
 The Uncaused Beginning of the Universe (1988) 
  What is important to note about these Friedmann equations is that if p, the density of matter in the universe, is positive, then the right side of the first equation is positive, and this entails that d2a/dt2, the acceleration of the expansion or the deceleration of the contraction, cannot be zero. 
  Equations (7) and (8) at most tend to show that acausal laws govern the change of condition of particles, such as the change of particle x's position from q1 to q2. 
  The equation describing this state is a quantum tunneling equation, specifically the bounce solution of the Euclidean version of the evolutionary equation of a universe with a closed RobertsonWalker metric. 
 www.qsmithwmu.com /the_uncaused_beginning_of_the_universe_(1988).htm (7386 words) 
