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Open AccessArticle

Modifications of Gravity Via Differential Transformations of Field Variables

1
Department of High Energy and Elementary Particle Physics, Saint Petersburg State University, 7-9 Universitetskaya Emb., St Petersburg 199034, Russia
2
Department of Mathematics and Mathematical Physics, Saint Petersburg State University, 7-9 Universitetskaya Emb., St Petersburg 199034, Russia
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(2), 240; https://doi.org/10.3390/sym12020240
Received: 15 January 2020 / Revised: 31 January 2020 / Accepted: 2 February 2020 / Published: 5 February 2020
(This article belongs to the Special Issue Cosmology)
We discuss field theories appearing as a result of applying field transformations with derivatives (differential field transformations, DFTs) to a known theory. We begin with some simple examples of DFTs to see the basic properties of the procedure. In this process, the dynamics of the theory might either change or be conserved. After that, we concentrate on the theories of gravity which appear as a result of various DFTs applied to general relativity, namely the mimetic gravity and Regge–Teitelboim embedding theory. We review the main results related to the extension of dynamics in these theories, as well as the possibility to write down the action of a theory after DFTs as the action of the original theory before DFTs plus an additional term. Such a term usually contains some constraints with Lagrange multipliers and can be interpreted as an action of additional matter, which might be of use in cosmological applications, e.g., for the explanation of the effects of dark matter. View Full-Text
Keywords: field theory; modified gravity; dark matter; Lagrange multipliers; isometric embedding; Regge–Teitelboim equations; embedding theory; mimetic gravity; disformal transformations; Hilbert–Palatini formulation field theory; modified gravity; dark matter; Lagrange multipliers; isometric embedding; Regge–Teitelboim equations; embedding theory; mimetic gravity; disformal transformations; Hilbert–Palatini formulation
MDPI and ACS Style

Sheykin, A.; Solovyev, D.; Sukhanov, V.; Paston, S. Modifications of Gravity Via Differential Transformations of Field Variables. Symmetry 2020, 12, 240.

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