On the Hubble constant and the cosmological constant

Abstract

We review the observational determinations of the Hubble constant which have been made in recent years. We conclude that the most likely value of H0 is 58 km s-1 Mpc-1 with uncertainties of +10 and -5. Thus the age of the standard big bang model is 11.2 Gyr. The discrepancy between this value and the ages of the oldest observed stars, 13-16 Gyr, appears to be real, necessitating some change in the standard model. A currently favoured procedure for coping with this widely-admitted difficulty for the theory which has been favoured by many cosmologists in recent years is a rebirth of the cosmological constant λ. Even with this constant, the observations constrain the model very severely. There are theoretical considerations as well. The problem with this constant, as it has been seen over much of the past half-century, is that it is required to have a physical dimensionality of (length)-2 and to have a magnitude of about 10-56 cm-2. Theoreticians have not favoured introducing such a quantity ab initio into cosmology, but attempts to explain the genesis of λ from particle physics have yielded results that are wide of what is required by immense factors ( ∼ 1050 to ∼ 10100). Using an approach from a scale-invariant theory of gravity, we show that λ can be derived correct to a factor of ∼ 2 within the modern Universe. This derivation does not appear to be applicable to earlier phases of the Universe, which give λ ≃ H2 rather than the relation λ ≃ H02 that a true cosmological constant would require. © 1997 RAS.