International Journal of Modern Physics D

The Lambda-Cold Dark Matter (ΛCDM) model describes successfully our Universe on large scales, as has been verified by a wide range of observations. A number of apparent inconsistencies have arisen between observations and ΛCDM predictions on small scales. In this work, the current status of observations on galactic and subgalactic scales is reviewed. Theoretical predictions and recent observations are brought together in order to reveal the nature and severity of the inconsistencies. Lastly, the progress towards the resolution of each one of these conflicts is briefly reviewed.

We present the results on the quantum birth of a hot FRW universe in de Sitter vacuum from a quantum fluctuation which contains radiation and strings or some quintessence with the equation of state p=-ε/3.The presence of radiation results in quantum tunnelling from a discrete energy level with a non-zero quantized temperature. Energy levels have non-zero width corresponding to temperature fluctuations. The observational constraint on the CMB anisotropy selects the admissible range of the model parameters. For the GUT scale initial de Sitter vacuum, the lower limit on temperature at the start of classical evolution is close to the values predicted by theories of reheating, while an upper limit is far from the threshold for a monopole rest mass. The probability of quantum birth from a level of non-zero energy is much bigger than the probability of quantum birth from nothing. The presence of material with p=-ε/3 mimics a positive curvature term which makes possible quantum tunnelling for an open and a flat universe. Most plausible case is a flat universe arising from an initial fluctuation with a small admixture of radiation and strings with the negative deficit angle.

Among the possible explanations for the puzzling observations of cosmic rays above the GZK cutoff there is growing interest in the ones that represent kinematical solutions, based either on general formulations of particle physics with small violations of Lorentz symmetry or on a quantum-gravity-motivated scheme for the breakdown of Lorentz symmetry. An unappealing aspect of these cosmic-ray-puzzle solutions is that they require the existence of a preferred class of inertial observers. Here I propose a new kinematical solution of the cosmic-ray puzzle, which does not require the existence of a preferred class of inertial observers. My proposal is a new example of a type of relativistic theories, the so-called "doubly-special-relativity" theories, which have already been studied extensively over the last two years. The core ingredient of the proposal is a deformation of Lorentz transformations in which also the Planck scale E_p (in addition to the speed-of-light scale c) is described as an invariant. Just like the introduction of the invariant c requires a deformation of the Galileian transformations into the Lorentz transformations, the introduction of the invariant E_p requires a deformation of the Lorentz transformations, but there is no special class of inertial observers. The Pierre Auger Observatory and the GLAST space telescope should play a key role in future developments of these investigations. I also emphasize that the doubly-special-relativity theory here proposed, besides providing a solution for the cosmic-ray puzzle, is also the first doubly-special-relativity theory with a natural description of macroscopic bodies, and may find applications in the context of a recently-proposed dark-energy scenario.

We investigate the matching of continuous gravitational wave (CGW) signals in an all sky search with reference to Earth based laser interferometric detectors. We consider the source location as the parameters of the signal manifold and templates corresponding to different source locations. It has been found that the matching of signals from locations in the sky that differ in their co-latitude and longitude by π radians decreases with source frequency. We have also made an analysis with the other parameters affecting the symmetries. We observe that it may not be relevant to take care of the symmetries in the sky locations for the search of CGW from the output of LIGO-I, GEO600 and TAMA detectors.

The properties of neutron star at temperatures 5 MeV, 10 MeV and 15 MeV are calculated by solving Tolmann–Oppenheimer–Volkoff (TOV) equation. The required equation of state of pure neutron matter is obtained using density dependent Sussex interaction. It is observed that maximum stable mass of the star corresponds to minimum gravitational radius for a given equation of state. Just like the limiting mass, limiting value of redshift, moment of inertia, Kepler frequency as well as Kepler period are observed in case of the neutron star. It is found that the star become somewhat 'massive' and 'fat' at higher temperatures. With the increase in temperature the moment of inertia and Kepler rotational period increase but redshift decreases and Kepler frequency slows down. We also predict that there is a possibility of pion condensation in pure neutron matter.

Spherically symmetric inhomogeneous dust collapse has been studied in higher dimensional space–time and the factors responsible for the appearance of a naked singularity are analyzed in the region close to the centre for the marginally bound case. It is clearly demonstrated that in the former case naked singularities do not appear in the space–time having more than five dimension, which appears to a strong result. The non-marginally bound collapse is also examined in five dimensions and the role of shear in developing naked singularities in this space–time is discussed in details. The five-dimensional space–time is chosen in the later case because we have exact solution in closed form only in five dimension and not in any other case.

In this paper Quantum Mechanics with Fundamental Length is chosen as Quantum Mechanics at Planck's scale. This is possible due to the theory of General Uncertainty Relations. Here Quantum Mechanics with Fundamental Length is obtained as a deformation of Quantum Mechanics. The distinguishing feature of the proposed approach in comparison with previous ones, lies in the fact that here the density matrix are subjected to deformation, whereas in the previous approaches only commutators are deformed. The density matrix obtained by deforming the quantum-mechanical one is named the density pro-matrix throughout this paper. Within our approach two main features of Quantum Mechanics are conserved: the probabilistic interpretation of the theory and the well-known measuring procedure corresponding to that interpretation. The proposed approach allows a description of the dynamics. In particular, the explicit form of the deformed Liouville's equation and the deformed Shrödinger's picture are given. Some implications of obtained results are discussed. In particular, the problem of singularity, the hypothesis of cosmic censorship, a possible improvement of the definition of statistical entropy and the problem of information loss in black holes are considered. It is shown that the results obtained here allow one to deduce in a simple and natural way the Bekenstein–Hawking's formula for black hole entropy in semiclassical approximation.

We propose that local Lorentz invariance is spontaneously violated at high energies, due to a nonvanishing vacuum expectation value of a vector field ϕ^μ, as a possible explanation of the observation of ultra-high energy cosmic rays with an energy above the GZK cutoff. Certain consequences of spontaneous breaking of Lorentz invariance in cosmology are discussed.

The one-loop effective action describing polarization of the vacuum due to virtual electron-positron pairs in the Maxwell theory of electromagnetism was obtained by Heisenberg and Euler, in the limit of a background field that is constant on the scale of the electron Compton-wavelength. The case of vanishing electric field and constant, ultra-strong magnetic field B≫B_c, where , yields a configuration whose energy density is less than that of the equivalent radiation field, suggesting why a magnetic field may be present in the early Universe back to the Planck era. For there is a similar but larger effect, allowing a "ferromagnetic" Yang–Mills vacuum state, in the grand-unified theory at temperatures , analyzed by Skalozub. Some further aspects of ultra-strong magnetic fields are discussed vis-à-vis the origin of the Galactic field B_g.

Bianchi type I magnetized cosmological models in the presence of a bulk viscous fluid are investigated. The source of the magnetic field is due to an electric current produced along the x-axis. The distribution consists of an electrically neutral viscous fluid with an infinite electrical conductivity. The coefficient of bulk viscosity is assumed to be a power function of mass density. The cosmological constant Λ is found to be positive and is a decreasing function of time which is supported by results from recent supernovae observations. The behaviour of the models in the presence and the absence of magnetic field are also discussed.

We study spacetimes of spherically symmetric anisotropic fluid with homothetic self-similarity. We find a class of solutions to the Einstein field equations by assuming that the tangential pressure of the fluid is proportional to its radial one and that the fluid moves along time-like geodesics. The energy conditions, and geometrical and physical properties of these solutions are studied and found that some of them represent gravitational collapse of an anisotropic fluid.