3. PARADIGM 2: = 1

It is tempting to believe that _m is unity. If it is not unity, one has to fine tune the initial curvature to one part in 10³⁰. Moreover inflationary models generally predict that is unity. However the evidence in favor of low _m, and specifically _m 0.3 is mounting. The most direct probe arises from counting rich galaxy clusters, both locally and as a function of redshift. The direct prediction of _m = 1 is that there should be a higher-than-observed local density of clusters, and strong evolution in number with redshift that is not seen. ¹⁸ However this conclusion has recently been disputed. ^{19 ,20}

An indirect argument comes from studies of Type Ia supernovae, which provide strong evidence for acceleration. This is most simply interpreted in terms of a positive cosmological constant. ^{21 ,22} The SN Ia data actually measure - _m. Combined with direct measures of _m both from galaxy peculiar velocities and from clusters, one infers that 0.7. Hence flatness is likely, and certainly well within observational uncertainties. Further evidence for the universe being spatially flat comes from the measurement of the location of the first acoustic peak in the cosmic microwave background anisotropy spectrum. The location reflects the angular size subtended by the horizon at last scattering, and has Fourier harmonic l = 220 ^-1/2. Current data requires ²³ 0.4, where = _m + .

Some possible pitfalls in this conclusion are that unbiased cluster surveys have yet to be completed. Use of wide field weak lensing maps will go a long way towards obtaining a definitive rich cluster sample. There is no accepted theory for Type Ia supernovae, and it is possible that evolutionary effects could conspire to produce a dimming that would mimic the effects of acceleration, at least to z ~ 1. Utilization of supernovae at z > 1 will eventually help distinguish evolutionary dimming or gray dust, the effects of which should be stronger at earlier epochs and hence with increasing z, from the effect of acceleration, which decreases at earlier epochs, that is with increasing z.