Cosmic Microwave Background Observables and Their Cosmological Implications

Abstract

We show that recent measurements of the power spectrum of cosmic microwave background anisotropies by Boomerang and MAXIMA can be mainly characterized by four observables: the position of the first acoustic peak, l₁ = 206 ± 6; the height of the first peak relative to COBE normalization, H₁ = 7.6 ± 1.4; the height of the second peak relative to the first, H₂ = 0.38 ± 0.04; and the height of the third peak relative to the first, H₃ = 0.43 ± 0.07. This phenomenological representation of the measurements complements more detailed likelihood analyses in multidimensional parameter space, clarifying the dependence on prior assumptions and the specific aspects of the data leading to the constraints. We illustrate their use in the flat ΛCDM family of models, where we find Ω_mh^3.8 > 0.079 (or nearly equivalently, the age of the universe t₀ < 13-14 Gyr) from l₁, and a baryon density Ω_bh² > 0.019, a matter density Ω_mh² < 0.42, and tilt n > 0.85 from the peak heights (95% confidence limit). With the aid of several external constraints, notably nucleosynthesis, the age of the universe, and the cluster abundance and baryon fraction, we construct the allowed region in the (Ω_m, h) plane; it points to high h (0.6 < h < 0.9) and moderate Ω_m (0.25 < Ω_m < 0.6).