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− α/R is examined and it is shown that it leads to equations whose solutions approach a de Sitter universe at late times. Thus, there is no need to introduce dark energy to explain the acceleration of the cosmological expansion.