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We investigate a conformal invariant gravitational model which is taken to hold at pre-inflationary era. The conformal invariance allows to make a dynamical distinction between the two unit systems (or conformal frames) usually used in cosmology and elementary particle physics. In this model we argue that when the universe suffers phase transitions, the resulting mass scales introduced by particle physics should have variable contributions to vacuum energy density. These variations are controlled by the conformal factor that appears as a dynamical field. We then deal with the cosmological consequences of this model. In particular, we shall show that there is an inflationary phase at early times. At late times, on the other hand, it provides a mechanism which makes a large effective cosmological constant relax to a sufficiently small value consistent with observations. Moreover, we shall show that the conformal factor acts as a quintessence field that leads the universe to accelerate at late times.
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