Annu. Rev. Astron. Astrophys. 1992. 30:
499-542
Copyright © 1992 by . 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* >
10^{3} 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microwave background fluctuations, while R.D. Blandford (unpublished)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).