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 .