New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects

Abstract

We present a general relativistic description of galaxy clustering in a FLRW universe. The observed redshift and position of galaxies are affected by the matter fluctuations and the gravity waves between the source galaxies and the observer, and the volume element constructed by using the observables differs from the physical volume occupied by the observed galaxies. Therefore, the observed galaxy fluctuation field contains additional contributions arising from the distortion in observable quantities and these include tensor contributions as well as numerous scalar contributions. We generalize the linear bias approximation to relate the observed galaxy fluctuation field to the underlying matter distribution in a gauge-invariant way. Our full formalism is essential for the consistency of theoretical predictions. As our first application, we compute the angular auto correlation of large-scale structure and its cross correlation with CMB temperature anisotropies. We comment on the possibility of detecting primordial gravity waves using galaxy clustering and discuss further applications of our formalism.

10 pages, 2 figures, accepted for publication in Physical Review D

References in corpus (22)

• The Sloan Digital Sky Survey: Technical Summary
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• The 2dF Galaxy Redshift Survey: Spectra and redshifts
• A Line of Sight Approach to Cosmic Microwave Background Anisotropies
• Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges
• Cosmological Perturbation Theory in the Synchronous vs. Conformal Newtonian Gauge
• Cosmological Constraints from the SDSS Luminous Red Galaxies
• An All-Sky Analysis of Polarization in the Microwave Background
• Spectroscopic Target Selection for the Sloan Digital Sky Survey: The Luminous Red Galaxy Sample
• The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
• Constraints on local primordial non-Gaussianity from large scale structure
• The effect of primordial non-Gaussianity on halo bias
• Measuring primordial non-gaussianity without cosmic variance
• Correlation of CMB with large-scale structure: I. ISW Tomography and Cosmological Implications
• Ray Tracing Simulations of Weak Lensing by Large-Scale Structure
• Fluctuations of the luminosity distance
• Analyzing weak lensing of the cosmic microwave background using the likelihood function
• A Complete Treatment of CMB Anisotropies in a FRW Universe
• Primordial non-Gaussianity: large-scale structure signature in the perturbative bias model
• Gauge-ready formulation of the cosmological kinetic theory in generalized gravity theories
• Complete Treatment of Galaxy Two-Point Statistics: Gravitational Lensing Effects and Redshift-Space Distortions
• The Sachs-Wolfe Effect: Gauge Independence and a General Expression

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