Tracing out massive fields in cosmology
Abstract
Cosmological correlators are calculated through the in-in formalism in (quasi-)de Sitter background. Its effective description is best represented by a reduced density matrix. In this work, we study how integrating out a massive field in de Sitter space determines the reduced density matrix of a light field at a finite observation time. Starting from a quasi-single-field model with non-linear couplings, we first evaluate the massive field wavefunctional at fixed final value and then trace over this value. The trace generates branch-mixing terms which are generally present in the Schwinger--Keldysh description. For a conformally coupled massive field, we show explicitly that the light field bispectrum from the effective description agrees with a full theory calculation. This example also shows that decay of a field at the future boundary does not by itself justify discarding its contribution to the trace. We discuss the differences between an exact nonlocal effective description and the local effective field theory obtained through a large mass expansion. We then identify which local cubic terms affect the late-time probability and which contribute only a wavefunctional phase. Finally, we organize the resulting kernels by response, noise, and Schwinger--Keldysh consistency conditions, and discuss the symmetry constraints on the reduced density matrix.
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BibTeX
@misc{sun2026tracing,
title = {{Tracing out massive fields in cosmology}},
author = {Guanhao Sun and Sam S. C. Wong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30370},
eprint = {2609.30370},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30370},
}
RIS
TY - UNPB
TI - Tracing out massive fields in cosmology
AU - Guanhao Sun
AU - Sam S. C. Wong
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30370
UR - https://arxiv.org/abs/2609.30370
AB - Cosmological correlators are calculated through the in-in formalism in (quasi-)de Sitter background. Its effective description is best represented by a reduced density matrix. In this work, we study how integrating out a massive field in de Sitter space determines the reduced density matrix of a light field at a finite observation time. Starting from a quasi-single-field model with non-linear couplings, we first evaluate the massive field wavefunctional at fixed final value and then trace over this value. The trace generates branch-mixing terms which are generally present in the Schwinger--Keldysh description. For a conformally coupled massive field, we show explicitly that the light field bispectrum from the effective description agrees with a full theory calculation. This example also shows that decay of a field at the future boundary does not by itself justify discarding its contribution to the trace. We discuss the differences between an exact nonlocal effective description and the local effective field theory obtained through a large mass expansion. We then identify which local cubic terms affect the late-time probability and which contribute only a wavefunctional phase. Finally, we organize the resulting kernels by response, noise, and Schwinger--Keldysh consistency conditions, and discuss the symmetry constraints on the reduced density matrix.
ER -