2.4. Microwave Background Acoustic Peaks

This is the most promising test. In less than a decade it is expected to provide the most stringent constraints on the cosmological parameters. The test uses the effect of the background cosmology on the geodesics of photons. Current ground-based and balloon-born experiments already provide preliminary constraints on the location of the first acoustic peak on sub-degree scales in the angular power spectrum of CMB temperature fluctuations, l (l + 1)C_l. The dependence of the peak location on the cosmological parameters enters via the combined effect of (a) the physical scale of the ``sound horizon'' that is proportional to the cosmological horizon at recombination, and (b) the geometry of space-time via the angular-diameter distance. In the vicinity of a flat model, the first peak is predicted at approximately the multipole (e.g., [11] [12])

(4)

New Developments: The next generation of post-COBE CMB satellites (MAP to be launched by NASA in 2001, and in particular COBRAS/SAMBA scheduled by ESA for 2004) are planned to obtain a precision at ~ 10 arc-minute resolution that will either rule out the current framework of GI for structure formation or will measure the cosmological parameters to high precision. Detailed evaluation of COBRAS/SAMBA shows that nominal performance and expected foreground subtraction noise will allow parameter estimation with the following accuracy: H₀ ± 1%, _tot ± 0.005, ± 0.02, _b ± 2%.

Pro: The precision hoped for is much better than attainable with any other known method. If the observations fit the model, the precision is such that the model will be confirmed beyond reasonable doubt. The constraints on _tot come mostly from geometrical effects. The interpretation is based on well understood physics of sound waves in the linear regime, and on the assumption of absence of any relevant preferred scale (in the megaparsecs to gigaparsec range) in the physics which generated the initial structure. The latter assumption can be checked directly by the observations themselves.

Con: The measurements might be messed up by unexpected foreground contamination (e.g., by diffuse matter in galaxy groups). The detailed measurements need to wait 5 to 10 years. The assumption of no preferred scale in the initial fluctuations may be wrong. If the observations do not fit the model, the whole paradigm behind current structure formation modeling will be excluded, and then no parameter estimates will be possible. However, this seems unlikely given the recent measurements from the ground and from balloons, which have already confirmed the existence of the first acoustic peak.

Current Results: Balloon and ground-based results have already confirmed the existence of the first acoustic peak, and have constrained it's location to the vicinity l ~ 200. The results of COBE's DMR (l ~ 10) provide an upper bound of _m + < 1.5 at the 95% confidence level for a scale-invariant initial spectrum (and the constraint becomes tighter for any ``redder'' spectrum, n < 1) [12]. Several balloon experiments (l ~ 50 - 200) strengthen this upper bound [13]. The CAT experiment (l ~ 350 - 700) yields a preliminary lower bound of _m + > 0.3 [14] (Fig. 1).

Figure 1. Current limits (~ 2) on the cosmological parameters m and from global measures: luminosity distance of SNIa, lens count, the location of the CMB peak, and the age versus Hubble constant. The short marks are the one-parameter 95% limits from SNIa and lenses for a flat universe. Also shown (vertical line) is the 95% lower bound on m from cosmic flows. The most likely value of m lies in the range 0.5 to 1. The Einstein-deSitter model is permitted. An open model with m 0.2 and = 0, or a flat model with m 0.3 and 0.7, are ruled out.