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Lapse function appears as Lagrange multiplier in Einstein-Hilbert action andits variation leads to the (0 0) equation of Einstein, which corresponds to theHamiltonian constraint equation. In higher order theory of gravity thesituation is not that simple. Here, we take up the curvature squared (R^2)action being supplemented by an appropriate boundary term in the background ofRobertson-Walker minisuperspace metric, and show how to identify the constraintequation and formulate the Hamiltonian without detailed constraint analysis.The action is finally expressed in the canonical form $A = \int(\dot h_{ij}\pi^{ij} + \dot K_{ij}\Pi^{ij} - N{\mathcal H})dt \sim d^3 x$, where, the lapsefunction appears as Lagrange multiplier, once again. Canonical quantizationyields Schr\"odinger like equation, with nice features. To show that our resultis not an artifact of having reduced the theory to a measure zero subset of itsconfiguration space, the role of the lapse function as Lagrangian multiplierhas also been investigated in Bianchi-I, Kantowski-Sachs and Bianchi-IIIminisuperspace metrics. Classical and semiclassical solutions have finally beenpresented.

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