  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.
