Kinematic Flow and the Emergence of Time
Creators
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1.
Institute for Advanced Study
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2.
National Center for Theoretical Sciences
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3.
California Institute of Technology
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4.
University of Chicago
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5.
Scuola Normale Superiore di Pisa
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.
Copyright and License
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Acknowledgement
We are grateful for feedback and discussions to Ana Achúcarro, Paolo Benincasa, Jan de Boer, Alessandra Caraceni, J. J. Carrasco, Xingang Chen, Claude Duhr, Alex Edison, Carolina Figueiredo, Dan Green, Thomas Grimm, Song He, Johannes Henn, Arno Hoefnagels, Yu-tin Huang, Michael Jones, Manki Kim, Barak Kol, Chia-Kai Kuo, Daniel Longenecker, Manuel Loparco, Scott Melville, Sebastian Mizera, Matteo Parisi, Julio Parra-Martinez, Nic Pavao, Andrzej Pokraka, Oliver Schlotterer, Leonardo Senatore, Chia-Hsien Shen, John Stout, Bernd Sturmfels, Simon Telen, Jaroslav Trnka, Kamran Salehi Vaziri, Dong-Gang Wang, and Alexander Zhiboedov. N. A. H. is supported by the U.S. Department of Energy (DOE) under Contract No. DE–SC0009988. D. B. is supported by a Yushan Professorship at National Taiwan University funded by the Ministry of Education (Taiwan). A. H. is supported by DOE (HEP) Award No. DE-SC0011632 and by the Walter Burke Institute for Theoretical Physics. A. J. is supported in part by DOE (HEP) Award No. DE-SC0009924. H. L. is supported by the Kavli Institute for Cosmological Physics at the University of Chicago through an endowment from the Kavli Foundation and its founder Fred Kavli. G. L. P. is supported by a Rita-Levi Montalcini fellowship from the Italian Ministry of Universities and Research (MUR) and by INFN (IS GSS-Pi). The research of N. A. H. and D. B. is funded by the European Union (ERC, UNIVERSE PLUS, 101118787).
Supplemental Material
The Supplemental Material has two parts. The first provides additional examples of the application of the kinematic flow rules. The second part briefly summarizes the direct bulk computation of cosmological correlations and describes the connection with the kinematic flow.
Additional Information
Views and opinions expressed are those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.
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Additional details
Funding
- United States Department of Energy
- DE–SC0009988
- Office of High Energy Physics
- DE-SC0011632
- United States Department of Energy
- DE-SC0009924
- National Taiwan University
- Ministry of Education
- California Institute of Technology
- Walter Burke Institute for Theoretical Physics -
- University of Chicago
- The Kavli Foundation
- Ministero dell'Università e della Ricerca
- Istituto Nazionale di Fisica Nucleare
- European Commission
- European Research Council
- 101118787