Canonical formulation of the curvature-squared action in the presence of a lapse function

Abstract

Lapse function appears as a Lagrange multiplier in the Einstein–Hilbert action and its variation leads to the equation of Einstein, which corresponds to the Hamiltonian constraint equation. In higher order theory of gravity the situation is not that simple. Here, we take up the curvature-squared (R2) action being supplemented by an appropriate boundary term in the background of Robertson–Walker minisuperspace metric, and show how to identify the constraint equation and formulate the Hamiltonian without detailed constraint analysis. The action is finally expressed in the canonical form , where the lapse function appears as the Lagrange multiplier, once again. Canonical quantization yields a Schrödinger-like equation, with nice features. To show that our result is not an artifact of having reduced the theory to a measure zero subset of its configuration space, the role of the lapse function as the Lagrangian multiplier has also been investigated in Bianchi-I, Kantowski–Sachs and Bianchi-III minisuperspace metrics. Classical and semiclassical solutions have finally been presented.