Degenerate Hamiltonian operator in higher-order canonical gravity — The problem and a remedy

Ostrogradski, 1850, Mem. Acad. St. Petersbg. Ser. VI, 4, 385 Whittaker, 1904 Dirac, 1950, Canad. J. Math., 2, 129, 10.4153/CJM-1950-012-1 Dirac, 1964 Horowitz, 1985, Phys. Rev. D, 31, 1169, 10.1103/PhysRevD.31.1169 York, 1972, Phys. Rev. Lett., 28, 1082, 10.1103/PhysRevLett.28.1082 Gibbons, 1977, Phys. Rev. D, 15, 2752, 10.1103/PhysRevD.15.2752 Pollock, 1988, Nuclear Phys. B, 306, 931, 10.1016/0550-3213(88)90448-8 Sanyal, 2001, Phy. Rev. D, 63, 10.1103/PhysRevD.63.064021 Sanyal, 2002, Classical Quantum Gravity, 19, 515, 10.1088/0264-9381/19/3/307 Sanyal, 2002, Phys. Lett. B, 542, 147, 10.1016/S0370-2693(02)02338-9 Sanyal, 2005, Gen. Relativ. Gravit., 37, 1957, 10.1007/s10714-005-0173-1 Debnath, 2014, Phys. Rev. D, 90, 10.1103/PhysRevD.90.047504 Sanyal, 2003, 109 Sanyal, 2012, Classical Quantum Gravity, 29, 10.1088/0264-9381/29/21/215007 Sarkar, 2017, IJGMMP, 14 Mondal, 2017, Phys. Rev. D, 96 Mandal, 2018, J. High Energy Phys., 05, 078, 10.1007/JHEP05(2018)078 Anderson, 1994, Ann. Physics, 232, 292, 10.1006/aphy.1994.1055 Buchbinder, 1987, Classical Quantum Gravity, 4, 1487, 10.1088/0264-9381/4/6/008 Deruelle, 2009, Phys. Rev. D, 80, 10.1103/PhysRevD.80.084032 Capozziello, 2012, Eur. Phys. J. C., 72, 2068, 10.1140/epjc/s10052-012-2068-0 Capozziello, 2014, IJGMMP, 11 Capozziello, 2011, MPLA, 26, 65, 10.1142/S021773231103458X Sarkar, 2013, Internat. J. Theoret. Phys., 52, 1194, 10.1007/s10773-012-1436-8 Sk, 2018, Internat. J. Modern Phys. D, 27, 1850, 10.1142/S0218271818500852 Dialektopoulos, 2018, IJGMMP, 15