Bispectrum islands: Bootstrap bounds on cosmological correlators

Inspired by the amplitude bootstrap program, the spirit of this work is to constrain the space of consistent inflationary correlation functions—specifically, the bispectrum of curvature perturbations—using fundamental principles such as unitarity, locality, analyticity, and symmetries. To this end, we assume a setup for inflation in which de Sitter isometries are only mildly broken by the slow roll of the inflaton field, and study the bispectrum imprinted by a generic hidden sector during inflation. Assuming that the hidden sector’s contributions to primordial non-Gaussianity are dominated by the exchange of a scalar operator (which does not preclude high-spin UV completions), we derive nontrivial positivity constraints on the resulting bispectrum <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>B</a:mi><a:mo stretchy="false">(</a:mo><a:msub><a:mrow><a:mi>k</a:mi></a:mrow><a:mrow><a:mn>1</a:mn></a:mrow></a:msub><a:mo>,</a:mo><a:msub><a:mrow><a:mi>k</a:mi></a:mrow><a:mrow><a:mn>2</a:mn></a:mrow></a:msub><a:mo>,</a:mo><a:msub><a:mrow><a:mi>k</a:mi></a:mrow><a:mrow><a:mn>3</a:mn></a:mrow></a:msub><a:mo stretchy="false">)</a:mo></a:mrow></a:math>. In particular, we show that <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>B</e:mi></e:math> must be negative in a certain region around the equilateral configuration. For instance, for isosceles triangles (with <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>k</g:mi><g:mn>2</g:mn></g:msub><g:mo>=</g:mo><g:msub><g:mi>k</g:mi><g:mn>3</g:mn></g:msub></g:math>) this region is given by <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mn>0.027</i:mn><i:mo>≲</i:mo><i:msub><i:mi>k</i:mi><i:mn>3</i:mn></i:msub><i:mo>/</i:mo><i:msub><i:mi>k</i:mi><i:mn>1</i:mn></i:msub><i:mo>≤</i:mo><i:mn>2</i:mn></i:math>. Furthermore, we demonstrate that unitarity imposes upper and lower bounds on the bispectrum shape, thereby carving out a where consistent shapes in our setup can reside. We complement our analysis by contemplating alternative setups where the coupling to the hidden sector is allowed to strongly break de Sitter boosts. We also identify situations that would push the bispectrum off the island and the profound physical features they would reveal.