The stochastic background from cosmic (super)strings: popcorn and (Gaussian) continuous regimes

In the era of the next generation of gravitational wave experiments a stochastic background from cusps of cosmic (super)strings is expected to be probed and, if not detected, to be significantly constrained. A popcorn-like background can be, for part of the parameter space, as pronounced as the (Gaussian) continuous contribution from unresolved sources that overlap in frequency and time. We study both contributions from unresolved cosmic string cusps over a range of frequencies relevant to ground based interferometers, such as LIGO/Virgo second generation (AdLV) and Einstein Telescope (ET) third generation detectors, the space antenna LISA and Pulsar Timing Arrays (PTA). We compute the sensitivity (at $2 \sigma$ level) in the parameter space for AdLV, ET, LISA and PTA. We conclude that the popcorn regime is complementary to the continuous background. Its detection could therefore enhance confidence in a stochastic background detection and possibly help determine fundamental string parameters such as the string tension and the reconnection probability.Comment: 21 pages, 11 figures ; revised version after correction of a typo in eq. 4.

Bargaining under incomplete information, fairness, and the hold-up problem

"In the hold-up problem incomplete contracts cause the proceeds of relationship-specific investments to be allocated by bargaining. This paper investigates the corresponding investment incentives if individuals have heterogeneous fairness preferences and thus differ in their bargaining behavior. Individual preferences are taken to be private information. Investments can then signal preferences and thereby influence beliefs and bargaining behavior. In consequence, individuals might choose high investments in order not to signal information that is unfavorable in the ensuing bargaining." [author's abstract

Elastic pion-nucleon scattering in chiral perturbation theory: A fresh look

Elastic pion-nucleon scattering is analyzed in the framework of chiral perturbation theory up to fourth order within the heavy-baryon expansion and a covariant approach based on an extended on-mass-shell renormalization scheme. We discuss in detail the renormalization of the various low-energy constants and provide explicit expressions for the relevant $\beta$-functions and the finite subtractions of the power-counting breaking terms within the covariant formulation. To estimate the theoretical uncertainty from the truncation of the chiral expansion, we employ an approach which has been successfully applied in the most recent analysis of the nuclear forces. This allows us to reliably extract the relevant low-energy constants from the available scattering data at low energy. The obtained results provide a clear evidence that the breakdown scale of the chiral expansion for this reaction is related to the $\Delta$-resonance. The explicit inclusion of the leading contributions of the $\Delta$-isobar is demonstrated to substantially increase the range of applicability of the effective field theory. The resulting predictions for the phase shifts are in an excellent agreement with the ones from the recent Roy-Steiner-equation analysis of pion-nucleon scattering

Cosmic String Cusps with Small-Scale Structure: Their Forms and Gravitational Waveforms

We present a method for the introduction of small-scale structure into strings constructed from products of rotation matrices. We use this method to illustrate a range of possibilities for the shape of cusps that depends on the properties of the small-scale structure. We further argue that the presence of structure at cusps under most circumstances leads to the formation of loops at the size of the smallest scales. On the other hand we show that the gravitational waveform of a cusp remains generally unchanged; the primary effect of small-scale structure is to smooth out the sharp waveform emitted in the direction of cusp motion.Comment: RevTeX, 8 pages. Replaced with version accepted for publication by PR

Equal sharing rules in partnerships

Partnerships are the prevalent organizational form in many industries. Profits are most frequently shared equally among the partners. The purpose of our paper is to provide a rationale for equal sharing rules. We show that with inequity averse partners the equal sharing rule is the unique sharing rule that maximizes the partners' incentives to exert effort. We further show that inequity aversion can enhance efficiency in partnerships of given size, but that it can also cause partnerships to be inefficiently small

On the size of the smallest scales in cosmic string networks

We present a method for the calculation of the gravitational back reaction cutoff on the smallest scales of cosmic string networks taking into account that not all modes on strings interact with all other modes. This results in a small scale structure cutoff that is sensitive to the initial spectrum of perturbations present on strings. From a simple model, we compute the cutoffs in radiation- and matter-dominated universes.Comment: 4 pages, revte

Thomas-Fermi Approximation for a Condensate with Higher-order Interactions

We consider the ground state of a harmonically trapped Bose-Einstein condensate within the Gross-Pitaevskii theory including the effective-range corrections for a two-body zero-range potential. The resulting non-linear Schr\"odinger equation is solved analytically in the Thomas-Fermi approximation neglecting the kinetic energy term. We present results for the chemical potential and the condensate profiles, discuss boundary conditions, and compare to the usual Thomas-Fermi approach. We discuss several ways to increase the influence of effective-range corrections in experiment with magnetically tunable interactions. The level of tuning required could be inside experimental reach in the near future.Comment: 8 pages, RevTex4 format, 5 figure

Gravitational wave bursts from cosmic (super)strings: Quantitative analysis and constraints

We discuss data analysis techniques that can be used in the search for gravitational wave bursts from cosmic strings. When data from multiple interferometers are available, we describe consistency checks that can be used to greatly reduce the false alarm rates. We construct an expression for the rate of bursts for arbitrary cosmic string loop distributions and apply it to simple known solutions. The cosmology is solved exactly and includes the effects of a late-time acceleration. We find substantially lower burst rates than previous estimates suggest and explain the disagreement. Initial LIGO is unlikely to detect field theoretic cosmic strings with the usual loop sizes, though it may detect cosmic superstrings as well as cosmic strings and superstrings with non-standard loop sizes (which may be more realistic). In the absence of a detection, we show how to set upper limits based on the loudest event. Using Initial LIGO sensitivity curves, we show that these upper limits may result in interesting constraints on the parameter space of theories that lead to the production of cosmic strings.Comment: Replaced with version accepted for publication in PR