. SNR of LISA will be 4–5 orders higher than that of Advanced LIGO for the default RGW. To estimate the spectrum, we adopt the maximum likelihood(ML)estimation, calculate the mean and covariance of signals, obtain the Gaussian probability density function(PDF) and the likelihood function, and derive expressions for the Fisher matrix and the equation of the ML estimate for the spectrum. The Newton-Raphson method is used to solve the equation by iteration. When the noise is dominantly large, a single LISA is not effective for estimating the RGW spectrum as the actual noise in signals is not known accurately. For cross-correlating a pair, the spectrum cannot be estimated from the integrated output signals either, and only one parameter can be estimated with the other two being either fixed or marginalized. We use the ensemble averaging method to estimate the RGW spectrum from the un-integrated output signals. We also adopt a correlation of un-integrated signals to estimate the spectrum and three parameters of RGW in a Bayesian approach. For all three methods, we provide simulations to illustrate their feasibility.

Galaxy formation in the reionization epoch as hinted by WideField Camera 3 observations of the Hubble Ultra Deep Field

We present a large sample of candidate galaxies at z ≈ 7 - 10, selected in the Hubble Ultra Deep Field using the new observations of the Wide Field Camera 3 that was recently installed on the Hubble Space Telescope. Our sample is composed of 20 z850-dropouts （four new discoveries）, 15 Y105-dropouts （nine new discoveries） and 20 J125-dropouts （all new discoveries）. The surface densities of the Z850-dropouts are close to what was predicted by earlier studies, however, those of the Y105- and J125-dropouts are quite unexpected. While no Y105- or J125-dropouts have been found at AB ≤ 28.0 mag, their surface densities seem to increase sharply at fainter levels. While some of these candidates seem to be close to foreground galaxies and thus could possibly be gravitationally lensed, the overall surface densities after excluding such cases are still much higher than what would be expected if the luminosity function does not evolve from z ～ 7 to 10. Motivated by such steep increases, we tentatively propose a set of Schechter function parameters to describe the luminosity functions at z ≈8 and 10. As compared to their counterpart at z ≈ 7, here L^＊ decreases by a factor of ～ 6.5 and Ф^＊ increases by a factor of 17-90. Although such parameters are not yet demanded by the existing observations, they are allowed and seem to agree with the data better than other alternatives. If these luminosity functions are still valid beyond our current detection limit, this would imply a sudden emergence of a large number of low-luminosity galaxies when looking back in time to z ≈ 10, which, while seemingly exotic, would naturally fit in the picture of the cosmic hydrogen reionization. These early galaxies could easily account for the ionizing photon budget required by the reionization, and they would imply that the global star formation rate density might start from a very high value at z ≈ 10, rapidly reach the minimum at z≈ 7, and start to rise again towards z ≈ 6. In this scenario, the majority of the stellar mass that the universe assembled through the reionization epoch seems still undetected by current observations at z ≈ 6.

Space-Time Geometry of Quark and Strange Quark Matter

We study quark and strange quark matter in the context of general relativity. For this purpose, we solve Einstein＇s field equations for quark and strange quark matter in spherical symmetric space-times. We analyze strange quark matter for the different equations of state （EOS） in the spherical symmetric space-times, thus we are able to obtain the space-time geometries of quark and strange quark matter. Also, we discuss the features of the obtained solutions. The obtained solutions are consistent with the results of Brookhaven Laboratory, i.e. the quark-gluon plasma has a vanishing shear （i.e. quark-gluon plasma is perfect）.

Bianchi-V string cosmological model and late time acceleration

We have searched for the existence of the late time acceleration of the universe with string fluid as the source of matter in Bianchi-V space-time. To derive a deterministic solution, we choose the scale factor to be an increasing function of time that yields a time dependent deceleration parameter, representing a model which generates a universe showing a transition from an early decelerating phase to a recent accelerating phase. The study reveals that strings dominate the early universe and eventually disappear from the universe for sufficiently large times, i.e. in the present epoch. This picture is consistent with current astronomical observations. The physical behavior of the universe is discussed in detail.

