Axion minicluster power spectrum and mass function

When Peccei-Quinn (PQ) symmetry breaking happens after inflation, the axion field takes random values in causally disconnected regions. This leads to fluctuations of order one in the axion energy density around the QCD epoch. These over-densities eventually decouple from the Hubble expansion and form so-called miniclusters. We present a semi-analytical method to calculate the average axion energy density, as well as the power spectrum, from the re-alignment mechanism in this scenario. Furthermore, we develop a modified Press & Schechter approach, suitable to describe the collapse of non-linear density fluctuations during radiation domination, which is relevant for the formation of axion miniclusters. It allows us to calculate the double differential distribution of gravitationally collapsed miniclusters as a function of their mass and size. For instance, assuming a PQ scale of $10^{11}$ GeV, minicluster masses range from about $5 \times 10^{-16}$ to $3 \times 10^{-13}$ solar masses and have sizes from about $4\times 10^4$ to $7\times 10^5$ km at the time they start to collapse.Comment: minor changes to the style of figs; corresponds to the version publ in JCAP; 25 pages, 7 figure

Non-isotropy in the CMB power spectrum in single field inflation

Contaldi et al. [1] have suggested that an initial period of kinetic energy domination in single field inflation may explain the lack of CMB power at large angular scales. We note that in this situation it is natural that there also be a spatial gradient in the initial value of the inflaton field, and that this can provide a spatial asymmetry in the observed CMB power spectrum, manifest at low multipoles. We investigate the nature of this asymmetry and comment on its relation to possible anomalies at low multipoles.Comment: 25 pages, 12 figures. In this revised version, we include the Integrated Sachs-Wolfe effect, which was missing from the original. This modifies some results in the low multipoles. The comparison with experiment is slightly better but the change is not statistically significan

A fresh look at linear cosmological constraints on a decaying dark matter component

We consider a cosmological model in which a fraction $f$ of the Dark Matter (DM) is allowed to decay in an invisible relativistic component, and compute the resulting constraints on both the decay width (or inverse lifetime) $\Gamma$ and $f$ from purely gravitational arguments. We report a full derivation of the Boltzmann hierarchy, correcting a mistake in previous literature, and compute the impact of the decay --as a function of the lifetime-- on the CMB and matter power spectra. From CMB only, we obtain that no more than 3.8 % of the DM could have decayed in the time between recombination and today (all bounds quoted at 95 % CL). We also comment on the important application of this bound to the case where primordial black holes constitute DM, a scenario notoriously difficult to constrain. For lifetimes longer than the age of the Universe, the bounds can be cast as $f\Gamma < 6.3\times10^{-3}$ Gyr$^{-1}$. For the first time, we also checked that degeneracies with massive neutrinos are broken when information from the large scale structure is used. Even secondary effects like CMB lensing suffice to this purpose. Decaying DM models have been invoked to solve a possible tension between low redshift astronomical measurements of $\sigma_8$ and $\Omega_{\rm m}$ and the ones inferred by Planck. We reassess this claim finding that with the most recent BAO, HST and $\sigma_8$ data extracted from the CFHT survey, the tension is only slightly reduced despite the two additional free parameters, loosening the bound to $f\Gamma < 15.9\times10^{-3}$ Gyr$^{-1}$. The bound however improves to $f\Gamma < 5.9\times10^{-3}$ Gyr$^{-1}$ if only data consistent with the CMB are included. This highlights the importance of establishing whether the tension is due to real physical effects or unaccounted systematics, for settling the reach of achievable constraints on decaying DM.Comment: 30p, 11 figures, comments welcom

Sports attendance: A survey of the Literature 1973-2007

Introduction – 1. Theoretical aspects – 2. Demand definition, data andempirical model – 3. Determinants of attendance (I): Economical aspects – 4.Determinants of attendance (II): Expected quality – 5. Determinants of attendance(III): Uncertainty of outcome – 6. Determinants of attendance (IV): Opportunity cost and other factors – Conclusions – Abstract In this paper, we show a review of the empirical analysis literature about the factors that explain attendance to the stadiums on different sports, mainly in the case of professional sports. Apart from the traditional economic determinants of demand (attendance), the sports events in which the performers have more quality and in those which exists uncertainty of outcome of the match or the championship, have a larger number of spectators. On the other hand, these are not the only factors that explain attendance. Variables that capture the opportunity cost of going to the stadium and other determinants, like unobservable factors associated to the contender teams, also have relevance at the time of analyzing this side of the demand related to professional teams of sports eventsAttendance, elasticity, quality, uncertainty of outcome

A Better Understanding of the Performance of Rate-1/2 Binary Turbo Codes that Use Odd-Even Interleavers

The effects of the odd-even constraint - as an interleaver design criterion - on the performance of rate-1/2 binary turbo codes are revisited. According to the current understanding, its adoption is favored because it makes the information bits be uniformly protected, each one by its own parity bit. In this paper, we provide instances that contradict this point of view suggesting for a different explanation of the constraint's behavior, in terms of distance spectrum

Agnesi Weighting for the Measure Problem of Cosmology

The measure problem of cosmology is how to assign normalized probabilities to observations in a universe so large that it may have many observations occurring at many different spacetime locations. I have previously shown how the Boltzmann brain problem (that observations arising from thermal or quantum fluctuations may dominate over ordinary observations if the universe expands sufficiently and/or lasts long enough) may be ameliorated by volume averaging, but that still leaves problems if the universe lasts too long. Here a solution is proposed for that residual problem by a simple weighting factor 1/(1+t^2) to make the time integral convergent. The resulting Agnesi measure appears to avoid problems other measures may have with vacua of zero or negative cosmological constant.Comment: 26 pages, LaTeX; discussion is added of how Agnesi weighting appears better than other recent measure

Quintessence and variation of the fine structure constant in the CMBR

We study dependence of the CMB temperature anisotropy spectrum on the value of the fine structure constant $\alpha$ and the equation of state of the dark energy component of the total density of the universe. We find that bounds imposed on the variation of $\alpha$ from the analysis of currently available CMB data sets can be significantly relaxed if one also allows for a change in the equation of state.Comment: 5 pages, 3 figures. Several references added and a few minor typos corrected in the revised versio