Cosmic Microwave Background Observables and Their Cosmological Implications

We show that recent measurements of the power spectrum of cosmic microwave background anisotropies by BOOMERanG and MAXIMA can be characterized by four observables, the position of the first acoustic peak l₁= 206 pm 6, the height of the first peak relative to COBE normalization H₁= 7. 6 pm 1. 4, the height of the second peak relative to the first H₂ = 0. 38 pm 0. 04, and the height of the third peak relative to the first H₃ = 0. 43 pm 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 LCDM family of models, where we find Omegaₘ h^3. 8 > 0. 079 (or nearly equivalently, the age of the universe t₀ 0. 019, a matter density Omegaₘ h² 0. 85 from the peak heights (95% CL). 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 (Omegaₘ, h) plane; it points to high h (0. 6< h < 0. 9) and moderate Omegaₘ (0. 25 < Omegaₘ < 0. 6).