Barrow, and Barrow and collaborators, have put forward theoretical modelswith variable fundamental constants including JBD theories. The experimentalevidence for an accelerating Universe points out to a deceleration parameterapproximately equal to -- 1. On the other hand, there is evidence for a timevarying fine structure constant alpha . We have included the above results in aJBD cosmological model modified by J.D. Barrow by including a time varyingspeed of light, thus, finding an exponential inflationary phase with variablesG, alpha and c . This means that the primordial value of alpha wasexponentially larger than its present value. Planck`s time may not be thenapproximately 10 to the power - 43 s ; the same may happen to other Planck`squantities. We found an exponentially time-decaying Cosmological term.
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