| Summary: | 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 {\em 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 problem is that the Hubble constant is required to be rather low: $H_0 \simeq 46$ km/s/Mpc; 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 ($\Omega_X \sim 0.1$) of matter which does not cluster on small scales, e.g. relic neutrinos with mass of order eV or a `quintessence' with $w \sim 0$, 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 {\em direct} evidence for a non-zero cosmological constant.
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