  We note that the standard LCDM cosmological model continues to face
fundamental problems. First, the model continues to depend wholly on two pieces
of undiscovered physics, namely dark energy and cold dark matter. Then, the
implied dark energy density is so small that it is unstable to quantum
correction and its size is fine-tuned to the almost impossible level of one
part in ~10^102; it is also difficult to explain the coincidence between the
dark energy, dark matter and baryon densities at the present day. Moreover, any
model with a positive cosmological constant also creates fundamental
difficulties for superstring theories of quantum gravity. We also review the
significant number of astrophysical observations which are now in contradiction
with the LCDM model. On the grounds that the SNIa Hubble diagram is prone to
evolutionary corrections and also that the CMB power spectrum may be
contaminated by the effects of foreground ionised gas, we argue that the
existence of such systematics could still allow more satisfactory, alternative,
models to appear. We suggest that if H_0<50kms^-1Mpc^-1 then a simpler,
inflationary model with Omega_baryon=1 might still be allowed with no need for
dark energy or cold dark matter.
