3.5. Other tests

There is a tremendous variety of ways in which a nonzero cosmological constant can manifest itself in observable phenomena. Here is an incomplete list of additional possibilities; see also [3, 7, 8].

• Observations of numbers of objects vs. redshift are a potentially sensitive test of cosmological parameters if evolutionary effects can be brought under control. Although it is hard to account for the luminosity evolution of galaxies, it may be possible to indirectly count dark halos by taking into account the rotation speeds of visible galaxies, and upcoming redshift surveys could be used to constrain the volume/redshift relation [122].

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• Alcock and Paczynski [123] showed that the relationship between the apparent transverse and radial sizes of an object of cosmological size depends on the expansion history of the universe. Clusters of galaxies would be possible candidates for such a measurement, but they are insufficiently isotropic; alternatives, however, have been proposed, using for example the quasar correlation function as determined from redshift surveys [124, 125], or the Lyman- forest [126].

• In a related effect, the dynamics of large-scale structure can be affected by a nonzero cosmological constant; if a protocluster, for example, is anisotropic, it can begin to contract along a minor axis while the universe is matter-dominated and along its major axis while the universe is vacuum-dominated. Although small, such effects may be observable in individual clusters [127] or in redshift surveys [128].

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• A different version of the distance-redshift test uses extended lobes of radio galaxies as modified standard yardsticks. Current observations disfavor universes with _M near unity ([129], and references therein).
• Inspiralling compact binaries at cosmological distances are potential sources of gravitational waves. It turns out that the redshift distribution of events is sensitive to the cosmological constant; although speculative, it has been proposed that advanced LIGO detectors could use this effect to provide measurements of [130].

• Finally, consistency of the age of the universe and the ages of its oldest constituents is a classic test of the expansion history. If stars were sufficiently old and H₀ and _M were sufficiently high, a positive would be necessary to reconcile the two, and this situation has occasionally been thought to hold. Measurements of geometric parallax to nearby stars from the Hipparcos satellite have, at the least, called into question previous determinations of the ages of the oldest globular clusters, which are now thought to be perhaps 12 billion rather than 15 billion years old (see the discussion in [87]). It is therefore unclear whether the age issue forces a cosmological constant upon us, but by now it seems forced upon us for other reasons.