Anisotropic massive strings in the scalar-tensor theory of gravitation

We present the model of an anisotropic universe with string fluid as the source of matter within the framework of the scalar-tensor theory of gravitation. An exact solution of field equations is obtained by applying Berman＇s law of variation to Hubble＇s parameter which yields a constant value of the deceleration parameter. The nature of classical potential is examined for the model under consideration. It has also been found that the massive strings dominate in the early universe and finally disap-pear from the universe. This is in agreement with current astronomical observations. The physical and dynamical properties of the model are also discussed.

Cosmological perturbations in a noncommutative braneworld inflation

We use the smeared, coherent state picture of noncommutativity to study evolution of perturbations in a noncommutative braneworld scenario. Within the stan- dard procedure of studying braneworld cosmological perturbations, we study the evo- lution of the Bardeen metric potential and curvature perturbations in this model. We show that in this setup, the early stage of the universe＇s evolution has a transient phan- tom evolution with imaginary effective sound speed.

Constraints on ultracompact minihalos using neutrino signals from gravitino dark matter decay

Ultracompact dark matter minihalos （UCMHs） would be formed during the early universe if there were large density perturbations. If dark matter can decay into particles described by the standard model, such as neutrinos, these objects would become potential astrophysical sources of emission which could be detected by in- struments such as IceCube. In this paper, we investigate neutrino signals from nearby UCMHs due to gravitino dark matter decay and compare these signals with the back- ground neutrino flux which is mainly from the atmosphere to obtain constraints on the abundance of UCMHs.

C-field cosmological models:revisited

We investigate plane symmetric spacetime filled with perfect fluid in the C-field cosmology of Hoyle and Narlikar. A new class of exact solutions has been obtained by considering the creation field C as a function of time only. To get the deterministic solution, it has been assumed that the rate of creation of matter-energy density is proportional to the strength of the existing C-field energy density. Several physical aspects and geometrical properties of the models are discussed in detail, especially showing that some of our solutions of C-field cosmology are free from singularity in contrast to the Big Bang cosmology. A comparative study has been carried out between two models, one singular and the other nonsingular, by contrasting the behaviour of the physical parameters. We note that the model in a unique way represents both the features of the accelerating as well as decelerating universe depending on the parameters and thus seems to provide glimpses of the oscillating or cyclic model of the universe without invoking any other agent or theory in allowing cyclicity.

Primordial black holes

Primordial black holes （PBHs） are a profound signature of primordial cosmological structures and provide a theoretical tool to study nontrivial physics of the early Universe. The mechanisms of PBH formation are discussed and observational constraints on the PBH spectrum, or effects of PBH evaporation, are shown to restrict a wide range of particle physics models, predicting an enhancement of the ultraviolet part of the spectrum of density perturbations, early dust-like stages, first order phase transitions and stages of superheavy metastable particle dominance in the early Universe. The mechanism of closed wall contraction can lead, in the inflationary Universe, to a new approach to galaxy formation, involving primordial clouds of massive BHs created around the intermediate mass or supermassive BH and playing the role of galactic seeds.

Cosmic microwave background constraints on the tensor-to-scalar ratio

One of the main goals of modern cosmic microwave background （CMB） missions is to measure the tensor-to-scalar ratio r accurately to constrain inflation models. Due to ignorance about the reionization history Xe （z）, this analysis is usu- ally done by assuming an instantaneous reionization Xe （z） which, however, can bias the best-fit value of r. Moreover, due to the strong mixing of B-mode and E-mode polarizations in cut-sky measurements, multiplying the sky coverage fraction fsky by the full-sky likelihood would not give satisfactory results. In this work, we forecast constraints on r for the Planck mission taking into account the general reionization scenario and cut-sky effects. Our results show that by applying an N-point interpo- lation analysis to the reionization history, the bias induced by the assumption of in- stantaneous reionization is removed and the value of r is constrained within 5% error level, if the true value of r is greater than about 0.1.