Constant-Roll Inflation: Analytical Formulae for Power Spectrum and Implications for Induced Gravitational Waves

arXiv:2606.24111 · astro-ph.CO · Submitted 2026-06-23 · Read on arXiv

Hayato Motohashi, Shi Pi, Yuichiro Tada, Jianing Wang

astro-ph.CO

Submitted: 2026-06-23

Comments: 38 pages, 19 figures

Code: https://github.com/JNWinGH/CR-solver

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Non-Gaussianity — 7× in this paper · explained in 2 episodes
• Bispectrum — 3× in this paper · explained in 3 episodes
• Reheating — 3× in this paper · explained in 2 episodes
• Abundance — 2× in this paper · explained in 1 episode
• Anisotropy — 2× in this paper · explained in 3 episodes
• Consistency — 2× in this paper · explained in 3 episodes
• Nine-Year Wilkinson Microwave Anisotropy Probe — 2× in this paper
• Nonminimal coupling — 2× in this paper · explained in 2 episodes
• Primordial non-Gaussianity — 2× in this paper · explained in 2 episodes
• pulsar timing arrays — 2× in this paper · explained in 2 episodes
• Homogeneity — 1× in this paper · explained in 2 episodes
• Primordial Black Holes (PBHs) — 1× in this paper · explained in 7 episodes
• Symmetry Breaking — 1× in this paper · explained in 3 episodes

Sources

• Strong Dynamics and Inflation: a review
• Lectures on Inflation
• Initial Conditions for Inflation - A Short Review
• Dynamics of cosmological scalar fields
• Introduction to the number of $e$-folds in slow-roll inflation
• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results
• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results
• Planck 2018 results. VI. Cosmological parameters
• Planck 2018 results. V. CMB power spectra and likelihoods
• Primordial Black Holes from Inflation and Quantum Diffusion
• Smooth vs instant inflationary transitions: steepest growth re-examined and primordial black holes
• Primordial Black Hole Formation in Starobinsky's Linear Potential Model
• Saddle point inflation from higher order corrections to Higgs/Starobinsky inflation
• Primordial black holes dark matter from inflection point models of inflation and the effects of reheating
• Double-peaked inflation model: Scalar induced gravitational waves and primordial-black-hole suppression from primordial non-Gaussianity
• Revisiting small-scale fluctuations in $\alpha$-attractor models of inflation
• One Small Step for an Inflaton, One Giant Leap for Inflation: a novel non-Gaussian tail and primordial black holes
• Logarithmic Duality of the Curvature Perturbation
• Primordial Black Hole Formation from the Upward Step Model: Avoiding Overproduction
• Eternal inflation near inflection points: a challenge to primordial black hole models

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