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 mainly characterized by four observables : the position of the first acoustic peak, iota (1) = 206 +/- 6; the height of the first peak relative to COBE normalization, H-1 = 7.6 +/- 1.4; the height of the second peak relative to the first, H-2 = 0.38 +/- 0.04; and the height of the third peak relative to the first, H-3 = 0.43 +/- 0.07. This phenomenological representation of the measurements c omplements more detailed likelihood analyses in multidimensional parameter space, clarifying the dependence on prior assumptions and the specific aspe cts of the data leading to the constraints. We illustrate their use in the flat Lambda CDM family of models, where we find Omega (m) h(3.8) > 0.079 (o r nearly equivalently, the age of the universe t(0) < 13-14 Gyr) from <iota >(1), and a baryon density Omega (b) h(2) > 0.019, a matter density Omega ( m) h(2) < 0.42, and tilt n > 0.85 from the peak heights (95% confidence lim it). 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 (Omega (m), h) plane; it points to hig h h (0.6 < h < 0.9) and moderate Omega (m) (0.25 < <Omega>(m) < 0.6).