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Kinematic Flow and the Emergence of Time

Nima Arkani-Hamed1, Daniel Baumann2,3,4, Aaron Hillman5,6, Austin Joyce7,8, Hayden Lee8, and Guilherme L. Pimentel9

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Phys. Rev. Lett. 135, 031602 – Published 18 July, 2025

DOI: https://doi.org/10.1103/dsjm-tckw

Abstract

Perhaps the most basic question we can ask about cosmological correlations is how their strength changes as we smoothly vary kinematic parameters. The answer is encoded in differential equations that govern this evolution in kinematic space. In this Letter, we introduce a new perspective on these differential equations. We show that, in the simplified setting of conformally coupled scalars in power-law Friedmann-Robertson-Walker spacetimes, the equations for arbitrary tree-level processes can be obtained from a small number of simple combinatorial rules. While this “kinematic flow” is defined purely in terms of boundary data, it reflects the physics of bulk time evolution. The unexpected regularity of the equations suggests the existence of an autonomously defined mathematical structure from which cosmological correlations and the time evolution of the associated spacetime emerge.

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Outline

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Phys. Rev. Lett. 135, 031602– Published 18 July, 2025
  • Received 17 July 2024
  • Revised 23 April 2025
  • Accepted 6 June 2025
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