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Register a new userCosmological Density and Power Spectrum from Peculiar Velocities: Nonlinear Corrections and PCA
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L. Silberman
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We allow for nonlinear effects in the likelihood analysis of galaxy peculiar velocities, and obtain ~35%-lower values for the cosmological density parameter Om and the amplitude of mass-density fluctuations. The power spectrum in the linear regime is assumed to be a flat LCDM model (h=0.65, n=1, COBE) with only Om as a free parameter. Since the likelihood is driven by the nonlinear regime, we break the power spectrum at k_b=0.2 h/Mpc and fit a power law at k>k_b. This allows for independent matching of the nonlinear behavior and an unbiased fit in the linear regime. The analysis assumes Gaussian fluctuations and errors, and a linear relation between velocity and density. Tests using proper mock catalogs demonstrate a reduced bias and a better fit. We find for the Mark3 and SFI data Om_m=0.32+-0.06 and 0.37+-0.09 respectively, with sigma_8*Om^0.6 = 0.49+-0.06 and 0.63+-0.08, in agreement with constraints from other data. The quoted 90% errors include cosmic variance. The improvement in likelihood due to the nonlinear correction is very significant for Mark3 and moderately so for SFI. When allowing deviations from LCDM, we find an indication for a wiggle in the power spectrum: an excess near k=0.05 and a deficiency at k=0.1 (cold flow). This may be related to the wiggle seen in the power spectrum from redshift surveys and the second peak in the CMB anisotropy. A chi^2 test applied to modes of a Principal Component Analysis (PCA) shows that the nonlinear procedure improves the goodness of fit and reduces a spatial gradient of concern in the linear analysis. The PCA allows addressing spatial features of the data and fine-tuning the theoretical and error models. It shows that the models used are appropriate for the cosmological parameter estimation performed. We address the potential for optimal data compression using PCA.
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We allow for nonlinear effects in the likelihood analysis of peculiar velocities, and obtain ~35%-lower values for the cosmological density parameter and for the amplitude of mass-density fluctuations. The power spectrum in the linear regime is assumed to be of the flat LCDM model (h=0.65, n=1) with only Om_m free. Since the likelihood is driven by the nonlinear regime, we break the power spectrum at k_b=0.2 h/Mpc and fit a two-parameter power-law at k>k_b. This allows for an unbiased fit in the linear regime. Tests using improved mock catalogs demonstrate a reduced bias and a better fit. We find for the Mark III and SFI data Om_m=0.35+-0.09$ with sigma_8*Om_m^0.6=0.55+-0.10 (90% errors). When allowing deviations from lcdm, we find an indication for a wiggle in the power spectrum in the form of an excess near k~0.05 and a deficiency at k~0.1 h/Mpc --- a cold flow which may be related to a feature indicated from redshift surveys and the second peak in the CMB anisotropy. A chi^2 test applied to principal modes demonstrates that the nonlinear procedure improves the goodness of fit. The Principal Component Analysis (PCA) helps identifying spatial features of the data and fine-tuning the theoretical and error models. We address the potential for optimal data compression using PCA.
We write the correlation function of dark matter particles, xi(r), as the sum of two terms - one which accounts for nonlinear evolution, and dominates on small scales, and another which is essentially the term from linear theory, and dominates on large scales. We use models of the number and spatial distribution of haloes and halo density profiles to describe the nonlinear term and its evolution. The result provides a good description of the evolution of xi(r) in simulations. We then use this decomposition to provide simple and accurate models of how the single particle velocity dispersion evolves with time, and how the first and second moments of the pairwise velocity distribution depend on scale. The key idea is to use the simple physics of linear theory on large scales, the simple physics of the virial theorem on small scales, and our model for the correlation function to tell us how to weight the two types of contributions (linear and nonlinear) to the pairwise velocity statistics. When incorporated into the streaming model, our results will allow a simple accurate description of redshift-space distortions over the entire range of linear to highly nonlinear regimes.
We constrain the velocity power spectrum shape parameter $Gamma$ in linear theory using the nine bulk-flow and shear moments estimated from four recent peculiar velocity surveys. For each survey, a likelihood function for $Gamma$ was found after marginalizing over the power spectrum amplitude $sigma_8Omega_m^{0.6}$ using constraints obtained from comparisons between redshift surveys and peculiar velocity data. In order to maximize the accuracy of our analyses, the velocity noise $sigma_*$ was estimated directly for each survey. A statistical analysis of the differences between the values of the moments estimated from different surveys showed consistency with theoretical predictions, suggesting that all the surveys investigated reflect the same large scale flows. The peculiar velocity surveys were combined into a composite survey yielding the constraint $Gamma=0.13^{+0.09}_{-0.05}$. This value is lower than, but consistent with, values obtained using redshift surveys and CMB data.
Peculiar velocities are a precious tool to study the large-scale distribution of matter in the local universe and test cosmological models. However, present measurements of peculiar velocities are based on empirical distance indicators, which introduce large error bars. Here we present a new method to measure the peculiar velocities, by directly estimating luminosity distances through waveform signals from inspiralling compact binaries and measuring redshifts from electromagnetic (EM) counterparts. In the future, with the distance uncertainty of GW events reducing to $0.1$ per cent by future GW detectors, the uncertainty of the peculiar velocity can be reduced to $10$ km/s at 100 mega parsecs. We find that dozens of GW events with EM counterparts can provide a Hubble constant $H_0$ uncertainty of $0.5%$ and the growth rate of structure with a $0.6%$ precision in the third-generation ground-base GW detectors, which can reconcile the $H_0$ tension and determine the origins for cosmic accelerated expansion.
We compare and combine likelihood functions of the cosmological parameters Omega_m, h and sigma_8, from peculiar velocities, CMB and type Ia supernovae. These three data sets directly probe the mass in the Universe, without the need to relate the galaxy distribution to the underlying mass via a biasing relation. We include the recent results from the CMB experiments BOOMERANG and MAXIMA-1. Our analysis assumes a flat Lambda CDM cosmology with a scale-invariant adiabatic initial power spectrum and baryonic fraction as inferred from big-bang nucleosynthesis. We find that all three data sets agree well, overlapping significantly at the 2 sigma level. This therefore justifies a joint analysis, in which we find a joint best fit point and 95 per cent confidence limits of Omega_m=0.28 (0.17,0.39), h=0.74 (0.64,0.86), and sigma_8=1.17 (0.98,1.37). In terms of the natural parameter combinations for these data sigma_8 Omega_m^0.6 = 0.54 (0.40,0.73), Omega_m h = 0.21 (0.16,0.27). Also for the best fit point, Q_rms-ps = 19.7 muK and the age of the universe is 13.2 Gyr.
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