The evolution of the scale factor $a\left(t\right)\mathrm{}$ in Friedmann models (those with zero pressure and a constant cosmological term $\Lambda )$ is well understood, and elegantly summarized in the review of Felten and Isaacman [Rev. Mod. Phys. 58, 689 (1986)]. Developments in particle physics and inflationary theory, however, increasingly indicate that $\Lambda$ ought to be treated as a dynamical quantity. We reexamine the evolution of the scale factor with a variable $\Lambda$ term, and also generalize the treatment to include nonzero pressure. New solutions are obtained and evaluated using a variety of observational criteria. Existing arguments for the inevitability of a big bang (i.e., an initial state with $a=0)$ are substantially weakened, and can be evaded in some cases with ${\Lambda }_0$ (the present value of $\Lambda )$ well below current experimental limits.

Generic violations of Lorentz symmetry can be described by an effective field theory framework that contains both general relativity and the Standard Model of particle physics called the Standard-Model extension (SME). We obtain new constraints on the gravitational sector of the SME using recently published final results from Gravity Probe B. These include for the first time an upper limit at the ${10}^{-3}$ level on the time-time component of the new tensor field responsible for inducing local Lorentz violation in the theory, and an independent limit at the ${10}^{-7}$ level on a combination of components of this tensor field.