  Bayesian model averaging is a procedure to obtain parameter constraints that
account for the uncertainty about the correct cosmological model. We use recent
cosmological observations and Bayesian model averaging to derive tight limits
on the curvature parameter, as well as robust lower bounds on the curvature
radius of the Universe and its minimum size, while allowing for the possibility
of an evolving dark energy component. Because flat models are favoured by
Bayesian model selection, we find that model-averaged constraints on the
curvature and size of the Universe can be considerably stronger than non
model-averaged ones. For the most conservative prior choice (based on
inflationary considerations), our procedure improves on non model-averaged
constraints on the curvature by a factor of ~ 2. The curvature scale of the
Universe is conservatively constrained to be R_c > 42 Gpc (99%), corresponding
to a lower limit to the number of Hubble spheres in the Universe N_U > 251
(99%).
