Abstract
Scalar-tensor theories of gravity provide an intriguing and compelling approach to the dark energy problem. They have received increased attention in recent years thanks to a wealth of developments both in the theoretical and experimental sides. The class of models known as “degenerate” provide a particularly interesting proposal. These theories extend general relativity by a single degree of freedom, despite their equations of motion being higher than second order, a virtue made possible by the existence of an additional constraint that removes the would-be instability associated to a ghost. This note presents a brief overview of the problem of matter coupling in degenerate scalar-tensor theories. It has been remarked that the presence of matter fields minimally coupled to the metric tensor can obstruct the degeneracy constraint, thus impairing the consistency of the theory. We explain through some illustrative examples the precise ways in which the extra degree of freedom may reappear. This occurs in the Hamiltonian language through a loss of constraints, which may happen either when the kinetic matrix is not block-diagonal in the presence of matter fields, or when the matter sector itself has constraints. We next turn to the more physically relevant case of fermionic matter, and show that spin-1/2 fermions evade these issues and can thus be consistently coupled to degenerate theories of scalar-tensor gravity.
Highlights
The extension of general relativity (GR) by additional light degrees of freedom is arguably the most natural way to provide a dynamical explanation of Dark Energy, thereby dispensing of the cosmological constant as the source of the observed late-time cosmic acceleration
The physically meaningful question should make a distinction of light versus heavy degrees of freedom, it has proved fruitful to demand the strict absence of additional fields beyond the aforementioned three, seeing that the resulting models often enjoy interesting properties that may have been difficult to discover through a more agnostic construction based on the rules of effective field theory
We focus our attention to the subset of DHOST theories that are at most quadratic in the second derivative of the scalar field, Sg [ g, φ] =
Summary
The extension of general relativity (GR) by additional light degrees of freedom is arguably the most natural way to provide a dynamical explanation of Dark Energy, thereby dispensing of the cosmological constant as the source of the observed late-time cosmic acceleration. DHOST theories provide a very interesting solution to the classification problem of scalar-tensor gravity They are consistent theories within the scope of that problem, at least according to the way we have formulated it, it is clear that physical consistency will reduce the space of allowed models by the imposition of further constraints. The mixing with matter fields can obstruct this constraint, leading to the reappearance of the ghost degree of freedom and an inconsistent theory This may occur even if matter is minimally coupled to the metric tensor, for an indirect coupling with the DHOST scalar is still present. In the remaining of this note we present a summary of the main results, referring the interested reader to [8] for details and relevant literature
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