Analytic results for slow-roll curved-space inflation and exponential potentials
Abstract
We derive analytic templates for the scalar and tensor primordial power spectra describing cosmologies that transition from kinetic dominance to slow-roll inflation in the presence of spatial curvature. Our results extend recent works in the literature, allowing us, in particular, to recover the scalar and tensor tilts analytically. We revisit the case of curvature-assisted single-exponential models in light of this framework. In the case of an open universe, the phase space of such models naturally includes cosmologies that start out in a kinetic-dominance regime followed by a parametrically controlled quasi-de Sitter phase. However, they do not fit in the framework of the templates, as their second Hubble slow-roll parameter remains of order one in the quasi-de Sitter regime.
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BibTeX
@misc{tsimpis2026analytic,
title = {{Analytic results for slow-roll curved-space inflation and exponential potentials}},
author = {Dimitrios Tsimpis and Govind Venugopal},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.16906},
eprint = {2606.16906},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.16906},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Analytic results for slow-roll curved-space inflation and exponential potentials
AU - Dimitrios Tsimpis
AU - Govind Venugopal
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2606.16906
UR - https://arxiv.org/abs/2606.16906
AB - We derive analytic templates for the scalar and tensor primordial power spectra describing cosmologies that transition from kinetic dominance to slow-roll inflation in the presence of spatial curvature. Our results extend recent works in the literature, allowing us, in particular, to recover the scalar and tensor tilts analytically. We revisit the case of curvature-assisted single-exponential models in light of this framework. In the case of an open universe, the phase space of such models naturally includes cosmologies that start out in a kinetic-dominance regime followed by a parametrically controlled quasi-de Sitter phase. However, they do not fit in the framework of the templates, as their second Hubble slow-roll parameter remains of order one in the quasi-de Sitter regime.
ER -