Massive gravity is not positive

Abstract

We derive new positivity bounds at finite momentum transfer, assuming a large separation between the mass <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>m</a:mi></a:math> of the lightest particle in the effective theory and the mass gap <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>M</c:mi></c:math> to new heavy states. Massive gravity parametrically violates these bounds unless the cutoff is within 1 order of magnitude of the graviton mass <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>M</e:mi><e:mo>≲</e:mo><e:mi>O</e:mi><e:mo stretchy="false">(</e:mo><e:mn>10</e:mn><e:mo stretchy="false">)</e:mo><e:mi>m</e:mi></e:math>. Nongravitational effective theories of massive spin-2 particles are similarly bounded. Published by the American Physical Society 2024