Some new cosmological results of quadratic Lagrangians

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Abstract
We present the field equations derived from a gravitational Lagrangian which includes a general combination of terms quadratic in the curvature tensor, assuming a space-time with one timelike dimension and two maximally symmetric spacelike subspaces, with arbitrary dimensions d and D. We then restrict ourselves to the case d=3, and find a general solution for the case of a radiation-dominated universe with a static pressureless internal space. Conditions for the existence of Friedmann-type solutions are derived and discussed. Finally we study the equations, again with a static internal space, for pressureless matter in both subspaces.