2. GLOBAL MEASURES

We adopt as our basic working hypothesis the standard cosmological model of Friedmann Robertson Walker (FRW), where we assume homogeneity and isotropy and describe gravity by general relativity. We limit the discussion to the matter-dominated era in the ``dust'' approximation.

The Friedmann equation that governs the universal expansion can be written in terms of the different contributions to the energy density (e.g., [1]):

(1)

Here, a(t) is the expansion factor of the universe, H(t) / a is the Hubble constant, _m(t) is mean the mass density, is the cosmological constant, and k is the curvature parameter. Hereafter, the above symbols for the cosmological parameters refer to their values at the present time, t₀.

We denote _{tot m} + , which by Eq. 1 equals 1 - _k; its value relative to unity determines whether the universe is open (k = - 1), flat (k = 0), or closed (k = + 1). Another quantity of interest is the deceleration parameter, q₀ - a / ², which by Eq. 1 is related to the other parameters via q₀ = _m/2 - .

The FRW model also predicts a relation between the dimensionless product H₀t₀ and the parameters _m and . For = 0, this product ranges between 1 and 2/3 for _m in the range 0 to 1 respectively, and it is computable for any values of _m and (Section 2.5).

The global measures commonly involve combinations of the cosmological parameters. Constraints in the _m - plane are displayed in Figure 1.