Horndeski's theory
Horndeski's theory is the most general theory of gravity in four dimensions whose Lagrangian is constructed out of the metric tensor and a scalar field and leads to second order equations of motion[clarification needed]. The theory was first proposed by Gregory Horndeski in 1974[1] and has found numerous applications, particularly in the construction of cosmological models of Inflation and dark energy.[2] Horndeski's theory contains many theories of gravity, including General relativity, Brans-Dicke theory, Quintessence, Dilaton, Chameleon and covariant Galileon[3] as special cases.
Horndeski's theory can be written in terms of an action as[4]
with the Lagrangian densities
Here is Newton's constant, represents the matter Lagrangian, to are generic functions of and , are the Ricci and Einstein tensors, is the Jordan frame metric, semicolon indicates covariant derivatives, commas indicate partial derivatives, , and repeated indices are summed over following Einstein's convention.
The free parameters of the theory, especially the contributions from and , are strongly constrained by the direct measurement of the speed of gravitational waves following GW170817.[5][6][7][8][9][10]
See also
References
- ^ Horndeski, Gregory Walter (1974-09-01). "Second-order scalar-tensor field equations in a four-dimensional space". International Journal of Theoretical Physics. 10 (6): 363–384. Bibcode:1974IJTP...10..363H. doi:10.1007/BF01807638. ISSN 0020-7748.
- ^ Clifton, Timothy; Ferreira, Pedro G.; Padilla, Antonio; Skordis, Constantinos (March 2012). "Modified Gravity and Cosmology". Physics Reports. 513 (1–3): 1–189. arXiv:1106.2476. Bibcode:2012PhR...513....1C. doi:10.1016/j.physrep.2012.01.001.
- ^ Deffayet, C.; Esposito-Farese, G.; Vikman, A. (2009-04-03). "Covariant Galileon". Physical Review D. 79 (8): 084003. arXiv:0901.1314. Bibcode:2009PhRvD..79h4003D. doi:10.1103/PhysRevD.79.084003. ISSN 1550-7998.
- ^ Kobayashi, Tsutomu; Yamaguchi, Masahide; Yokoyama, Jun'ichi (2011-09-01). "Generalized G-inflation: Inflation with the most general second-order field equations". Progress of Theoretical Physics. 126 (3): 511–529. arXiv:1105.5723. Bibcode:2011PThPh.126..511K. doi:10.1143/PTP.126.511. ISSN 0033-068X.
- ^ Lombriser, Lucas; Taylor, Andy (2016-03-16). "Breaking a Dark Degeneracy with Gravitational Waves". Journal of Cosmology and Astroparticle Physics. 2016 (3): 031–031. arXiv:1509.08458. Bibcode:2016JCAP...03..031L. doi:10.1088/1475-7516/2016/03/031. ISSN 1475-7516.
- ^ Bettoni, Dario; Ezquiaga, Jose María; Hinterbichler, Kurt; Zumalacárregui, Miguel (2017-04-14). "Speed of Gravitational Waves and the Fate of Scalar-Tensor Gravity". Physical Review D. 95 (8): 084029. arXiv:1608.01982. Bibcode:2017PhRvD..95h4029B. doi:10.1103/PhysRevD.95.084029. ISSN 2470-0010.
- ^ Creminelli, Paolo; Vernizzi, Filippo (2017-10-16). "Dark Energy after GW170817". arXiv:1710.05877 [astro-ph.CO].
- ^ Sakstein, Jeremy; Jain, Bhuvnesh (2017-10-16). "Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories". arXiv:1710.05893 [astro-ph.CO].
- ^ Ezquiaga, Jose María; Zumalacárregui, Miguel (2017-12-18). "Dark Energy After GW170817: Dead Ends and the Road Ahead". Physical Review Letters. 119 (25): 251304. arXiv:1710.05901. Bibcode:2017PhRvL.119y1304E. doi:10.1103/PhysRevLett.119.251304.
- ^ Grossman, Lisa (2017-10-24). "What detecting gravitational waves means for the expansion of the universe". Science News. Retrieved 2017-11-08.