We show that gravity models, such as f(Lm), f(gμνTμν) and f(TμνTμν), that modify the introduction of
the material source in the usual Einstein-Hilbert action by adding only
matter-related terms to the matter Lagrangian density Lm are
equivalent to general relativity with nonminimal interactions. Through the
redefinition Lm+f→Lmtot,
these models are exactly GR, yet the usual material field Tμν and its
accompanying partner, viz., the modification field Tμνmod
interact nonminimally. That is,
∇μTμν=−Qν=−∇μTμνmod, where
Qν is the interaction kernel that governs the rate of energy transfer.
We focus on the particular model, the energy-momentum squared gravity, where
the usual material field Tμν brings in an accompanying energy-momentum
squared field , Tμνemsf along with a sui generis nonminimal
interaction between them. Compared to usual phenomenological nonminimal
interaction models in the literature, EMSF gives rise to more intricate
interaction kernels having covariant formulation even with simple forms of the
f function. We elaborate upon EMSF via some different aspects: a DE component
induced from the interaction of sources such as cold dark matter and
relativistic species with their accompanying EMSFs generating interacting DE-DM
models, mimicking noncanonical scalar field, etc., or a Hoyle-type creation
field generating steady-state universe models extended to fluids other than
dust and a mimicker of modified generalized Chaplygin gas. We also demonstrate
the proper calculation of second metric variation of Lm, as
well as in models that contain scalars like gμνTμν,RμνTμν and GμνTμν.Comment: 16 pages, no figures and table