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Title: Role of matter in modified gravity: a search for new interactions

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Abstract:

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In this talk, I will focus on the process of building classical
gravitational theories. For a given theory, we start by defining some
physical viability principles, formulate these into viability criteria,
then finally develop a mathematical representation. However, these steps
are typically taken in vacuum; including the matter sector is almost an
afterthought. Recent developments in scalar-tensor theories indicate
that different mathematical representations (or, the choice of field
variables) can correspond to different theories, as result of an
inaccurate formulation of the viability principles. For instance, until
recently, it was thought that the Horndeski action provided the most
complete representation of a Lorentz invariant scalar-tensor theory. We
now know that allowing for auxiliary fields, Horndeski action can be
further generalised to Beyond-Horndeski/DHOST theories.

The point of my talk is that a mismatch between a viability principle
(qualitative) and the viability criteria (quantitative) can be minimised
in a framework where one is agnostic about the “right choice” of
gravity-matter coupling. This idea goes back to the 90s, to Bekenstein
who proposed the use of distinct geometries for gravitation and matter.
The approach can potentially reveal previously unrecognised interactions
in almost all field theoretic formulations of modified gravity theories.
I will discuss two specific applications of this idea in the context of:
i. a massive spin–2 theory; ii. a vector-tensor with an Abelian gauge
field.