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The inflationary scenario requires that the universe have negligible curvature along constant-density surfaces. In the Friedmann-Lemaitre cosmology that leaves us with two free parameters, Hubble's constant H0 and the density parameter Ω0 (or, equivalently, the cosmological constant Λ). The author discusses here tests of this set of models from local and high-redshift observations. The data agree reasonably well with Ω0 ≡ 0.2.
P. J. E. Peebles (Sat,) studied this question.