Abstract
The cosmological polytope and bootstrap programs have revealed interesting connections between positive geometries, modern on-shell methods and bootstrap principles studied in the amplitudes community with the wavefunction of the Universe in toy models of FRW cosmologies. To compute these FRW correlators, one often faces integrals that are too difficult to evaluate by direct integration. Borrowing from the Feynman integral community, the method of (canonical) differential equations provides an efficient alternative for evaluating these integrals. Moreover, we further develop our geometric understanding of these integrals by describing the associated relative twisted cohomology. Leveraging recent progress in our understanding of relative twisted cohomology in the Feynman integral community, we give an algorithm to predict the basis size and simplify the computation of the differential equations satisfied by FRW correlators.
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Acknowledgments
AP would like to thank Sebastian Mizera for pointing out the relevance of hyperplane arrangements in the cosmological context, Nima Arkani-Hamed and Aaron Hillman for stimulating discussions, as well as the Institute for Advanced Study for its hospitality. SD and AP would also like to thank Heliudson de Oliveira Bernardo, Claudia Fevola and Henrik Munch for useful discussions. SD and AP are especially grateful to Anastasia Volovich and Marcus Spradlin for valuable feedback throughout the project and help in simplifying equation (3.59). This work was supported in part by the US Department of Energy under contract DESC0010010 Task F (SD) and by Simons Investigator Award #376208 (AP).
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De, S., Pokraka, A. Cosmology meets cohomology. J. High Energ. Phys. 2024, 156 (2024). https://doi.org/10.1007/JHEP03(2024)156
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DOI: https://doi.org/10.1007/JHEP03(2024)156