<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>R</mml:mi></mml:math>curvature corrections as the source of the cosmological acceleration

Corrections to Einstein's equations that become important at small curvatures are considered. The field equations are derived using a Palatini variation in which the connection and metric are varied independently. In contrast with the Einstein-Hilbert variation, which yields fourth order equations, the Palatini approach produces second order equations in the metric. The Lagrangian $L(R)=R\ensuremath{-}{\ensuremath{\alpha}}^{2}/R$ is examined and it is shown that it leads to equations whose solutions approach a de Sitter universe at late times. Thus, the inclusion of $1/R$ curvature terms in the gravitational action offers an alternative explanation for the cosmological acceleration.

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