Homogeneous Cosmological Models with Bounded Potential
Abstract
Under the assumption that there exists a finite global upper bound to the gravitational potential, 2Gm/c2r, it is shown that simply connected homogeneous models based on the WalkerRobertson line element must have zero mean density if the curvature parameter le is 0 or 1. For homogeneous models with k = +1, all global potential bounds less than or equal to the Schwarzschild limit imply a positive cosmological constant. If the potential is globally less than 0.912 (spherical space) or 0 75 (elliptical space), and if the physically realizable pressures are at all future epochs bounded below by zero and above by photon gas pressure, pc2/3, k = + 1 models will expand monotonically without limitfor all future time Asymptotic values for large times are in the usual notations: H = c ~f (X/3), q = 1, p = 0, and p = 0. Under the same conditions, the present value of the deceleration parameter is less than 1, so that the asymptotic value is approached from below. The cosmological constant is bounded below by 3H02/c2, where H0 is the present value of the Hubble parameter
 Publication:

The Astrophysical Journal
 Pub Date:
 March 1968
 DOI:
 10.1086/149514
 Bibcode:
 1968ApJ...151.1171E