The<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: Inflation without a phase transition

A pure gravity inflationary model for the Universe is examined which is based on adding an \ensuremath{\epsilon}${R}^{2}$ term to the usual gravitational Lagrangian. The classical evolution is worked out, including eventual particle production and the subsequent join to radiation-dominated Friedmann behavior. We show that this model gives significant inflation essentially independent of initial conditions. The model has only one free parameter which is bounded from above by observational constraints on scalar and tensorial perturbations and from below by both the need for standard baryogenesis and the need for galaxy formation. This requires ${10}^{11}$${\ensuremath{\epsilon}}^{\mathrm{\ensuremath{-}}1/2}$${10}^{13}$ GeV.