Primordial Inflation and Present-Day Cosmological Constant from Extra Dimensions
Abstract
A semiclassical gravitation model is outlined which makes use of the Casimir energy density of vacuum fluctuations in extra compactified dimensions to produce the present-day cosmological constant as rhoLAMBDA ~ M8/MP4, where MP is the Planck scale and M is the weak interaction scale. The model is based on (4+D)-dimensional gravity, with D = 2 extra dimensions with radius b(t) curled up at the ADD length scale b0 = MP/M2 ~ 0.1 mm. Vacuum fluctuations in the compactified space perturb b0 very slightly, generating a small present-day cosmological constant. The radius of the compactified dimensions is predicted to be b0 = k1/4 0.09 mm (or equivalently M = 2.4 TeV/k1/8), where the Casimir energy density is k/b4. Primordial inflation of our three-dimensional space occurs as in the cosmology of the ADD model as the inflaton b(t), which initially is on the order of 1/M ~ 10-17 cm, rolls down its potential to b0.
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