Stochastic Biasing and Weakly Non-linear Evolution of Power Spectrum

Distribution of galaxies may be a biased tracer of the dark matter distribution and the relation between the galaxies and the total mass may be stochastic, non-linear and time-dependent. Since many observations of galaxy clustering will be done at high redshift, the time evolution of non-linear stochastic biasing would play a crucial role for the data analysis of the future sky surveys. In this paper, we develop the weakly non-linear analysis and attempt to clarify the non-linear feature of the stochastic biasing. We compute the one-loop correction of the power spectrum for the total mass, the galaxies and their cross correlation. Assuming the local functional form for the initial galaxy distribution, we investigate the time evolution of the biasing parameter and the correlation coefficient. On large scales, we first find that the time evolution of the biasing parameter could deviate from the linear prediction in presence of the initial skewness. However, the deviation can be reduced when the initial stochasticity exists. Next, we focus on the quasi-linear scales, where the non-linear growth of the total mass becomes important. It is recognized that the scale-dependence of the biasing dynamically appears and the initial stochasticity could affect the time evolution of the scale-dependence. The result is compared with the recent N-body simulation that the scale-dependence of the halo biasing can appear on relatively large scales and the biasing parameter takes the lower value on smaller scales. Qualitatively, our weakly non-linear results can explain this trend if the halo-mass biasing relation has the large scatter at high redshift.Comment: 29pages, 7 postscript figures, submitted to Ap

Upper limits on neutrino masses from the 2dFGRS and WMAP: the role of priors

Solar, atmospheric, and reactor neutrino experiments have confirmed neutrino oscillations, implying that neutrinos have non-zero mass, but without pinning down their absolute masses. While it is established that the effect of neutrinos on the evolution of cosmic structure is small, the upper limits derived from large-scale structure data could help significantly to constrain the absolute scale of the neutrino masses. In a recent paper the 2dF Galaxy Redshift Survey (2dFGRS) team provided an upper limit m_nu,tot < 2.2 eV, i.e. approximately 0.7 eV for each of the three neutrino flavours, or phrased in terms of their contributioin to the matter density, Omega_nu/Omega_m < 0.16. Here we discuss this analysis in greater detail, considering issues of assumed 'priors' like the matter density Omega_m and the bias of the galaxy distribution with respect the dark matter distribution. As the suppression of the power spectrum depends on the ratio Omega_nu/Omega_m, we find that the out-of- fashion Mixed Dark Matter Model, with Omega_nu=0.2, Omega_m=1 and no cosmological constant, fits the 2dFGRS power spectrum and the CMB data reasonably well, but only for a Hubble constant H_0<50 km/s/Mpc. As a consequence, excluding low values of the Hubble constant, e.g. with the HST Key Project is important in order to get a strong constraint on the neutrino masses. We also comment on the improved limit by the WMAP team, and point out that the main neutrino signature comes from the 2dFGRS and the Lyman alpha forest.Comment: 24 pages, 12 figures Minor changes to matched version published in JCA

Cardiovascular Health Improvements with Diet and Exercise Intervention

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