High-Accuracy Semi-Analytic Mode Functions, Ultraviolet Regularity, and Particle Creation in the Hybrid Approach to mLQC-I
Abstract
We construct high-accuracy semi-analytic mode functions for scalar cosmological perturbations in mLQC-I within the hybrid approach to study ultraviolet regularity and gravitational particle creation. The evolution comprises an asymptotic pre-de Sitter branch, a pre-inflationary region containing the quantum bounce, and inflation. In the intermediate region, we construct the complete third-order uniform asymptotic solution and introduce adaptive defect correction. The third-order approximation achieves sub-percent complex-mode accuracy for representative higher-wavenumber modes; defect-corrected solutions agree with numerical evolution at the 0.00001% level over the tested low-wavenumber range. Retaining amplitudes and phases provides a controlled basis for future precision calculations of primordial power spectra and non-Gaussian correlations. We compare the de Sitter vacuum selected in the remote contracting branch with a fourth-order adiabatic state imposed at the bounce. Finite-wavenumber matching and the strict ultraviolet limit require different asymptotic treatments: extrapolating the leading connection to infinite wavenumber yields a spurious constant negative-frequency coefficient and an apparent ultraviolet divergence. Instead, the large-wavenumber de Sitter mode agrees with the fourth-order adiabatic expansion through the order required for energy-momentum tensor renormalization, and smooth exact evolution preserves this ultraviolet structure. Finite and intermediate modes can nevertheless undergo nonadiabatic Bogoliubov mixing and particle creation. Finite-mode particle production thus coexists with ultraviolet regularity. The ultraviolet argument also extends to the dressed-metric approach in its corresponding large-wavenumber regime, while quantitative mode functions must be recalculated using its effective mass.
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BibTeX
@misc{saeed2026highaccuracy,
title = {{High-Accuracy Semi-Analytic Mode Functions, Ultraviolet Regularity, and Particle Creation in the Hybrid Approach to mLQC-I}},
author = {Jamal Saeed and Rui Pan and Anzhong Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10802},
eprint = {2610.10802},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10802},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - High-Accuracy Semi-Analytic Mode Functions, Ultraviolet Regularity, and Particle Creation in the Hybrid Approach to mLQC-I
AU - Jamal Saeed
AU - Rui Pan
AU - Anzhong Wang
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10802
UR - https://arxiv.org/abs/2610.10802
AB - We construct high-accuracy semi-analytic mode functions for scalar cosmological perturbations in mLQC-I within the hybrid approach to study ultraviolet regularity and gravitational particle creation. The evolution comprises an asymptotic pre-de Sitter branch, a pre-inflationary region containing the quantum bounce, and inflation. In the intermediate region, we construct the complete third-order uniform asymptotic solution and introduce adaptive defect correction. The third-order approximation achieves sub-percent complex-mode accuracy for representative higher-wavenumber modes; defect-corrected solutions agree with numerical evolution at the 0.00001% level over the tested low-wavenumber range. Retaining amplitudes and phases provides a controlled basis for future precision calculations of primordial power spectra and non-Gaussian correlations. We compare the de Sitter vacuum selected in the remote contracting branch with a fourth-order adiabatic state imposed at the bounce. Finite-wavenumber matching and the strict ultraviolet limit require different asymptotic treatments: extrapolating the leading connection to infinite wavenumber yields a spurious constant negative-frequency coefficient and an apparent ultraviolet divergence. Instead, the large-wavenumber de Sitter mode agrees with the fourth-order adiabatic expansion through the order required for energy-momentum tensor renormalization, and smooth exact evolution preserves this ultraviolet structure. Finite and intermediate modes can nevertheless undergo nonadiabatic Bogoliubov mixing and particle creation. Finite-mode particle production thus coexists with ultraviolet regularity. The ultraviolet argument also extends to the dressed-metric approach in its corresponding large-wavenumber regime, while quantitative mode functions must be recalculated using its effective mass.
ER -