Abstract
The curvature correction to the Lagrangian of vacuum fluctuations is studied. After a brief tour through the vacuum expectation value of the energy–momentum tensor 〈Tμν〉 and comparing this with the semiclassical averaging value of Tμν, it is found that vacuum polarization due to curvature determines the effective cosmological constant and the gravitational constant in such a way that the quantum corrections of order R2 are inevitable in the high curvature regime. Considering the asymptotic past and future as vacuum states of the Universe, a Cosmological Duality Conjecture (CDC) is put forward that “if there are terms proportional toRn (n > 0), there are also terms proportional toR−m (m >0) in the gravitational Lagrangian.” The CDC indicates a cyclic cosmological evolution where the late-time dark energy phase comes to an end and a collapsing phase begins with reversal of the arrow of time.
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