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

作者：Tsujikawa Shinji^*

来源：Journal of Cosmology and Astroparticle Physics, 2015, 2015(4): 043.

DOI：10.1088/1475-7516/2015/04/043

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

It is known that Horndeski theories can be transformed to a,sub-class of Gleyzes-Langlois-Piazza-Vernizzi (MTV) theories under the disformal transformation of the metric g(mu v) -> Omega(2)(phi)g(mu v) + Gamma(phi, X)del(mu)phi del(v)phi, where Omega is a function of a scalar field phi and Gamma is another function depending on both phi and X - g(mu v)del(mu)phi del(v)phi. We show that, with the choice of unitary gauge, both curvature and tensor perturbations on the Hat isotropic cosmological background are generally invariant under the disformal transformation. By means of the effective field theories (mcompassing florndeski and GLPV theories, we obtain the secondorder actions of scalar/tensor perturbations and present the relations for physical quantities betAveen 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.

• 出版日期2015-4