Curvature correction to vacuum fluctuations and cosmic evolution with cosmological duality

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 〈T_μν〉 and comparing this with the semiclassical averaging value of T_μν, 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.