$\Lambda$CDM Cosmology for Astronomers

Abstract

The homogeneous, isotropic, and flat $\Lambda$CDM universe favored by observations of the cosmic microwave background can be described using only Euclidean geometry, locally correct Newtonian mechanics, and the basic postulates of special and general relativity. We present simple derivations of the most useful equations connecting astronomical observables (redshift, flux density, angular diameter, brightness, local space density,...) with the corresponding intrinsic properties of distant sources (lookback time, distance, spectral luminosity, linear size, specific intensity, source counts,...). We also present an analytic equation for lookback time that is accurate within 0.1% for all redshifts $z$. The exact equation for comoving distance is an elliptic integral that must be evaluated numerically, but we found a simple approximation with errors $<0.2$% for all redshifts up to $z\approx 50$.

15 pages, 19 figures To be published in PASP

References in corpus (4)

• Cosmic Star Formation History
• A 2.4% Determination of the Local Value of the Hubble Constant
• K-corrections and filter transformations in the ultraviolet, optical, and near infrared
• Planck intermediate results. XLVI. Reduction of large-scale systematic effects in HFI polarization maps and estimation of the reionization optical depth

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