Inflationary Lambda-Universe with Time Varying Fundamental Constants
  Barrow, and Barrow and collaborators, have put forward theoretical models with variable fundamental constants including JBD theories. The experimental evidence for an accelerating Universe points out to a deceleration parameter approximately equal to -- 1. On the other hand, there is evidence for a time varying fine structure constant alpha . We have included the above results in a JBD cosmological model modified by J.D. Barrow by including a time varying speed of light, thus, finding an exponential inflationary phase with variables G, alpha and c . This means that the primordial value of alpha was exponentially larger than its present value. Planck`s time may not be then approximately 10 to the power - 43 s ; the same may happen to other Planck`s quantities. We found an exponentially time-decaying Cosmological term. 
Marcelo Samuel Berman and Luis A. Trevisan