Conformal Cosmology and the Age of the Universe ∗

We show that within the cosmology associated with conformal gravity the age of the universe is given as 1/H 0 , to thus overcome the current cosmological age crisis. We show that while the parameter Ω mat = ρ mat /ρ C takes on all values between zero and infinity in conformal gravity, nonetheless it is of order one (but not identically equal to one) for half a Hubble time to thus naturally explain its current closeness to one without fine tuning. We show that the cosmological constant is naturally of order the energy density ρ mat of ordinary matter again without fine tuning. We compare and contrast conformal cosmology with that of the standard Friedmann cosmology. For a theory which has long since been declared to be the true and correct cosmological theory, the standard Friedmann model is currently beset by a surprisingly large number of problems. The definitive new Hubble Space Telescope (Freedman et al 1994) determination of the value of the Hubble parameter H 0 causes the standard Ω mat = 1, Ω vac = 0 Friedmann model age t 0 = 2/3H 0 for the universe to now be less than that of some of its constituents. While the age prediction for the model can be increased by allowing for a non-zero cosmological constant vacuum energy contribution Ω vac (see e.g. Krauss and Turner 1995 who actually argue for such a non-zero value from a variety of cosmological considerations), unless this contribution is constrained according to the inflationary universe requirement Ω tot = Ω mat + Ω vac = 1, the celebrated flatness problem would then reappear. However, the fine tuning problem which would then be required of Ω vac to enforce this desired Ω tot = 1 would then be no less than 60 or so orders of magnitude more severe than the flatness problem tuning problem for which inflation was proposed in the first place (Guth 1981). New