Hořava (Hořava-Lifshitz) Gravity  

In General > s.a. gravity theories; Lifshitz-Type Theories; quantum spacetime dimensionality.
* Idea: A non-relativistic renormalizable theory of gravitation which reduces to Einstein's general relativity at large distances but violates Lorentz invariance at small distances and introduces anisotropic spacetime scaling; Proposed as a candidate for a UV completion of Einstein's theory.
@ General references: Hořava JHEP(09)-a0812 [z = 2 membrane precursor]; Hořava PRD(09)-a0901 [z = 3 proposal]; Nikolić MPLA(10)-a0904 [and notion of particles]; Volovik JETPL(09)-a0904 [and emergent gravity, condensed-matter examples]; Charmousis et al JHEP(09)-a0905 [strong-coupling problems]; Li & Pang JHEP(09)-a0905 [canonical formulation problems]; Germani et al JHEP(09)-a0906 [as gauge-fixed vector-tensor theory of gravity]; Mukohyama JCAP(09)-a0906 [caustic avoidance]; Hořava & Melby-Thompson GRG(11)-a0909 [conformal infinity]; Merali SA(09)dec; Soo et al PLB(11)-a1007 [as a master constraint theory]; Padilla JPCS(10)-a1009; Sotiriou JPCS(11)-a1010 [status]; Pinzul CQG(11)-a1010 [spectral-geometry approach]; Bemfica a1010 [diffeomorphism invariance]; Visser JPCS(11)-a1103 [personal perspective]; Alexander et al PRD(12)-a1206 [from a Fermionic Aether in Ashtekar gravity]; Wang IJMPD(17)-a1701 [progress report].
@ Hamiltonian formulation: Donnelly & Jacobson PRD(11)-a1106; Bellorín & Restuccia PRD(11)-a1106 [lowest-order effective action]; Mukohyama et al PRD(15)-a1504 [non-projectable theory]; > s.a. other versions below.
@ Extra scalar-graviton mode: Cai et al PRD(09)-a0905; Blas et al JHEP(09)-a0906 [and inconsistency]; Kobakhidze PRD(10)-a0906; Afshordi PRD(09)-a0907 [the low-energy limit is the cuscuton model]; Park CQG(11)-a0910 [decoupling and consistency]; Koyama & Arroja JHEP(10)-a0910; Papazoglou & Sotiriou PLB(10)-a0911 [extended theory, strong coupling]; Wang & Wu PRD(11)-a1009 [stability and strong coupling]; Zhu et al PRD(11)-a1108 [elimination by local U(1) symmetry].
@ Consistency, issues: Henneaux et al PRD(10)-a0912; Bellorín & Restuccia IJMPD(12)-a1004; Cartas-Fuentevilla a1304.
@ Related topics: Calcagni PRD(10)-a0905 [+ scalar field, and detailed balance]; Bogdanos & Saridakis CQG(10)-a0907 [ghost-like scalar instabilities]; Myung PLB(09)-a0907, PLB(09)-a0909 [and generalized uncertainty principle]; Bellorín & Restuccia PRD(11)-a1010 [non-projectable, constraint structure]; Vernieri & Sotiriou PRD(12)-a1112, JPCS(13)-a1212 [detailed balance]; Bellorín et al PRD(12) [constraints and positive energy]; Rembieliński PLB(14)-a1309 [hidden Lorentz symmetry]; Alencar et al PLB(15)-a1505 [effective spacetime dimension]; Frusciante et al PDU(16)-a1508 [Effective Field Theory formalism]; Pinzul a1603-proc [spectral geometry approach].
> Related topics: see Effective Field Theory; phenomenology of hořava gravity [including solutions]; positive-energy theorem; quantum theory.
> Online resources: see Wikipedia page.

Different Versions > s.a. born-infeld theory.
* Non-projectable: The commutator of two local Hamiltonian constraints leads to severely restrictive secondary constraints and "troubles".
* Projectable: It has an integrated Hamiltonian constraint and consistent constraint algebra, and also an extra graviton mode, which can be problematic and is eliminated in Einstein's theory by the local Hamiltonian constraint.
@ General references: Sotiriou et al PRL(09)-a0904 [phenomenologically viable extension], JHEP(09)-a0905 [classical evolution equations, graviton propagators]; Weinfurtner et al JPCS(10)-a1002 [projectable]; Chiang et al JCAP(10)-a1007 [constraints from cosmological acceleration]; Carloni et al PRD(10) [first-order, Hamiltonian and f(R) cosmology]; Shu a1009 [with stable ground state]; Restuccia & Sotomayor PRD(13)-a1302 [without extra modes and equivalent to general relativity at the linearized level]; Chaichian et al PRD(15)-a1509 [without the unwanted scalar graviton].
@ Covariant version: Hořava & Melby-Thompson PRD(10)-a1007 [extra U(1) symmetry and "non-relativistic general covariance"]; da Silva CQG(11)-a1009 [alternative approach]; Alexandre & Pasipoularides PRD(11)-a1010 [spherical solutions]; Huang & Wang PRD(11)-a1011; Hořava CQG(11)-a1101-GR19 [and causal dynamical triangulations].
@ Healthy extension: Blas et al PRL(10)-a0909; Klusoň JHEP(10)-a1004, PRD(10) [Hamiltonian formulation], PRD(10) [and ghost condensation]; Kimpton & Padilla JHEP(10)-a1003; Blas et al JHEP(11)-a1007 [healthy non-projectable extension, and phenomenology].
@ Mixed-derivative extension: Colombo et al PRD(15)-a1410; Coates et al PRD(16)-a1604.
@ f(R) gravity: Klusoň JHEP(09)-a0907, PRD(10)-a0910; Wang MPLA(11)-a1003 [dark sector]; Chaichian et al PLB(10)-a1006 [Hamiltonian analysis]; Koutsoumbas & Pasipoularides PRD(10)-a1006 [quadratic and cubic terms]; Klusoň PRD(11)-a1108 [equivalence of f(R) and scalar-tensor theories].
@ And MOND: Romero et al MPLA(10)-a1003; Sanders PRD(11) [hiding Lorentz-invariance violation].
@ And other theories of gravity: Jacobson PRD(10)-a1001, PRD(14)-a1310 [and Einstein-aether theory]; Lee et al PLB(11)-a1003 [Brans-Dicke theory]; Alexandre et al PRD(10)-a1004 [Liouville-Lifshitz theory]; > s.a. dynamical triangulations.
@ Other dimensionalities: Exirifard a0911 [higher-dimensional]; Sotiriou et al PRD(11)-a1103 [lower-dimensional].

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