Rotational perturbations of Friedmann universes

Several new analytic solutions for rotational perturbations of the Friedmann metrics are found in order to incorporate the possibility of a rotating universe. The field equations impose restrictions on the matter rotation $\omega (r, t)$ and some of the solutions for $\Omega (r, t)$, which is related to the local dragging of inertial frames, are expressed in terms of hypergeometric functions. Uniform rotation is shown to be incompatible with the present universe ($P=0\mathrm{}$) and with the radiation-dominated universe ($P=\frac{\rho }{3}$). Geodesics of the metric are studied to reveal the intrinsic nature of the rotation and to elucidate the role of $\Omega$.