Cosmology with Curvature - Saturated Gravitational Lagrangian R / √

We argue that the Lagrangian for gravity should remain bounded at large curvature, and interpolate between the weak-field tested Einstein-Hilbert LagrangianLEH = R/16πG and a pure cosmological constant for large R with the curvature-saturated ansatz Lcs = LEH/ √ 1+ l4 R2, where l is a length parameter expected to be a few orders of magnitude above the Planck length. The curvature-dependent effective gravitational constant defined by dL/d R = 1/16πGeff is Geff = G √ 1+ l4 R2 , and tends to infinity for large R, in contrast to most other approaches where Geff → 0. The theory possesses neither ghosts nor tachyons, but it fails to be linearization stable. In a curvature saturated cosmology, the coordinates with ds2 = a2[da2/B(a)− dx2 − dy2 − dz2] are most convenient since the curvature scalar becomes a linear function of B(a). Cosmological solutions with a singularity of type R→±∞ are possible which have a bounded energy-momentum tensor everywhere; such a behaviour is excluded in Einstein’s theory. In synchronized time, the metric is given by