Beyond Positivity Bounds and the Fate of Massive Gravity

Physical Review Letters
Brando BellazziniFrancesco Sgarlata

Abstract

We constrain effective field theories by going beyond the familiar positivity bounds that follow from unitarity, analyticity, and crossing symmetry of the scattering amplitudes. As interesting examples, we discuss the implications of the bounds for the Galileon and ghost-free massive gravity. The combination of our theoretical bounds with the experimental constraints on the graviton mass implies that the latter is either ruled out or unable to describe gravitational phenomena, let alone to consistently implement the Vainshtein mechanism, down to the relevant scales of fifth-force experiments, where general relativity has been successfully tested. We also show that the Galileon theory must contain symmetry-breaking terms that are at most one-loop suppressed compared to the symmetry-preserving ones. We comment as well on other interesting applications of our bounds.

References

Feb 9, 2005·Physical Review Letters·James G WilliamsDale H Boggs
Mar 16, 2007·Physical Review Letters·Jacques DistlerIra Z Rothstein
Jun 13, 2009·Physical Review Letters·Eric A BergshoeffPaul K Townsend
Jul 21, 2011·Physical Review Letters·Claudia de RhamAndrew J Tolley
Mar 10, 2012·Physical Review Letters·S F Hassan, Rachel A Rosen
Aug 16, 2014·Physical Review Letters·Clifford Cheung, Grant N Remmen
Jan 1, 2014·The European Physical Journal. C, Particles and Fields·Brando BellazziniJohn Terning
Jan 1, 2014·Living Reviews in Relativity·Claudia de Rham
Feb 18, 2017·Physical Review Letters·Clifford Cheung, Grant N Remmen
Oct 21, 2017·Physical Review Letters·Brando BellazziniJavi Serra

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Citations

Dec 15, 2018·Physical Review Letters·Claudia de Rham, Scott Melville
Jan 11, 2020·Physical Review Letters·Brando BellazziniJavi Serra
Dec 2, 2020·Physical Review Letters·Cen Zhang, Shuang-Yong Zhou

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