Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories

Shinji Tsujikawa*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

39 Citations (Scopus)


It is known that Horndeski theories can be transformed to a sub-class of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories under the disformal transformation of the metric gμν → Ω2(φ)gμν + Γ(φ,X)∇μφ∇νφ, where Ω is a function of a scalar field φ and Γ is another function depending on both φ and X = gμνμφ∇νφ. We show that, with the choice of unitary gauge, both curvature and tensor perturbations on the flat isotropic cosmological background are generally invariant under the disformal transformation. By means of the effective field theories encompassing Horndeski and GLPV theories, we obtain the second-order actions of scalar/tensor perturbations and present the relations for physical quantities between the two frames. The invariance of the inflationary power spectra under the disformal transformation is explicitly proved up to next-to-leading order in slow-roll. In particular, we identify the existence of the Einstein frame in which the tensor power spectrum is of the same form as that in General Relativity and derive the condition under which the spectrum of gravitational waves in GLPV theories is red-tilted.

Original languageEnglish
Article number043
JournalJournal of Cosmology and Astroparticle Physics
Issue number4
Publication statusPublished - 2015 Apr 27
Externally publishedYes


  • cosmological perturbation theory
  • cosmology of theories beyond the SM
  • inflation
  • modified gravity

ASJC Scopus subject areas

  • Astronomy and Astrophysics


Dive into the research topics of 'Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories'. Together they form a unique fingerprint.

Cite this