How Flat is Our Universe Really?
  Distance measurement provide no constraints on curvature independent of
assumptions about the dark energy, raising the question, how flat is our
Universe if we make no such assumptions? Allowing for general evolution of the
dark energy equation of state with 20 free parameters that are allowed to cross
the phantom divide, w(z) = -1, we show that while it is indeed possible to
match the first peak in the Cosmic Microwave Background with non-flat models
and arbitrary Hubble constant, H_0, the full WMAP7 and supernova data alone
imply -0.12 < \Omega_k < 0.01 (2\sigma). If we add an H_0 prior, this tightens
significantly to \Omega_k = 0.002 \pm 0.009 . These constitute the most
conservative and model-independent constraints on curvature available today,
and illustrate that the curvature-dynamics degeneracy is broken by current
data, with a key role played by the Integrated Sachs Wolfe effect rather than
the distance to the surface of last scattering. If one imposes a quintessence
prior on the dark energy (-1 \leq w(z) \leq 1) then just the WMAP7 and
supernova data alone force the Universe to near flatness: \Omega_k = 0.013 \pm
0.012. Finally, allowing for curvature, we find that all datasets are
consistent with a Harrison-Zel'dovich spectral index, n_s = 1, at 2\sigma,
illustrating the interplay between early and late-universe constraints.
