Do field theories exist for dark energy/matter? Has a mathematical theory ever been composed to describe either dark energy or dark matter (or both)? In other words, the standard model describes fermions and bosons; does a model exist to describe dark energy or dark matter, even in the simplest form? To specify, I'm not talking about theories that predict that dark matter is hidden fermions (fermionic WIMPS or MACHOS), but a real, independent field theory (or other kind of theory) of dark energy or dark matter.
 A: You can read, for example, about Mimetic Gravity. This model assumes that a (non-dynamical) scalar degree of freedom enters in the Einstein Hilbert action by the replacement $$g_{\mu\nu}\mapsto (g^{\alpha\beta}\partial_\alpha\phi\partial_\beta\phi) g_{\mu\nu}.$$
This redefinition can be related to the concept of disformal transformation and change between frames (Einstein frame, Jordan Frame, and many more in between). In this model you can show that it is possible to reproduce a mimetic (dark) matter contribution to the budget. This framework can accommodate also a mimetic (dark) energy component (for the late time acceleration) and can be used as inflationary model (early time acceleration). It is a new theory with roots well deep into the Scalar-Vector-Tensor (TeVeS) theory of gravity with also a bridge into the Horndeski theory. Hope this help.


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*Cosmology with Mimetic Matter, Ali H. Chamseddine, Viatcheslav Mukhanov, Alexander Vikman (https://arxiv.org/abs/1403.3961)

*Disformal Transformations, Veiled General Relativity and Mimetic Gravity, Nathalie Deruelle, Josephine Rua (https://arxiv.org/abs/1407.0825)
