Extending the symmetry of the massless Klein-Gordon equation under the general disformal transformation
arXiv:2208.10953 · doi:10.1142/S0217751X23500045
Abstract
The Klein-Gordon equation, one of the most fundamental equations in field theory, is known to be not invariant under conformal transformation. However, its massless limit exhibits symmetry under Bekenstein's disformal transformation, subject to some conditions on the disformal part of the metric variation. In this study, we explore the symmetry of the Klein-Gordon equation under the general disformal transformation encompassing that of Bekenstein and a hierarchy of `sub-generalisations' explored in the literature (within the context of inflationary cosmology and scalar-tensor theories). We find that the symmetry in the massless limit can be extended under this generalisation provided that the disformal factors takes a special form in relation to the conformal factor. Upon settling the effective extension of symmetry, we investigate the invertibility of the general disformal transformation to avoid propagating non-physical degrees of freedom upon changing the metric. We derive the inverse transformation and the accompanying restrictions that make this inverse possible.
14 pages, accepted for publication in International Journal of Modern Physics A, deleted some unimportant details, clarified that the `orthogonality condition' does not make the field overdetermined, rewritten parts for clarity
References in corpus (13)
- Healthy theories beyond Horndeski
- Horndeski theory and beyond: a review
- Exploring gravitational theories beyond Horndeski
- Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
- Disformal Theories of Gravity: From the Solar System to Cosmology
- Hairy black holes in DHOST theories: Exploring disformal transformation as a solution-generating method
- Disformal transformation of cosmological perturbations
- Invertible disformal transformations with higher derivatives
- Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories
- Adiabatic regularisation of power spectra in -inflation
- Transformation of Primordial Cosmological Perturbations Under the General Extended Disformal Transformation
- Adiabatic regularisation of power spectra in nonminimally coupled chaotic inflation
- Disformal transformations and the motion of a particle in semi-classical gravity