Higher-Order Theories of Quantum Gravity  

In General > s.a. classical higher-order theories; covariant quantum gravity [stability of Minkowski space].
* Results: With the usual quadratic action the theory is renormalizable and asymptotically free [@ Tomboulis], but non-unitary (the quartic Γ terms in R2 give spin-2 ghosts in the propagators) and with H unbounded below [@ Stelle, etc]; However, it has been conjectured that the ghost does not appear in the physical spectrum, based on a QCD analogy; A theory with infinitely many derivative terms in the action is super-renormalizable.
@ General references: Asorey et al IJMPA(97); Mielke PRD(08)-a0707 [topological action]; Accioly et al PRD(18)-a1707 [features].
@ Renormalization: Utiyama & DeWitt JMP(62); Stelle PRD(77); Mazzitelli PRD(92); Fukuma & Matsuura PTP(02); de Berredo-Peixoto & Shapiro PRD(05)ht/04 [Gauss-Bonnet term, 4−ε]; Chaves a0808 [with quadratic terms]; Modesto PRD(12)-a1107 [super-renormalizability]; Modesto a1305-MG13 [super-renormalizable higher-derivative theories]; Modesto & Rachwal NPB(14)-a1408 [super-renormalizable and finite theories]; Modesto & Shapiro PLB(16)-a1512 [superrenormalizable, with complex ghosts]; > s.a. asymptotic safety.
@ Related topics: Accioly et al IJTP(00) [computing the propagator]; Kleidis et al PLB(02)ht [with massive scalar]; Bodendorfer & Neiman PRD(14)-a1304 [loop quantization, and Wald entropy formula]; Bonezzi et al PRD(14)-a1407 [as a Chern-Simons theory].
> Related topics: see Hierarchy Problem; path-integral quantum gravity; quantum gravity; semiclassical quantum gravity; Stückelberg Trick.

Specific Types of Theories > s.a. types of higher-order theories.
@ Quadratic gravity: Mazzitelli PRD(92), Tomboulis PLB(96)ht [relationship with general relativity, and renormalization]; Holdom & Ren PRD(16)-a1512 [quadratic and Einstein-Hilbert terms, quantum phase transition], IJMPD(16)-a1605-GRF; Álvarez et al JCAP(17)-a1703 [first-order formalism]; Lehners & Stelle a1909 [and inflation].
@ f(R) theories: Cognola et al JCAP(05)ht, Cognola & Zerbini JPA(06)in [one-loop covariant, around de Sitter spacetime]; Ahmed a1112 [2D]; Ohkuwa & Ezawa CQG(12)-a1203, CQG(13) [third quantization]; > s.a. unimodular gravity.
@ f(R) theories, lqg approach: Fatibene et al CQG(10)-a1003; Zhang & Ma PRL(11)-a1101, PRD(11)-a1107; Ma JPCS(12)-a1112; Amorós et al PRD(14)-a1402 [lqc]; Chen PRD(19)-a1811 [R2 lqc, effective dynamics].
@ 3D: Deser PRL(09) [ghost-free, UV-finite theory]; Helayël-Neto et al EPJC(10)-a1002.
@ Infinite-derivative theories: Talaganis et al CQG(15)-a1412, Talaganis & Mazumdar a1704 [UV behavior].
@ Other types: Narain & Anishetty PLB(12) [fourth-order derivative gravity, perturbatively renormalizable and unitary]; Modesto AR-a1202, a1402, Modesto & Rachwal NPB(15)-a1503 [super-renormalizable theory in any spacetime dimensionality]; Christiansen a1612 [Euclidean four-derivative theory].

And Quantum Cosmology
@ General references: Hawking & Luttrell NPB(84); van Elst et al CQG(94)gq [R + R3 action]; Pimentel et al CQG(97) [pure R2 action]; Davis GRG(00) [string-motivated]; Fabris & Reuter GRG(00); Sanyal & Modak PRD(01)gq, CQG(02)gq/01 [R + R2 action]; Shojai & Shojai GRG(08)-a0801 [spatially flat]; Tkach MPLA(09)-a0808 [ghost-free theory and hierarchy problem].
@ FLRW minisuperspace: Sanyal PLB(02)gq [Schrödinger equation and interpretation]; Vázquez-Báez & Ramírez AMP(17)-a1706 [quadratic f(R) theories].

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