Particle content of (scalar curvature)2 gravities revisited

Studying the spectrum of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mo stretchy="false">(</a:mo><a:mi>scalar</a:mi><a:mtext> </a:mtext><a:mi>curvature</a:mi><a:msup><a:mrow><a:mo stretchy="false">)</a:mo></a:mrow><a:mrow><a:mn>2</a:mn></a:mrow></a:msup></a:mrow></a:math> gravities on Minkowski background inevitably results in a catch-22: any consistent interpretation of the particle dynamics dictates that no accidental gauge symmetries emerge, a requirement that cannot be fulfilled when these theories are studied on Minkowski. Being artifacts of the linearized approximation on top of Minkowski spacetime, accidental symmetries do not persist at higher orders and degrees of freedom are reintroduced via interactions, suggesting that the analysis of the particle content is hindered by strong coupling effects. Such undesirable symmetries are absent already at the leading nontrivial order in perturbations on nonflat backgrounds, e.g. de Sitter spacetime, which are the appropriate ones for studying the particle dynamics of these theories.