Higher-Order Gravitational Perturbations of the Cosmic Microwave Background

Abstract

We study the behavior of light rays in perturbed Robertson-Walker cosmologies, calculating the redshift between an observer and the surface of last scattering to second order in the metric perturbation. At first order we recover the classic results of Sachs and Wolfe, and at second order we delineate the various new effects which appear; there is no {\it a priori} guarantee that these effects are significantly smaller than those at first order, since there are large length scales in the problem which could lead to sizable prefactors. We find that second order terms of potential observational interest may be interpreted as transverse and longitudinal lensing by foreground density perturbations, and a correction to the integrated Sachs-Wolfe effect.

arXiv comment21 pages, one figure; minor corrections, new references

References in corpus (15)

• Toward Understanding CMB Anisotropies and Their Implications
• Reionization and cosmic microwave background distortions: a complete treatment of second order Compton scattering
• Re-Ionization and its Imprint on the Cosmic Microwave Background
• A Two-Fluid Approximation for Calculating the Cosmic Microwave Background Anisotropies
• Large-Angle Cosmic Microwave Background Anisotropies in an Open Universe
• Null Geodesics in Perturbed Spacetimes
• Doppler Peaks in the Angular Power Spectrum of the Cosmic Microwave Background: A Fingerprint of Topological Defects
• Cosmological-Constant Cold Dark Matter Models and the COBE Two-Year Sky maps
• The Small Scale Integrated Sachs-Wolfe Effect
• The Doppler Peaks from Cosmic Texture
• Spectral Analysis of Microwave Background Perturbations Induced by Cosmic Strings
• The Imprint of Proper Motion of Nonlinear Structures on the Cosmic Microwave Background
• Beyond the Thin Lens Approximation
• The Imprint of $\Omega$ on the Cosmic Microwave Background
• The Effect of Gravitational Scattering on the Anisotropy of the Cosmic Background Radiation

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