Constraints on the neutrino mass and the primordial magnetic field from the matter density fluctuation parameter σ8\sigma_8

We have made an analysis of limits on the neutrino mass based upon the formation of large-scale structure in the presence of a primordial magnetic field. We find that a new upper bound on the neutrino mass is possible based upon fits to the cosmic microwave background and matter power spectrum when the existing independent constraints on the matter density fluctuation parameter $\sigma_8$ and the primordial magnetic field are taken into account.Comment: 6 pages, 2 figures, final version to appear in Phys. Rev. D, to match proof

Incentive Efficient Risk Sharing in Settlement Mechanism

The purpose of this paper is to address a question concerning risk management in continuing, multi-party, contractual, clearing and settlement arrangements through which large-value payments are typically made. We are particularly interested in the issues of incentive compatibility when athird party possesses a private information concerning the riskiness of transfers being made. If a third party possesses private information that would be of value in determining how best to settle a payment, how does the exposure of that party to the settlement risk affect the quality of information that the party chooses to provide? In this paper, we address the question by analyzing a specific class of parametric environments of a schematic, formal, model of a settlement arrangement or a payment netwrok.

Constraints on the Primordial Magnetic Field from σ8\sigma_8

A primordial magnetic field (PMF) can affect the evolution of density field fluctuations in the early universe.In this paper we constrain the PMF amplitude $B_\lambda$ and power spectral index $n_\mathrm{B}$ by comparing calculated density field fluctuations with observational data, i.e. the number density fluctuation of galaxies.We show that the observational constraints on cosmological density fluctuations, as parameterized by $\sigma_8$, lead to strong constraints on the amplitude and spectral index of the PMF.Comment: 11 pages, 1 figure, accepted for publication as Phys. Rev.

The Search for a Primordial Magnetic Field

Magnetic fields appear wherever plasma and currents can be found. As such, they thread through all scales in Nature. It is natural, therefore, to suppose that magnetic fields might have been formed within the high temperature environments of the big bang. Such a primordial magnetic field (PMF) would be expected to arise from and/or influence a variety of cosmological phenomena such as inflation, cosmic phase transitions, big bang nucleosynthesis, the cosmic microwave background (CMB) temperature and polarization anisotropies, the cosmic gravity wave background, and the formation of large-scale structure. In this review, we summarize the development of theoretical models for analyzing the observational consequences of a PMF. We also summarize the current state of the art in the search for observational evidence of a PMF. In particular we review the framework needed to calculate the effects of a PMF power spectrum on the CMB and the development of large scale structure. We summarize the current constraints on the PMF amplitude $B_\lambda$ and the power spectral index $n_B$ and discuss prospects for better determining these quantities in the near future.Comment: 40 pages, 13 figures, Accepted for Physics Reports 23 Feb 2012. Available online 3 March 2012. In press, corrected proo

Sharing the Risk of Settlement Failure: Synopsis

Two policies toward payments-system risk are common, but superficially appear to be contradictory. One policy is to restrict the exposure to risk generated by one participant to other participants who are, by one measure or another, directly concerned with the risky participant. The other policy is to provide a "safety net," typically provided by government and funded by taxes collected from all participants and even from non-participants, to share losses due to "systemic risk." In this paper, we provide a model in which both of these policies can be constituents of an economically efficient regime of payments-risk management.

Optimal double stopping of a Brownian bridge

We study optimal double stopping problems driven by a Brownian bridge. The objective is to maximize the expected spread between the payoffs achieved at the two stopping times. We study several cases where the solutions can be solved explicitly by strategies of threshold type

Primordial Magnetic Field Effects on the CMB and Large Scale Structure

Magnetic fields are everywhere in nature and they play an important role in every astronomical environment which involves the formation of plasma and currents. It is natural therefore to suppose that magnetic fields could be present in the turbulent high temperature environment of the big bang. Such a primordial magnetic field (PMF) would be expected to manifest itself in the cosmic microwave background (CMB) temperature and polarization anisotropies, and also in the formation of large- scale structure. In this review we summarize the theoretical framework which we have developed to calculate the PMF power spectrum to high precision. Using this formulation, we summarize calculations of the effects of a PMF which take accurate quantitative account of the time evolution of the cut off scale. We review the constructed numerical program, which is without approximation, and an improvement over the approach used in a number of previous works for studying the effect of the PMF on the cosmological perturbations. We demonstrate how the PMF is an important cosmological physical process on small scales. We also summarize the current constraints on the PMF amplitude $B_\lambda$ and the power spectral index $n_B$ which have been deduced from the available CMB observational data by using our computational framework.Comment: 26 pages, 13 figures. arXiv admin note: substantial text overlap with arXiv:1001.201

New Constraints on the Primordial Magnetic Field

We present the newest statistical and numerical analysis of the matter and cosmic microwave background power spectrum with effects of the primordial magnetic field (PMF) included. New limits to the PMF strength and power spectral index are obtained based upon the accumulated data for both the matter and CMB power spectra on small angular scales. We find that a maximum develops in the probability distribution for a magnitude of the PMF of $|B_\lambda| = 0.85 \pm 1.25(\pm 1\sigma)$ nG on a comoving scale of at 1 Mpc, corresponding to upper limits of $\mathbf{< 2.10 nG} (68$ and $\mathbf{< 2.98 nG} (95$. While for the power spectral index we find $n_\mathrm{B}= -2.37^{+0.88}_{-0.73}(\pm 1\sigma)$, corresponding to upper limits of $\mathbf{< -1.19} (68$ and $\mathbf{< -0.25} (95\mathrm{CL})$. This result provides new constraints on models for magnetic field generation and the physics of the early universe. We conclude that future observational programs for the CMB and matter power spectrum will likely provide not only upper limits but also lower limits to the PMF parameters.Comment: 7 pages, 3 figures, 1 table, final version to appear in Phys. Rev. D, to match proof

Constraints on the Evolution of the Primordial Magnetic Field from the Small-Scale Cosmic Microwave Background Angular Anisotropy

Recent observations of the cosmic microwave background (CMB) have extended the measured power spectrum to higher multipoles $l\gtrsim$1000, and there appears to be possible evidence for excess power on small angular scales. The primordial magnetic field (PMF) can strongly affect the CMB power spectrum and the formation of large scale structure. In this paper, we calculate the CMB temperature anisotropies generated by including a power-law magnetic field at the photon last-scattering surface (PLSS). We then deduce an upper limit on the PMF based on our theoretical analysis of the power excess on small angular scales. We have taken into account several important effects such as the modified matter sound speed in the presence of a magnetic field. An upper limit to the field strength of $|B_\lambda|\lesssim$ 4.7 nG at the present scale of 1 Mpc is deduced. This is obtained by comparing the calculated theoretical result including the Sunyaev-Zeldovich (SZ) effect with recent observed data on the small-scale CMB anisotropies from the $Wilkinson Microwave Anisotropy Probe$ (WMAP), the Cosmic Background Imager (CBI), and the Arcminute Cosmology Bolometer Array Receiver (ACBAR). We discuss several possible mechanisms for the generation and evolution of the PMF.Comment: 27 pages, 4 figures, accepted to ApJ April 10, 200