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Our understanding of quantum correlators in cosmological spacetimes,including those that we can observe in cosmological surveys, has improvedqualitatively in the past few years. Now we know many constraints that theseobjects must satisfy as consequences of general physical principles, such assymmetries, unitarity and locality. Using this new understanding, we derive themost general scalar four-point correlator, i.e., the trispectrum, to all ordersin derivatives for manifestly local contact interactions. To obtain this resultwe use techniques from commutative algebra to write down all possible scalarfour-particle amplitudes without assuming invariance under Lorentz boosts. Wethen input these amplitudes into a contact reconstruction formula thatgenerates a contact cosmological correlator in de Sitter spacetime from acontact scalar or graviton amplitude. We also show how the same procedure canbe used to derive higher-point contact cosmological correlators. Our resultsfurther extend the reach of the boostless cosmological bootstrap and build anew connection between flat and curved spacetime physics.

From Amplitudes to Contact Cosmological Correlators