1/R 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 to the Einstein-Hilbert variation, which yields fourth order equations, the Palatini approach 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 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.