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Astron. Astrophys. 353, 1-9 (2000)

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5. Observational constraints

Models with a cosmological term [FORMULA] (or [FORMULA] equivalently) must comply with certain observational constraints for which a clear survey was given by Overduin & Cooperstock (1998).

Of course, the flatness constraint [FORMULA], where [FORMULA] and [FORMULA] are the present values of [FORMULA] and [FORMULA] with [FORMULA], cannot apply for the present model since a space-time with positive curvature can never become completely flat.

Observations concerning CBM fluctuations, gravitational lens statistics, supernovas etc. restrict [FORMULA] to a range [FORMULA]. The value 0.85 used for the calculations in this paper is in fair agreement with this and can be taken even smaller when [FORMULA] is raised correspondingly.

The age of the universe is another quantity imposing rather stringent conditions on possible values of [FORMULA]. The present model has an infinite age of the universe. However, the time [FORMULA] elapsed after the phase transition until today, coinciding with the time that was available for the creation of the elements observed in the universe and the evolution of stars and galaxies, should observe the same conditions as the age of universes with finite past. It was numerically evaluated for the present model, and its value presented in Table 1 is in very good agreement with the latest requirements derived from observational data (see e.g. Riess et al. 1998).

Another constraint is provided by the requirement that, in a closed universe, the antipode must be further away than the most distant object for which gravitational lensing is observed. For the present model, according to Table 1 the distance of our antipode is [FORMULA] ly which is still far beyond our horizon, so the gravitational lensing constraint is well observed.

By nonsingular models the maximum red-shift constraint must be observed which requires that the maximal value of the red-shift


([FORMULA] time of emission), obtained by inserting for [FORMULA] the smallest value that S assumes in the model, must be at least as large as the greatest red-shift observed. In the present model, [FORMULA] ly, the minimal value of S is [FORMULA], and therefore the greatest possible red-shift is much greater than the greatest one observed.

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© European Southern Observatory (ESO) 2000

Online publication: December 8, 1999