Constant-Roll Inflation as a Competitive Alternative to Slow-Roll Inflation
Abstract
Starting from the constant-roll condition, which involves the constant-roll parameter β, which is a fundamental constant in the constant-roll inflationary models, we derive the scalar power spectrum and obtain an analytic expression for the scalar spectral index ns in terms of β and the number of remaining e-folds Ñ. The resulting relation is non-monotonic in β, allowing two distinct constant-roll branches, one with β<0 and one with β>0, to reproduce nearly the same observed scalar tilt. We constrain β using Planck 2018 CMB data, and further using the combined Planck 2018 + ACT DR6 data. For Planck 2018, the posterior distribution of β exhibits a bimodal structure associated with the two analytical branches, while the combined Planck+ACT analysis tightens the allowed range of β and shows continued consistency with the β=0 slow-roll-like spectral point. The data constrain β to be small, but do not require it to vanish exactly. We also estimate the inflationary mass scale M by using the observed scalar-amplitude normalization at the pivot scale. Both the negative and positive β branches give a high-scale inflationary normalization of order M∼10−5MPl. We show that the β→ 0 limit is only spectrally slow-roll like, but does not reproduce standard slow-roll dynamics. Our results show that constant-roll inflation is observationally competitive with the usual slow-roll inflationary paradigm. The constant roll inflation model is supported by the latest CMB observations equally well or marginally better when compared with the slow roll inflation model.
Related
- Analytic results for slow-roll curved-space inflation and exponential potentials
- A Global Overview of Starobinsky Inflation beyond slow-roll with CMB-BAO data
- Ultra-slow-roll Inflation with Non-perturbative Non-Gaussianity and Scalar Induced Gravitational Waves
- Slow-Roll Inflation at Arbitrary Order
- UV artefacts in ultra-slow-roll models of inflation
BibTeX
@misc{biswas2026constantroll,
title = {{Constant-Roll Inflation as a Competitive Alternative to Slow-Roll Inflation}},
author = {Sandip Biswas and Rajib Saha and Kaushik Bhattacharya},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32865},
eprint = {2609.32865},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32865},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Constant-Roll Inflation as a Competitive Alternative to Slow-Roll Inflation
AU - Sandip Biswas
AU - Rajib Saha
AU - Kaushik Bhattacharya
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32865
UR - https://arxiv.org/abs/2609.32865
AB - Starting from the constant-roll condition, which involves the constant-roll parameter β, which is a fundamental constant in the constant-roll inflationary models, we derive the scalar power spectrum and obtain an analytic expression for the scalar spectral index n_s in terms of β and the number of remaining e-folds Ñ. The resulting relation is non-monotonic in β, allowing two distinct constant-roll branches, one with β<0 and one with β>0, to reproduce nearly the same observed scalar tilt. We constrain β using Planck 2018 CMB data, and further using the combined Planck 2018 + ACT DR6 data. For Planck 2018, the posterior distribution of β exhibits a bimodal structure associated with the two analytical branches, while the combined Planck+ACT analysis tightens the allowed range of β and shows continued consistency with the β=0 slow-roll-like spectral point. The data constrain β to be small, but do not require it to vanish exactly. We also estimate the inflationary mass scale M by using the observed scalar-amplitude normalization at the pivot scale. Both the negative and positive β branches give a high-scale inflationary normalization of order M∼10^−5M_Pl. We show that the β→ 0 limit is only spectrally slow-roll like, but does not reproduce standard slow-roll dynamics. Our results show that constant-roll inflation is observationally competitive with the usual slow-roll inflationary paradigm. The constant roll inflation model is supported by the latest CMB observations equally well or marginally better when compared with the slow roll inflation model.
ER -