40 research outputs found
Non-linear dynamics of cosmic strings with non-scaling loops
At early stages the dynamics of cosmic string networks is expected to be
influenced by an excessive production of small loops at the scales of initial
conditions l_{min}. To understand the late time behavior we propose a very
simple analytical model of strings with a non-scaling population of loops. The
complicated non-linear dynamics is described by only a single parameter N ~
2/(1-C(l_{min})) where C(l) is a correlation function of the string tangent
vectors. The model predicts an appearance of two new length scales: the
coherence length \xi ~ t/N^2 and the cross-correlation length \chi ~ t/N. At
the onset of evolution N ~ 10 and at late times N is expected to grow
logarithmically due to cosmological stretching and emission of small loops. The
very late time evolution might be modified further when the gravitational
back-reaction scale grows larger than l_{min}.Comment: 5 pages, minor corrections, accepted for publication in Physical
Review
Cosmic string loops: large and small, but not tiny
We develop an analytical model to study the production spectrum of loops in
the cosmic string network. In the scaling regime, we find two different scales
corresponding to large (one order below horizon) and small (few orders below
horizon) loops. The very small (tiny) loops at the gravitational back reaction
scale are absent, and thus, our model has no ultra-violet divergences. We
calculate the spectrum of loops and derive analytical expressions for the
positions and magnitudes of the small and large scale peaks. The small loops
are produced by large bursts of similar loops moving with very high velocities
in the same direction. We describe the shape of large loops, which would
usually consist of few kinks and few cusps per oscillation cycle. We also argue
that the typical size of large loops is set by the correlation length, which
does not depend on the intercommutation probability p, while the interstring
distance scales as p^{1/3}.Comment: 6 pages, 1 figure, power-law approximation is replaced with
exponentia
Scaling of cosmic string loops
We study the spectrum of loops as a part of a complete network of cosmic
strings in flat spacetime. After a long transient regime, characterized by
production of small loops at the scale of the initial conditions, it appears
that a true scaling regime takes over. In this final regime the characteristic
length of loops scales as , in contrast to earlier simulations which
found tiny loops. We expect the expanding-universe behavior to be qualitatively
similar. The large loop sizes have important cosmological implications. In
particular, the nucleosynthesis bound becomes , much
tighter than before.Comment: Added discussion of gravitational wave bounds; other minor change
Numerical search for a fundamental theory
We propose a numerical test of fundamental physics based on the complexity
measure of a general set of functions, which is directly related to the
Kolmogorov (or algorithmic) complexity studied in mathematics and computer
science. The analysis can be carried out for any scientific experiment and
might lead to a better understanding of the underlying theory. From a
cosmological perspective, the anthropic description of fundamental constants
can be explicitly tested by our procedure. We perform a simple numerical search
by analyzing two fundamental constants: the weak coupling constant and the
Weinberg angle, and find that their values are rather atypical.Comment: 6 pages, 3 figures, RevTeX, expansion and clarification, references
adde
Cosmic string scaling in flat space
We investigate the evolution of infinite strings as a part of a complete
cosmic string network in flat space. We perform a simulation of the network
which uses functional forms for the string position and thus is exact to the
limits of computer arithmetic. Our results confirm that the wiggles on the
strings obey a scaling law described by universal power spectrum. The average
distance between long strings also scales accurately with the time. These
results suggest that small-scale structure will also scale in expanding
universe, even in the absence of gravitational damping.Comment: 13 pages,7 figure
Stochastic inflation on the brane
Chaotic inflation on the brane is considered in the context of stochastic
inflation. It is found that there is a regime in which eternal inflation on the
brane takes place. The corresponding probability distributions are found in
certain cases. The stationary probability distribution over a comoving volume
and the creation probability of a de Sitter braneworld yield the same
exponential behaviour. Finally, nonperturbative effects are briefly discussed.Comment: 9 page
Quantum effects in gravitational wave signals from cuspy superstrings
We study the gravitational emission, in Superstring Theory, from fundamental
strings exhibiting cusps. The classical computation of the gravitational
radiation signal from cuspy strings features strong bursts in the special null
directions associated to the cusps. We perform a quantum computation of the
gravitational radiation signal from a cuspy string, as measured in a
gravitational wave detector using matched filtering and located in the special
null direction associated to the cusp. We study the quantum statistics
(expectation value and variance) of the measured filtered signal and find that
it is very sharply peaked around the classical prediction. Ultimately, this
result follows from the fact that the detector is a low-pass filter which is
blind to the violent high-frequency quantum fluctuations of both the string
worldsheet, and the incoming gravitational field.Comment: 16 pages, no figur
Cosmic string loop distribution on all length scales and at any redshift
We analytically derive the expected number density distribution of Nambu-Goto
cosmic string loops at any redshift soon after the time of string formation to
today. Our approach is based on the Polchinski-Rocha model of loop formation
from long strings which we adjust to fit numerical simulations and complement
by a phenomenological modelling of gravitational backreaction. Cosmological
evolution drives the loop distribution towards scaling on all length scales in
both the radiation and matter era. Memory of any reasonable initial loop
distribution in the radiation era is shown to be erased well before Big Bang
Nucleosynthesis. In the matter era, the loop distribution reaches full scaling,
up to some residual loops from the radiation era which may be present for
extremely low string tension. Finally, the number density of loops below the
gravitational cutoff is shown to be scale independent, proportional to a
negative power of the string tension and insensitive to the details of the
backreaction modelling. As an application, we show that the energy density
parameter of loops today cannot exceed 10^(-5) for currently allowed string
tension values, while the loop number density cannot be less than 10^(-6) per
Mpc^3. Our result should provide a more robust basis for studying the
cosmological consequences of cosmic string loops.Comment: 24 pages, 4 figures, uses iopart. References added, matches published
versio
A prescription for probabilities in eternal inflation
Some of the parameters we call ``constants of Nature'' may in fact be
variables related to the local values of some dynamical fields. During
inflation, these variables are randomized by quantum fluctuations. In cases
when the variable in question (call it ) takes values in a continuous
range, all thermalized regions in the universe are statistically equivalent,
and a gauge invariant procedure for calculating the probability distribution
for is known. This is the so-called ``spherical cutoff method''. In
order to find the probability distribution for it suffices to consider a
large spherical patch in a single thermalized region. Here, we generalize this
method to the case when the range of is discontinuous and there are
several different types of thermalized region. We first formulate a set of
requirements that any such generalization should satisfy, and then introduce a
prescription that meets all the requirements. We finally apply this
prescription to calculate the relative probability for different bubble
universes in the open inflation scenario.Comment: 15 pages, 5 figure
Towards a gauge invariant volume-weighted probability measure for eternal inflation
An improved volume-weighted probability measure for eternal inflation is
proposed. For the models studied in this paper it leads to simple and
intuitively expected gauge-invariant results.Comment: 16 pages, 3 figs, few misprints corrected, comments adde