Higher-Order Theories of Quantum Gravity| 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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