Initial conditions for R+ε<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>cosmology

A pure gravity cosmology based on the R+\ensuremath{\epsilon}${R}^{2}$ Lagrangian is known to exhibit inflation for a wide range of initial conditions. In this paper we use the wave function from quantum cosmology to describe this inflation as a chaotic inflationary phase immediately following the quantum creation of the Universe. We evaluate, compare, and discuss the distributions over initial conditions that are fixed by the two boundary-condition proposals of Hartle and Hawking (``no boundary'') and Vilenkin (``tunneling from nothing''). We find that among all classical inflationary trajectories that begin on the classical-quantum boundary, those that lead to an inflation of at least 70 e-foldings make up a fraction of \ensuremath{\sim}exp${(\mathrm{\ensuremath{-}}10}^{12}$) in the former case and \ensuremath{\sim}1-exp(-8\ifmmode\times\else\texttimes\fi{}${10}^{10}$) in the latter. Thus, in the simplest interpretation, the observable Universe would be the outcome of a rare event for the first boundary-condition proposal and a typical event for the second.