An alternative to the cosmological ``concordance model''

Precision measurements of the cosmic microwave background by WMAP are believed to have established a flat Lambda -dominated universe, seeded by nearly scale-invariant adiabatic primordial fluctuations. However by relaxing the hypothesis that the fluctuation spectrum can be described by a single power law, we demonstrate that an Einstein-de Sitter universe with zero cosmological constant can fit the data as well as the best concordance model. Moreover unlike a Lambda -dominated universe, such an universe has no strong integrated Sachs-Wolfe effect, so is in better agreement with the low quadrupole seen by WMAP. The main concern is that the Hubble constant is required to be rather low: H₀ =~ 46 km s^-1 Mpc^-1; we discuss whether this can be consistent with observations. Furthermore for universes consisting only of baryons and cold dark matter, the amplitude of matter fluctuations on cluster scales is too high, a problem which seems generic. However, an additional small contribution (Omega_X ~ 0.1) of matter which does not cluster on small scales, e.g. relic neutrinos with mass of order eV or a ``quintessence'' with w ~ 0, can alleviate this problem. Such models provide a satisfying description of the power spectrum derived from the 2dF galaxy redshift survey and from observations of the Ly-alpha forest. We conclude that Einstein-de Sitter models can indeed accommodate all data on the large scale structure of the Universe, hence the Hubble diagram of distant type Ia supernovae remains the only direct evidence for a non-zero cosmological constant.