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 $0.1 t$, 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 $G\mu \lesssim 10^{-7}$, 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 $\chi$) 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 $\chi$ is known. This is the so-called ``spherical cutoff method''. In order to find the probability distribution for $\chi$ 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 $\chi$ 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