Cosmic microwave background anisotropies in the CDM model: A covariant and gauge-invariant approach

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  • 28 April 1998
Abstract
We present a fully covariant and gauge-invariant calculation of the evolution of anisotropies in the Cosmic Microwave Background (CMB) radiation. We use the physically appealing covariant approach to cosmological perturbations, which ensures that all variables are gauge-invariant and have a clear physical interpretation. We derive the complete set of frame-independent linearised equations describing the (Boltzmann) evolution of anisotropy and inhomogeneity in an almost Friedmann-Robertson-Walker (FRW) Cold Dark Matter (CDM) universe. These equations include the contributions of scalar, vector and tensor modes in a unified manner. Frame-independent equations describing scalar perturbations, which are valid for any value of the background curvature, are obtained by placing appropriate covariant restrictions on the gauge-invariant variables. We derive the analytic solution of these equations in the early radiation dominated universe, and present the results of a numerical simulation of the standard CDM model. Our results confirm those obtained by other groups, who have worked carefully with non-covariant methods in specific gauges, but are derived here in a completely transparent fashion.

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