Canonical formulation of higher-order theory of gravity has been attempted over decades. Different routes lead to different phase-space structures of the Hamiltonian. Although, these Hamiltonians are canonically equivalent at the classical level, their quantum counterparts may not be same, due to nonlinearity. Earlier, it has been proved that ‘Dirac constraint analysis’ (after taking care of divergent terms) and ‘Modified Horowitz’ Formalism’ lead to identical phase-space structure of the Hamiltonian for the gravitational action with scalar curvature squared terms. For the sake of completeness, this paper expatiates the extension of the same work for a general fourth-order gravitational action. Canonical quantization and semiclassical approximation are performed to explore that such a quantum theory transits successfully to a classical de-Sitter Universe. Inflation is also studied. Inflationary parameters show excellent agreement with the recently released Planck’s data.

中文翻译：

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高阶引力理论的典型等价、量化和膨胀

几十年来，人们一直在尝试对高阶引力理论进行规范表述。不同的路径导致哈密顿量的不同相空间结构。尽管这些哈密顿量在经典水平上是规范等价的，但由于非线性，它们的量子对应物可能不一样。早些时候，已经证明“狄拉克约束分析”（在考虑了发散项之后）和“修正霍洛维茨”形式主义”导致具有标量曲率平方项的引力作用的哈密顿量相同的相空间结构。为了完整起见，本文阐述了相同工作对一般四阶引力作用的扩展。进行规范量化和半经典近似以探索这种量子理论成功地过渡到经典的去西特宇宙。还研究了通货膨胀。通胀参数与最近发布的普朗克数据非常吻合。