Abstract
Our understanding of quantum correlators in cosmological spacetimes, including those that we can observe in cosmological surveys, has improved qualitatively in the past few years. Now we know many constraints that these objects must satisfy as consequences of general physical principles, such as symmetries, unitarity and locality. Using this new understanding, we derive the most general scalar four-point correlator, i.e., the trispectrum, to all orders in derivatives for manifestly local contact interactions. To obtain this result we use techniques from commutative algebra to write down all possible scalar four-particle amplitudes without assuming invariance under Lorentz boosts. We then input these amplitudes into a contact reconstruction formula that generates a contact cosmological correlator in de Sitter spacetime from a contact scalar or graviton amplitude. We also show how the same procedure can be used to derive higher-point contact cosmological correlators. Our results further extend the reach of the boostless cosmological bootstrap and build a new connection between flat and curved spacetime physics.
Highlights
The interaction of relativistic massless spin-2 particles in Minkowski space cannot break Lorentz boosts, neither explicitly nor spontaneously [1]
We derive the most general scalar four-point correlator, i.e., the trispectrum, to all orders in derivatives for manifestly local contact interactions. To obtain this result we use techniques from commutative algebra to write down all possible scalar four-particle amplitudes without assuming invariance under Lorentz boosts. We input these amplitudes into a contact reconstruction formula that generates a contact cosmological correlator in de Sitter spacetime from a contact scalar or graviton amplitude
We should mention that we work at the level of the IR finite part of the wavefunction coefficients, which are forced to be real by unitarity in the form of the cosmological optical theorem [11, 16, 27,28,29] — see refs. [30,31,32] for the anti de Sitter (AdS) side of this story and refs. [33,34,35] for connecting results in AdS space to dS space
Summary
After a lightning introduction to the wavefunction of the universe and the Schrödinger picture approach to quantum field theory in de Sitter space, we review the main results that we will use in the rest of the paper, namely the bootstrap rules for boostless contact interactions in de Sitter space [13] and the manifestly local test recently derived in ref. [14]. Taking the boundary perspective of the bootstrap approach, here we mainly focus on cosmological correlators evaluated in the asymptotic future, at the so-called (future, spacelike, conformal) boundary of de Sitter space
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