Title: Quantum Cosmology of Quadratic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> Theories with a FRW Metric
Abstract: We study the quantum cosmology of a quadratic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>f</mml:mi><mml:mfenced separators="|"><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:mfenced></mml:math> theory with a FRW metric, via one of its equivalent Horndeski type actions, where the dynamic of the scalar field is induced. The classical equations of motion and the Wheeler-DeWitt equation, in their exact versions, are solved numerically. There is a free parameter in the action from which two cases follow: inflation + exit and inflation alone. The numerical solution of the Wheeler-DeWitt equation depends strongly on the boundary conditions, which can be chosen so that the resulting wave function of the universe is normalizable and consistent with Hermitian operators.