Spherical Curvature Inhomogeneities in String Cosmology

We study the evolution of non-linear spherically symmetric inhomogeneities in string cosmology. Friedmann solutions of different spatial curvature are matched to produce solutions which describe the evolution of non-linear density and curvature inhomogeneities. The evolution of bound and unbound inhomogeneities are studied. The problem of primordial black hole formation is discussed in the string cosmological context and the pattern of evolution is determined in the pre- and post-big-bang phases of evolution.Comment: 19 pages, Latex, 4 figure

Bounds on the cosmological abundance of primordial black holes from diffuse sky brightness: single mass spectra

We constrain the mass abundance of unclustered primordial black holes (PBHs), formed with a simple mass distribution and subject to the Hawking evaporation and particle absorption from the environment. Since the radiative flux is proportional to the numerical density, an upper bound is obtained by comparing the calculated and observed diffuse background values, (similarly to the Olbers paradox in which point sources are considered) for finite bandwidths. For a significative range of formation redshifts the bounds are better than several values obtained by other arguments $\Omega_{pbh} \leq 10^{-10}$; and they apply to PBHs which are evaporating today.Comment: 20 pages, 5 figures, to appear in PR

Poincar\'e recurrences in Hamiltonian systems with a few degrees of freedom

Hundred twenty years after the fundamental work of Poincar\'e, the statistics of Poincar\'e recurrences in Hamiltonian systems with a few degrees of freedom is studied by numerical simulations. The obtained results show that in a regime, where the measure of stability islands is significant, the decay of recurrences is characterized by a power law at asymptotically large times. The exponent of this decay is found to be $\beta \approx 1.3$. This value is smaller compared to the average exponent $\beta \approx 1.5$ found previously for two-dimensional symplectic maps with divided phase space. On the basis of previous and present results a conjecture is put forward that, in a generic case with a finite measure of stability islands, the Poncar\'e exponent has a universal average value $\beta \approx 1.3$ being independent of number of degrees of freedom and chaos parameter. The detailed mechanisms of this slow algebraic decay are still to be determined.Comment: revtex 4 pages, 4 figs; Refs. and discussion adde

Singularity structure in Veneziano's model

We consider the structure of the cosmological singularity in Veneziano's inflationary model. The problem of choosing initial data in the model is shown to be unsolved -- the spacetime in the asymptotically flat limit can be filled with an arbitrary number of gravitational and scalar field quanta. As a result, the universe acquires a domain structure near the singularity, with an anisotropic expansion of its own being realized in each domain.Comment: 16 pages, 2 figures, shorter then journal version; references added, discussion slightly expande

Limits on the Time Evolution of Space Dimensions from Newton's Constant

Limits are imposed upon the possible rate of change of extra spatial dimensions in a decrumpling model Universe with time variable spatial dimensions (TVSD) by considering the time variation of (1+3)-dimensional Newton's constant. Previous studies on the time variation of (1+3)-dimensional Newton's constant in TVSD theory had not been included the effects of the volume of the extra dimensions and the effects of the surface area of the unit sphere in D-space dimensions. Our main result is that the absolute value of the present rate of change of spatial dimensions to be less than about 10^{-14}yr^{-1}. Our results would appear to provide a prima facie case for ruling the TVSD model out. We show that based on observational bounds on the present-day variation of Newton's constant, one would have to conclude that the spatial dimension of the Universe when the Universe was at the Planck scale to be less than or equal to 3.09. If the dimension of space when the Universe was at the Planck scale is constrained to be fractional and very close to 3, then the whole edifice of TVSD model loses credibility.Comment: 22 pages, accepted for publication in Int.J.Mod.Phys.

Spatially Homogeneous String Cosmologies

We determine the most general form of the antisymmetric $H$-field tensor derived from a purely time-dependent potential that is admitted by all possible spatially homogeneous cosmological models in 3+1-dimensional low-energy bosonic string theory. The maximum number of components of the $H$ field that are left arbitrary is found for each homogeneous cosmology defined by the Bianchi group classification. The relative generality of these string cosmologies is found by counting the number of independent pieces of Cauchy data needed to specify the general solution of Einstein's equations. The hierarchy of generality differs significantly from that characteristic of vacuum and perfect-fluid cosmologies. The degree of generality of homogeneous string cosmologies is compared to that of the generic inhomogenous solutions of the string field equations.Comment: 16 pages, Latex, assumptions clarified, calculations unchanged, published in Phys. Rev.

Qualitative properties of scalar-tensor theories of Gravity

The qualitative properties of spatially homogeneous stiff perfect fluid and minimally coupled massless scalar field models within general relativity are discussed. Consequently, by exploiting the formal equivalence under conformal transformations and field redefinitions of certain classes of theories of gravity, the asymptotic properties of spatially homogeneous models in a class of scalar-tensor theories of gravity that includes the Brans-Dicke theory can be determined. For example, exact solutions are presented, which are analogues of the general relativistic Jacobs stiff perfect fluid solutions and vacuum plane wave solutions, which act as past and future attractors in the class of spatially homogeneous models in Brans-Dicke theory.Comment: 19 page

The Behaviour Of Cosmological Models With Varying-G

We provide a detailed analysis of Friedmann-Robertson-Walker universes in a wide range of scalar-tensor theories of gravity. We apply solution-generating methods to three parametrised classes of scalar-tensor theory which lead naturally to general relativity in the weak-field limit. We restrict the parameters which specify these theories by the requirements imposed by the weak-field tests of gravitation theories in the solar system and by the requirement that viable cosmological solutions be obtained. We construct a range of exact solutions for open, closed, and flat isotropic universes containing matter with equation of state $p\leq \frac{1}{3}\rho$ and in vacuum. We study the range of early and late-time behaviours displayed, examine when there is a `bounce' at early times, and expansion maxima in closed models.Comment: 58 pages LaTeX, 6 postscript figures, uses eps

Louis Joel Mordell's time in London

The celebrated number theorist Louis Joel Mordell spent around two and a half decades working in Manchester and for most of the rest of his career he was based in St John’s College, Cambridge. There was, however, a brief period when he was based in London. The standard biographies of Mordell’s life by and largely tend to overlook this period almost to the point of being deceptive about it. In this paper we will address this imbalance by discussing this chapter in Mordell’s life in more detail

Singularity-free cosmological solutions in quadratic gravity

We study a general field theory of a scalar field coupled to gravity through a quadratic Gauss-Bonnet term $\xi(\phi) R^2_{GB}$. The coupling function has the form $\xi(\phi)=\phi^n$, where $n$ is a positive integer. In the absence of the Gauss-Bonnet term, the cosmological solutions for an empty universe and a universe dominated by the energy-momentum tensor of a scalar field are always characterized by the occurrence of a true cosmological singularity. By employing analytical and numerical methods, we show that, in the presence of the quadratic Gauss-Bonnet term, for the dual case of even $n$, the set of solutions of the classical equations of motion in a curved FRW background includes singularity-free cosmological solutions. The singular solutions are shown to be confined in a part of the phase space of the theory allowing the non-singular solutions to fill the rest of the space. We conjecture that the same theory with a general coupling function that satisfies certain criteria may lead to non-singular cosmological solutions.Comment: Latex, 25 pages, 6 figures, some explanatory sentences and Comments added, version to appear in Physical Review