How BAO measurements can fail to detect quintessence

We model the nonlinear growth of cosmic structure in different dark energy models, using large volume N-body simulations. We consider a range of quintessence models which feature both rapidly and slowly varying dark energy equations of state, and compare the growth of structure to that in a universe with a cosmological constant. The adoption of a quintessence model changes the expansion history of the universe, the form of the linear theory power spectrum and can alter key observables, such as the horizon scale and the distance to last scattering. The difference in structure formation can be explained to first order by the difference in growth factor at a given epoch; this scaling also accounts for the nonlinear growth at the 15% level. We find that quintessence models which feature late $(z<2)$, rapid transitions towards $w=-1$ in the equation of state, can have identical baryonic acoustic oscillation (BAO) peak positions to those in $\Lambda$CDM, despite being very different from $\Lambda$CDM both today and at high redshifts $(z \sim 1000)$. We find that a second class of models which feature non-negligible amounts of dark energy at early times cannot be distinguished from $\Lambda$CDM using measurements of the mass function or the BAO. These results highlight the need to accurately model quintessence dark energy in N-body simulations when testing cosmological probes of dynamical dark energy.Comment: 10 pages, 7 figures, to appear in the Invisible Univers International Conference AIP proceedings serie

Asteroseismic signatures of helium gradients in late F-type stars

Element diffusion is expected to occur in all kinds of stars : according to the relative effect of gravitation and radiative acceleration, they can fall or be pushed up in the atmospheres. Helium sinks in all cases, thereby creating a gradient at the bottom of the convective zones. This can have important consequences for the sound velocity, as has been proved in the sun with helioseismology. We investigate signatures of helium diffusion in late F-type stars by asteroseismology. Stellar models were computed with different physical inputs (with or without element diffusion) and iterated in order to fit close-by evolutionary tracks for each mass. The theoretical oscillation frequencies were computed and compared for pairs of models along the tracks. Various asteroseismic tests (large separations, small separations, second differences) were used and studied for the comparisons. The results show that element diffusion leads to changes in the frequencies for masses larger than 1.2 Msun. In particular the helium gradient below the convective zone should be detectable through the second differences.Comment: 8 pages, 11 figures, 2 tables Accepted for publication in Astronomy and Astrophysics. The official date of acceptance is 03/05/200

Reply to comment by B. Andreotti et al. on "Solving the mystery of booming sand dunes"

This reply addresses three main issues raised in the comment of Andreotti et al. [2008]. First, the turning of ray paths in a granular material does not preclude the propagation of body waves and the resonance condition described by Vriend et al. [2007]. The waveguide model still holds in the dune for the observed velocities, even with a velocity increase with depth as implied by Andreotti et al. [2008]. Secondly, the method of initiation of spontaneous avalanching does not influence the booming frequency. The frequency is independent of the source once sustained booming starts; it depends on the subsurface structure of the dune. Thirdly, if all data points from Vriend et al. [2007] are included in the analysis (and not an average or selection), no correlation is observed between the sustained booming frequency and average particle diameter

Lensing Corrections to Features in the Angular Two-Point Correlation Function and Power Spectrum

It is well known that magnification bias, the modulation of galaxy or quasar source counts by gravitational lensing, can change the observed angular correlation function. We investigate magnification-induced changes to the shape of the observed correlation function w(\theta) and the angular power spectrum C_{\ell}, paying special attention to the matter-radiation equality peak and the baryon wiggles. Lensing mixes the correlation function of the source galaxies with the matter correlation at the lower redshifts of the lenses. Since the lenses probe structure nearer to the observer, the angular scale dependence of the lensing terms is different from that of the sources, thus the observed correlation function is distorted. We quantify how the lensing corrections depend on the width of the selection function, the galaxy bias b, and the number count slope s. The correction increases with redshift and larger corrections are present for sources with steep number count slopes and/or broad redshift distributions. The most drastic changes to C_{\ell} occur for measurements at z >~1.5 and \ell <~ 100. For the source distributions we consider, magnification bias can shift the matter-radiation equality scale by 1-6% at z ~ 1.5 and by z ~ 3.5 the shift can be as large as 30%. The baryon bump in \theta^2w(\theta) is shifted by <~ 1% and the width is typically increased by ~10%. Shifts of >~ 0.5% and broadening of >~ 20% occur only for very broad selection functions and/or galaxies with (5s-2)/b>~2. However, near the baryon bump the magnification correction is not constant but a gently varying function which depends on the source population. Depending on how the w(\theta) data is fitted, this correction may need to be accounted for when using the baryon acoustic scale for precision cosmology.Comment: v2: 8 pages, 5 figures, text and figures condensed, references adde

Extending the halo mass resolution of NN-body simulations

We present a scheme to extend the halo mass resolution of N-body simulations of the hierarchical clustering of dark matter. The method uses the density field of the simulation to predict the number of sub-resolution dark matter haloes expected in different regions. The technique requires as input the abundance of haloes of a given mass and their average clustering, as expressed through the linear and higher order bias factors. These quantities can be computed analytically or, more accurately, derived from a higher resolution simulation as done here. Our method can recover the abundance and clustering in real- and redshift-space of haloes with mass below $\sim 7.5 \times 10^{13}h^{-1}M_{\odot}$ at $z=0$ to better than 10%. We demonstrate the technique by applying it to an ensemble of 50 low resolution, large-volume $N$-body simulations to compute the correlation function and covariance matrix of luminous red galaxies (LRGs). The limited resolution of the original simulations results in them resolving just two thirds of the LRG population. We extend the resolution of the simulations by a factor of 30 in halo mass in order to recover all LRGs. With existing simulations it is possible to generate a halo catalogue equivalent to that which would be obtained from a $N$-body simulation using more than 20 trillion particles; a direct simulation of this size is likely to remain unachievable for many years. Using our method it is now feasible to build the large numbers of high-resolution large volume mock galaxy catalogues required to compute the covariance matrices necessary to analyse upcoming galaxy surveys designed to probe dark energy.Comment: 11 pages, 7 Figure

Simultaneous Border-Collision and Period-Doubling Bifurcations

We unfold the codimension-two simultaneous occurrence of a border-collision bifurcation and a period-doubling bifurcation for a general piecewise-smooth, continuous map. We find that, with sufficient non-degeneracy conditions, a locus of period-doubling bifurcations emanates non-tangentially from a locus of border-collision bifurcations. The corresponding period-doubled solution undergoes a border-collision bifurcation along a curve emanating from the codimension-two point and tangent to the period-doubling locus here. In the case that the map is one-dimensional local dynamics are completely classified; in particular, we give conditions that ensure chaos.Comment: 22 pages; 5 figure

Configuration Complexities of Hydrogenic Atoms

The Fisher-Shannon and Cramer-Rao information measures, and the LMC-like or shape complexity (i.e., the disequilibrium times the Shannon entropic power) of hydrogenic stationary states are investigated in both position and momentum spaces. First, it is shown that not only the Fisher information and the variance (then, the Cramer-Rao measure) but also the disequilibrium associated to the quantum-mechanical probability density can be explicitly expressed in terms of the three quantum numbers (n, l, m) of the corresponding state. Second, the three composite measures mentioned above are analytically, numerically and physically discussed for both ground and excited states. It is observed, in particular, that these configuration complexities do not depend on the nuclear charge Z. Moreover, the Fisher-Shannon measure is shown to quadratically depend on the principal quantum number n. Finally, sharp upper bounds to the Fisher-Shannon measure and the shape complexity of a general hydrogenic orbital are given in terms of the quantum numbers.Comment: 22 pages, 7 figures, accepted i