468 research outputs found
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 ; 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 . This value is
smaller compared to the average exponent 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 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 -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 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 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 . The coupling function has
the form , where 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 , 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
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