BBN For Pedestrians

The simplest, `standard' model of Big Bang Nucleosynthesis (SBBN) assumes three light neutrinos (N_nu = 3) and no significant electron neutrino asymmetry, leaving only one adjustable parameter: the baryon to photon ratio eta. The primordial abundance of any one nuclide can, therefore, be used to measure the baryon abundance and the value derived from the observationally inferred primordial abundance of deuterium closely matches that from current, non-BBN data, primarily from the WMAP survey. However, using this same estimate there is a tension between the SBBN-predicted 4He and 7Li abundances and their current, observationally inferred primordial abundances, suggesting that N_nu may differ from the standard model value of three and/or that there may be a non-zero neutral lepton asymmetry (or, that systematic errors in the abundance determinations have been underestimated or overlooked). The differences are not large and the allowed ranges of the BBN parameters permitted by the data are quite small. Within these ranges, the BBN-predicted abundances of D, 3He, 4He, and 7Li are very smooth, monotonic functions of eta, N_nu, and the lepton asymmetry. It is possible to describe the dependencies of these abundances (or powers of them) upon the three parameters by simple, linear fits which, over their ranges of applicability, are accurate to a few percent or better. The fits presented here have not been maximized for their accuracy but, for their simplicity. To identify the ranges of applicability and relative accuracies, they are compared to detailed BBN calculations; their utility is illustrated with several examples. Given the tension within BBN, these fits should prove useful in facilitating studies of the viability of proposals for non-standard physics and cosmology, prior to undertaking detailed BBN calculations.Comment: Submitted to a Focus Issue on Neutrino Physics in New Journal of Physics (www.njp.org

Invalidation of the Kelvin Force in Ferrofluids

Direct and unambiguous experimental evidence for the magnetic force density being of the form $M\nabla B$ in a certain geometry - rather than being the Kelvin force $M\nabla H$ - is provided for the first time. (M is the magnetization, H the field, and B the flux density.)Comment: 4 pages, 4 figure

BBN and the Primordial Abundances

The relic abundances of the light elements synthesized during the first few minutes of the evolution of the Universe provide unique probes of cosmology and the building blocks for stellar and galactic chemical evolution, while also enabling constraints on the baryon (nucleon) density and on models of particle physics beyond the standard model. Recent WMAP analyses of the CBR temperature fluctuation spectrum, combined with other, relevant, observational data, has yielded very tight constraints on the baryon density, permitting a detailed, quantitative confrontation of the predictions of Big Bang Nucleosynthesis with the post-BBN abundances inferred from observational data. The current status of this comparison is presented, with an emphasis on the challenges to astronomy, astrophysics, particle physics, and cosmology it identifies.Comment: To appear in the Proceedings of the ESO/Arcetri Workshop on "Chemical Abundances and Mixing in Stars in the Milky Way and its Satellites", eds., L. Pasquini and S. Randich (Springer-Verlag Series, "ESO Astrophysics Symposia"

The Effect of Bound Dineutrons upon BBN

We have examined the effects of a bound dineutron, n2, upon big bang nucleosynthesis (BBN) as a function of its binding energy B_n2. We find a weakly bound dineutron has little impact but as B_n2 increases its presence begins to alter the flow of free nucleons to helium-4. Due to this disruption, and in the absence of changes to other binding energies or fundamental constants, BBN sets a reliable upper limit of B_n2 <~ 2.5 MeV in order to maintain the agreement with the observations of the primordial helium-4 mass fraction and D/H abundance

Collective neutrino flavor transitions in supernovae and the role of trajectory averaging

Non-linear effects on supernova neutrino oscillations, associated with neutrino self-interactions, are known to induce collective flavor transitions near the supernova core for theta_13 \neq 0. In scenarios with very shallow electron density profiles, these transformations have been shown to couple with ordinary matter effects, jointly producing spectral distortions both in normal and inverted hierarchy. In this work we consider a complementary scenario, characterized by higher electron density, as indicated by post-bounce shock-wave simulations. In this case, early collective flavor transitions are decoupled from later, ordinary matter effects. Moreover, such transitions become more amenable to both numerical computations and analytical interpretations in inverted hierarchy, while they basically vanish in normal hierarchy. We numerically evolve the neutrino density matrix in the region relevant for self-interaction effects. In the approximation of averaged intersection angle between neutrino trajectories, our simulations neatly show the collective phenomena of synchronization, bipolar oscillations, and spectral split, recently discussed in the literature. In the more realistic (but computationally demanding) case of non-averaged neutrino trajectories, our simulations do not show new significant features, apart from the smearing of ``fine structures'' such as bipolar nutations. Our results seem to suggest that, at least for non-shallow matter density profiles, averaging over neutrino trajectories plays a minor role in the final outcome. In this case, the swap of nu_e and nu_{\mu,\tau} spectra above a critical energy may represent an unmistakable signature of the inverted hierarchy, especially for theta_{13} small enough to render further matter effects irrelevant.Comment: v2 (27 pages, including 9 eps figures). Typos removed, references updated. Minor comments added. Corrected numerical errors in Eq.(6). Matches the published versio

