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Register a new userCovariant Decomposition of The Nonlinear Galaxy Number Counts and Their Monopole
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Added by
Yonadav Barry Ginat
Publication date
2021
fields
Physics
and research's language is
English
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We present a fully nonlinear and relativistically covariant expression for the observed galaxy density contrast. Building on a null tetrad tailored to the cosmological observers past light cone, we find a decomposition of the nonlinear galaxy over-density into manifestly gauge-invariant quantities, each of which has a clear physical interpretation as a cosmological observable. This ensures that the monopole of the galaxy over-density field is properly accounted for. We anticipate that this decomposition will be useful for future work on nonlinearities in galaxy number counts, for example, deriving the relativistic expression for the galaxy bispectrum. We then specialise our results to conformal Newtonian gauge, with a Hubble parameter either defined globally or measured locally, illustrating the significance of the different contributions to the observed monopole of the galaxy density.
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Next generation surveys will be capable of determining cosmological parameters beyond percent level. To match this precision, theoretical descriptions should look beyond the linear perturbations to approximate the observables in large scale structure. A quantity of interest is the Number density of galaxies detected by our instruments. This has been focus of interest recently, and several efforts have been made to explain relativistic effects theoretically, thereby testing the full theory. However, the results at nonlinear level from previous works are in disagreement. We present a new and independent approach to computing the relativistic galaxy number counts to second order in cosmological perturbation theory. We derive analytical expressions for the full second order relativistic observed redshift, for the angular diameter distance and for the volume spanned by a survey. Finally, we compare our results with previous works which compute the general distance-redshift relation, finding that our result is in agreement at linear order.
Sunyaev-Zeldovich (SZ) surveys are promising probes of cosmology - in particular for Dark Energy (DE) -, given their ability to find distant clusters and provide estimates for their mass. However, current SZ catalogs contain tens to hundreds of objects and maximum likelihood estimators may present biases for such sample sizes. In this work we use the Monte Carlo approach to determine the presence of bias on cosmological parameter estimators from cluster abundance as a function of the area and depth of the survey, and the number of cosmological parameters fitted. Assuming perfect knowledge of mass and redshift some estimators have non-negligible biases. For example, the bias of $sigma_8$ corresponds to about $40%$ of its statistical error bar when fitted together with $Omega_c$ and $w_0$. Including a SZ mass-observable relation decreases the relevance of the bias, for the typical sizes of current surveys. The biases become negligible when combining the SZ data with other cosmological probes. However, we show that the biases from SZ estimators do not go away with increasing sample sizes and they may become the dominant source of error for an all sky survey at the South Pole Telescope (SPT) sensitivity. The results of this work validate the use of the current maximum likelihood methods for present SZ surveys, but highlight the need for further studies for upcoming experiments. [abridged]
We present a detailed derivation of the observed galaxy number over-density on cosmological scales up to second order in perturbation theory. We include all relativistic effects that arise from observing on the past lightcone. The derivation is in a general gauge, and applies to all dark energy models (including interacting dark energy) and many modified gravity models. The result will be important for accurate cosmological parameter estimation, including non-Gaussianity, since all projection effects need to be taken into account. It also offers the potential for new probes of General Relativity, dark energy and modified gravity. This paper accompanies Paper I which presents the key results for the concordance model in Poisson gauge.
We study up to second order the galaxy number over-density that depends on magnification in redshift space on cosmological scales for a concordance model. The result contains all general relativistic effects up to second order which arise from observing on the past light cone, including all redshift and lensing distortions, contributions from velocities, Sachs-Wolfe, integrated SW and time-delay terms. We find several new terms and contributions that could be potentially important for an accurate calculation of the bias on estimates of non-Gaussianity and on precision parameter estimates.
Our velocity relative to the cosmic microwave background (CMB) generates a dipole from the CMB monopole, which was accurately measured by COBE. The relative velocity also modulates and aberrates the CMB fluctuations, generating a small signature of statistical isotropy violation in the covariance matrix. This signature was first measured by Planck 2013. Galaxy surveys are similarly affected by a Doppler boost. The dipole generated from the number count monopole has been extensively discussed, and measured (at very low accuracy) in the NVSS and TGSS radio continuum surveys. For the first time, we present an analysis of the Doppler imprint on the number count fluctuations, using the bipolar spherical harmonic formalism to quantify these effects. Next-generation wide-area surveys with a high redshift range are needed to detect the small Doppler signature in number count fluctuations. We show that radio continuum surveys with the SKA should enable a detection at $gtrsim 3 sigma$ in Phase 2, with marginal detection possible in Phase 1.
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