  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.
