Eur. Phys. J. Plus (2021) 136: 46
https://doi.org/10.1140/epjp/s13360-020-01048-6

Review

Non-canonical volume-form formulation of modified gravity theories and cosmology

¹ Physics Department, Ben-Gurion University of the Negev, 84105, Be’er Sheva, Israel
² Frankfurt Institute for Advanced Studies (FIAS), Ruth-Moufang-Strasse 1, 60438, Frankfurt, Germany
³ Bahamas Advanced Study Institute and Conferences, 4A Ocean Heights, Hill View Circle, Stella Maris, Long Island, Bahamas
⁴ Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria

^a BENIDAV@post.bgu.ac.il

Received: 25 October 2020
Accepted: 23 December 2020
Published online: 5 January 2021

Abstract

A concise description is presented in the basic features of the formalism of non-canonical spacetime volume forms and its application in modified gravity theories and cosmology. The well-known unimodular gravity theory appears as a very special case. Concerning the hot issues facing cosmology now, we specifically briefly outline the construction of: (a) unified description of dark energy and dark matter as manifestations of a single material entity—a special scalar field “darkon”; (b) quintessential models of universe evolution with a gravity “inflaton”-assisted dynamical Higgs mechanism—dynamical suppression/generation of spontaneous electroweak gauge symmetry breaking in the “early”/“late” universe; (c) unification of dark energy and dark matter with diffusive interaction among them; and (d) mechanism for suppression of fifth force without fine-tuning.