Neutrino Scattering, Absorption and Annihilation above the accretion disks of Gamma Ray Bursts

The central engine that drives gamma ray burst (GRB) explosions may derive from the ability of electrons/positrons and nucleons to tap into the momentum and energy from the large neutrino luminosity emitted by an accretion disk surrounding a black hole. This transfer of momentum and energy occurs due to neutrino absorption, scattering, and annihilation and the non-spherical geometry of the source both increases the annihilation efficiency and, close to the black hole, directs the momentum transfer towards the disk axis. We present annihilation efficiencies and the momentum/energy transfers for a number of accretion disk models and compute the critical densities of infalling material below which the transfer of neutrino momentum/energy will lead to an explosion. Models in which the neutrinos and antineutrinos become trapped within the disk have noticeably different momentum and energy deposition structure compared to thin disk models that may lead to significant differences in the explosion dynamics

Residence Time Statistics for Normal and Fractional Diffusion in a Force Field

We investigate statistics of occupation times for an over-damped Brownian particle in an external force field. A backward Fokker-Planck equation introduced by Majumdar and Comtet describing the distribution of occupation times is solved. The solution gives a general relation between occupation time statistics and probability currents which are found from solutions of the corresponding problem of first passage time. This general relationship between occupation times and first passage times, is valid for normal Markovian diffusion and for non-Markovian sub-diffusion, the latter modeled using the fractional Fokker-Planck equation. For binding potential fields we find in the long time limit ergodic behavior for normal diffusion, while for the fractional framework weak ergodicity breaking is found, in agreement with previous results of Bel and Barkai on the continuous time random walk on a lattice. For non-binding potential rich physical behaviors are obtained, and classification of occupation time statistics is made possible according to whether or not the underlying random walk is recurrent and the averaged first return time to the origin is finite. Our work establishes a link between fractional calculus and ergodicity breaking.Comment: 12 page

Neutrino masses and the number of neutrino species from WMAP and 2dFGRS

We have performed a thorough analysis of the constraints which can be put on neutrino parameters from cosmological observations, most notably those from the WMAP satellite and the 2dF galaxy survey. For this data we find an upper limit on the sum of active neutrino mass eigenstates of \sum m_nu < 1.0 eV (95% conf.), but this limit is dependent on priors. We find that the WMAP and 2dF data alone cannot rule out the evidence from neutrinoless double beta decay reported by the Heidelberg-Moscow experiment. In terms of the relativistic energy density in neutrinos or other weakly interacting species we find, in units of the equivalent number of neutrino species, N_nu, that N_nu = 4.0+3.0-2.1 (95% conf.). When BBN constraints are added, the bound on N_\nu is 2.6+0.4-0.3 (95% conf.), suggesting that N_nu could possibly be lower than the standard model value of 3. This can for instance be the case in models with very low reheating temperature and incomplete neutrino thermalization. Conversely, if N_nu is fixed to 3 then the data from WMAP and 2dFGRS predicts that 0.2458 < Y_P < 0.2471, which is significantly higher than the observationally measured value. The limit on relativistic energy density changes when a small $\nu_e$ chemical potential is present during BBN. In this case the upper bound on N_nu from WMAP, 2dFGRS and BBN is N_nu < 6.5. Finally, we find that a non-zero \sum m_nu can be compensated by an increase in N_nu. One result of this is that the LSND result is not yet ruled out by cosmological observations.Comment: 10 pages, 6 figure

Precision Primordial 4^4He Measurement with CMB Experiments

Big bang nucleosynthesis (BBN) and the cosmic microwave background (CMB) are two major pillars of cosmology. Standard BBN accurately predicts the primordial light element abundances ($^4$He, D, $^3$He and $^7$Li), depending on one parameter, the baryon density. Light element observations are used as a baryometers. The CMB anisotropies also contain information about the content of the universe which allows an important consistency check on the Big Bang model. In addition CMB observations now have sufficient accuracy to not only determine the total baryon density, but also resolve its principal constituents, H and $^4$He. We present a global analysis of all recent CMB data, with special emphasis on the concordance with BBN theory and light element observations. We find $\Omega_{B}h^{2}=0.025+0.0019-0.0026$ and $Y_{p}=0.250+0.010-0.014$ (fraction of baryon mass as $^4$He) using CMB data alone, in agreement with $^4$He abundance observations. With this concordance established we show that the inclusion of BBN theory priors significantly reduces the volume of parameter space. In this case, we find $\Omega_{B}h^2=0.0244+0.00137-0.00284$ and $Y_p = 0.2493+0.0006-0.001$. We also find that the inclusion of deuterium abundance observations reduces the $Y_p$ and $\Omega_{B}h^2$ ranges by a factor of $\sim$2. Further light element observations and CMB anisotropy experiments will refine this concordance and sharpen BBN and the CMB as tools for precision cosmology.Comment: 7 pages, 3 color figures made minor changes to bring inline with journal versio