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Corrections to Einstein's equations that become important at small curvaturesare considered. The field equations are derived using a Palatini variation inwhich the connection and metric are varied independently. In contrast to theEinstein-Hilbert variation, which yields fourth order equations, the Palatiniapproach produces second order equations in the metric. The Lagrangian$L(R)=R-\alpha^2/R$ is examined and it is shown that it leads to equationswhose solutions approach a de Sitter universe at late times. Thus, theinclusion of 1/R curvature terms in the gravitational action offers analternative explanation for the cosmological acceleration.Comment: 7 pages, latex, minor changes, new references adde

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

<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

1/Rcurvature corrections as the source of the cosmological acceleration