The linear power spectrum of observed source number counts

We relate the observable number of sources per solid angle and redshift to the underlying proper source density and velocity, background evolution and line-of-sight potentials. We give an exact result in the case of linearized perturbations assuming general relativity. This consistently includes contributions of the source density perturbations and redshift distortions, magnification, radial displacement, and various additional linear terms that are small on sub-horizon scales. In addition we calculate the effect on observed luminosities, and hence the result for sources observed as a function of flux, including magnification bias and radial-displacement effects. We give the corresponding linear result for a magnitude-limited survey at low redshift, and discuss the angular power spectrum of the total count distribution. We also calculate the cross-correlation with the CMB polarization and temperature including Doppler source terms, magnification, redshift distortions and other velocity effects for the sources, and discuss why the contribution of redshift distortions is generally small. Finally we relate the result for source number counts to that for the brightness of line radiation, for example 21-cm radiation, from the sources.

[1]  O. Lahav,et al.  Cosmological baryonic and matter densities from 600 000 SDSS luminous red galaxies with photometric redshifts , 2006, astro-ph/0605303.

[2]  Magnification-temperature correlation: The dark side of integrated Sachs-Wolfe measurements , 2006, astro-ph/0611539.

[3]  A. Lewis,et al.  Lensed CMB power spectra from all-sky correlation functions , 2005, astro-ph/0502425.

[4]  Jaiyul Yoo,et al.  Complete Treatment of Galaxy Two-Point Statistics: Gravitational Lensing Effects and Redshift-Space Distortions , 2008, 0808.3138.

[5]  E. Gaztañaga,et al.  Anisotropic magnification distortion of the 3D galaxy correlation. I. Real space , 2007, 0706.1071.

[6]  Roman Scoccimarro.  Redshift-space distortions, pairwise velocities and nonlinearities , 2004 .

[7]  W. Percival,et al.  Forecasting cosmological constraints from redshift surveys , 2008, 0810.1518.

[8]  Jaiyul Yoo.  General Relativistic Description of the Observed Galaxy Power Spectrum: Do We Understand What We Measure? , 2010, 1009.3021.

[9]  Newtonian versus relativistic nonlinear cosmology , 2005, astro-ph/0512636.

[10]  L. Samushia,et al.  Simulating redshift-space distortions for galaxy pairs with wide angular separation , 2010, 1006.1652.

[11]  R. Sachs.  Gravitational waves in general relativity. VI. The outgoing radiation condition , 1961, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[12]  Institute for Advanced Study,et al.  New perspective on galaxy clustering as a cosmological probe: General relativistic effects , 2009, 0907.0707.

[13]  A. Slosar,et al.  Scale-dependent bias from primordial non-Gaussianity in general relativity , 2009, 0902.1084.

[14]  T. Matsubara.  The Gravitational Lensing in Redshift-Space Correlation Functions of Galaxies and Quasars , 2000, astro-ph/0004392.

[15]  E. Gaztañaga,et al.  Lensing corrections to features in the angular two-point correlation function and power spectrum , 2007, 0708.0031.

[16]  E. Rozo,et al.  Size bias in galaxy surveys. , 2009, Physical review letters.

[17]  S. Matarrese,et al.  Effect of inhomogeneities on the luminosity distance-redshift relation: Is dark energy necessary in a perturbed universe? , 2005, astro-ph/0501152.

[18]  M. Zaldarriaga,et al.  Connection between Newtonian simulations and general relativity , 2011, 1101.3555.

[19]  D. Huterer,et al.  Imprints of primordial non-Gaussianities on large-scale structure: Scale-dependent bias and abundance of virialized objects , 2007, 0710.4560.

[20]  A. Lewis,et al.  Weak gravitational lensing of the CMB , 2006, astro-ph/0601594.

[21]  M. Birkinshaw,et al.  The luminosity distance in perturbed FLRW space-times , 2003, astro-ph/0310841.

[22]  S. Dodelson,et al.  Weak lensing effects on the galaxy three-point correlation function , 2008, 0804.0373.

[23]  A. Melchiorri,et al.  Searching for integrated Sachs–Wolfe effect beyond temperature anisotropies: CMB E-mode polarization–galaxy cross-correlation , 2005, astro-ph/0511054.

[24]  A. Lewis,et al.  Nonlinear redshift-space power spectra , 2008, 0808.1724.

[25]  F. Bernardeau,et al.  Full-sky lensing shear at second order , 2009, 0911.2244.

[26]  Donald Hamilton,et al.  The evolving universe. Selected topics on large-scale structure and on the properties of galaxies , 1998 .

[27]  J. Gunn.  A Fundamental Limitation on the Accuracy of Angular Measurements in Observational Cosmology , 1967 .

[28]  T. Giannantonio,et al.  The effect of reionization on the cosmic microwave background–density correlation , 2007, 0706.0274.

[29]  Fluctuations of the luminosity distance , 2005, astro-ph/0511183.

[30]  S. Dodelson,et al.  Universal Weak Lensing Distortion of Cosmological Correlation Functions , 2008, 0806.0331.

[31]  J. Hwang,et al.  Second-order perturbations of a zero-pressure cosmological medium: Comoving versus synchronous gauge , 2006, astro-ph/0601041.

[32]  M. Sasaki.  The magnitude-redshift relation in a perturbed Friedmann universe , 1987 .

[33]  N. Kaiser.  Clustering in real space and in redshift space , 1987 .

[34]  C. Hirata.  Tidal alignments as a contaminant of redshift space distortions , 2009, 0903.4929.

[35]  J. Peacock,et al.  Stable clustering, the halo model and non-linear cosmological power spectra , 2002, astro-ph/0207664.

[36]  Rebecca Whitaker Msfc.  The Evolving Universe , 2008 .

[37]  I. Szapudi,et al.  Non-perturbative effects of geometry in wide-angle redshift distortions , 2008, 0802.2940.

[38]  Redshift-Space Distortions of the Correlation Function in Wide-Angle Galaxy Surveys , 1997, astro-ph/9712007.

[39]  N. Turok,et al.  Looking for a cosmological constant with the Rees-Sciama effect. , 1996, Physical review letters.

[40]  Correlated fluctuations in luminosity distance and the importance of peculiar motion in supernova surveys , 2005, astro-ph/0512159.

[41]  The Correlation Function in Redshift Space: General Formula with Wide-Angle Effects and Cosmological Distortions , 1999, astro-ph/9908056.

[42]  Anthony Challinor,et al.  The shape of the CMB lensing bispectrum , 2011, 1101.2234.

[43]  21 cm angular-power spectrum from the dark ages , 2007, astro-ph/0702600.

[44]  Uros Seljak,et al.  Extracting primordial Non-Gaussianity without cosmic variance. , 2008, Physical review letters.

[45]  Steven Furlanetto,et al.  Cosmology at low frequencies: The 21 cm transition and the high-redshift Universe , 2006 .

[46]  Robert C. Nichol,et al.  The clustering of luminous red galaxies in the Sloan Digital Sky Survey imaging data , 2006, astro-ph/0605302.