Annu. Rev. Astron. Astrophys. 1992. 30: 499-542 Copyright © 1992 by Annual Reviews. All rights reserved

4.1 Existence of High-Redshift Objects

Bounce cosmologies are ruled out by the mere existence of high-redshift phenomena. High-redshift quasars are known with z = 4.89 (Schneider et al 1991). The restriction on _M implied by Equation 13 is thus _M < 0.01, which is quite unlikely on direct observational grounds, and also incompatible with the successful predictions of the theory of big bang nuelcosynthesis (Olive et al 1990, Peebles et al 1991). Thermalization of the microwave background at z > 10³ implies _M < 2 x 10^-9, which is surely impossible (Trimble 1987).

The case against loitering cosmologies is strong, though not quite so airtight. At one time, there was some belief that an excess number of quasars with z 1.95 pointed to the existence of a loitering model with _M 0.106, = 1.361 (Burbidge 1967, Shklovsky 1967). However, if a loitering phase lasts long enough, then the point of the universe antipodal to us becomes visible, at high magnification and with various exotic effects. Petrosian et al (1967), Shklovsky (1967), and Rowan-Robinson (1968) investigated this for redshifts around 1.95.

More recently, Gott (1985), Gott & Rees (1987), and Gott et al (1989) have found constraints on the redshift of the antipodes (and therefore any loiter) arising from gravitational lensing. Under rather general assumptions, they find that no quasar at a redshift larger than that of the antipodes can be lensed to more than one image. The existence of the lensed quasar QSO 2016 at a redshift z = 3.27 then bounds possible values of significantly away from the critical value of Equation 12 if _M 0.03 - as seems quite likely on dynamical grounds (see below; Lahav et al 1991; note, however, Paczynski's caveat mentioned in Gott 1985). Durrer & Kovner (1990) have argued that the range 0.01 < _M < 0.03 is conceivably viable and have investigated possible effects of antipodal focusing of cosmic microwave background fluctuations, while R.D. Blandford (unpublished) has directed attention to peculiarities in the observed lens. Such arguments seem forced, however. To circumvent these limits on _M, one can postulate a time-variable cosmological constant (Sahni et al 1992), but such models are also artificial.

We have already noted (Section 3.5) that linear density perturbations can grow by a large factor during a loitering phase. However, the existence of high-redshift quasars (lensed or not) argues against the theoretical invocation of a loitering cosmology to magnify perturbations: Since the gravitational condensation that creates (or fuels) the quasar (E.L. Turner 1991) must come after the perturbations have grown, the implied redshift of loiter should be larger than the redshift of any observed quasar: this is inconsistent with the firm fact that _M > 0.01 (Equations 13 or 14).