PHYSICALLY PERMITTED COSMOLOGICAL MODELS WITH NONZERO COSMOLOGICAL CONSTANT

Cosmological models with nonzero cosmological constant have been reconsidered. We have found, in agreement with earlier results by Glanfield, that there are two particular values of the cosmological constant, LAMBDA-M (being less-than-or-equal-to 0 for OMEGA-0 less-than-or-equal-to 1 and positive otherwise) and LAMBDA-C (with LAMBDA-M < LAMBDA-C). Exploding models with LAMBDA less-than-or-equal-to LAMBDA-M or LAMBDA greater-than-or-equal-to LAMBDA-C are oscillating. But the latter are not physically permitted because they never reach the present situation of the universe. Nonexploding models with LAMBDA > LAMBDA-C are also theoretically possible, but, in general, they are physically improbable because, other than losing the explanatory capabilities of the models with a big bang, they started to expand from a nonsingular situation too short a time ago. Finally, models with LAMBDA-M < LAMBDA < LAMBDA-C are of the inflexional type, with an endless expansion. Thus, the value LAMBDA-C plays in fact the role of an upper limit to the value of the cosmological constant. Analytical expressions for the critical values of LAMBDA are given. A lower limit to LAMBDA could result from time scale considerations. Given the current lowest estimates of the age of the oldest globular clusters, the condition H0t0 greater-than-or-equal-to 1 has to hold for any H0 > 65 km s-1 Mpc-1. On that assumption it is shown that the range of permitted values of LAMBDA is very small. In particular, for the inflation preferred model, k = 0, that range is only 0.74 less-than-or-equal-to LAMBDA-c2/3H0(2) less-than-or-equal-to 1. For such a particular case, the (m, z) and (theta, z) theoretical predictions are given. They are not very different from the standard relations. In any case, it is shown from the above relations that, contradictory conditions on LAMBDA are required to improve the agreement with the observational data taken at their face value.