Report
A complete analysis of inflation with piecewise quadratic potential
| العنوان: | A complete analysis of inflation with piecewise quadratic potential |
|---|---|
| المؤلفون: | Wang, Xinpeng, Ma, Xiao-Han, Sasaki, Misao |
| سنة النشر: | 2024 |
| المجموعة: | Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| مصطلحات موضوعية: | Astrophysics - Cosmology and Nongalactic Astrophysics, General Relativity and Quantum Cosmology, High Energy Physics - Phenomenology |
| الوصف: | We conduct a thorough study of the comoving curvature perturbation $\mathcal{R}$ in single-field inflation with two stages, represented by a piecewise quadratic potential, where both the first and second derivatives are allowed to be discontinuous at the transition point. We calculate the evolution of $\mathcal{R}$ by combining the perturbative and non-perturbative methods consistently, and obtain the power spectrum and the non-Gaussian features in the probability distribution function. We find that both the spectrum and the statistics of $\mathcal{R}$ depend significantly on the second derivatives of the potential at both the first and second stages. Furthermore, we find a new parameter constructed from the potential parameters, which we call $\alpha$, plays a decisive role in determining various features in the spectrum such as the amplitude, the slope, and the existence of a dip. In particular, we recover the typical $k^4$ growth of the spectrum in most cases, but the maximum growth rate of $k^5(\log k)^2$ can be obtained by fine-tuning the parameters. Then, using the $\delta N$ formalism valid on superhorizon scales, we give fully nonlinear formulas for $\cal{R}$ in terms of the scalar field perturbation $\delta\phi$ and its time derivative. In passing, we point out the importance of the nonlinear evolution of $\delta\phi$ on superhorizon scales. Finally, using the Press-Schechter formalism for simplicity, we discuss the effect of the non-Gaussian tails of the probability distribution function on the primordial black hole formation. Comment: Prepared for a book in memory of Alexei Starobinsky "Open Issues in Gravitation and Cosmology", to be published by Springer. 41 pages, 16 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2412.16463 |
| رقم الانضمام: | edsarx.2412.16463 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |