分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： We study the comoving curvature perturbation $\mathcal{R}$ in the single-field inflation models whose potential can be approximated by a piecewise quadratic potential $V(\varphi)$ by using the $\delta N$ formalism. We find a general formula for $\mathcal{R}(\delta\varphi)$, consisting of a sum of logarithmic functions of the field perturbation $\delta\varphi$ at the point of interest, as well as of the field velocity perturbations $\delta\pi_*$ at the boundaries of each quadratic piece, which are functions of $\delta\varphi$ through the equation of motion. Each logarithmic expression has an equivalent dual expression, due to the second-order nature of the equation of motion for $\varphi$. We also clarify the condition under which $\mathcal{R}(\delta\varphi)$ reduces to a single logarithm, which yields either the renowned "exponential tail" of the probability distribution function of $\mathcal{R}$ or a Gumbel-distribution-like tail.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： We study the power spectrum of the comoving curvature perturbation $\cal R$ in the model that glues two linear potentials of different slopes, originally proposed by Starobinsky. We find that the enhanced power spectrum reaches its maximum at the wavenumber which is $\pi$ times the junction scale. The peak is $\sim2.61$ times larger than the ultraviolet plateau. We also show that its near-peak behavior can be well approximated by a constant-roll model, once we define the effective ultra-slow-roll $e$-folding number appropriately by considering the contribution from non-single-clock phase only. Such an abrupt transition to non-attractor phase can leave some interesting characteristic features in the energy spectrum of the scalar-induced gravitational waves, which are detectable in the space-borne interferometers if the primordial black holes generated at such a high peak are all the dark matter.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： We study the comoving curvature perturbation $\mathcal{R}$ in the single-field inflation models whose potential can be approximated by a piecewise quadratic potential $V(\varphi)$ by using the $\delta N$ formalism. We find a general formula for $\mathcal{R}(\delta\varphi)$, consisting of a sum of logarithmic functions of the field perturbation $\delta\varphi$ at the point of interest, as well as of the field velocity perturbations $\delta\pi_*$ at the boundaries of each quadratic piece, which are functions of $\delta\varphi$ through the equation of motion. Each logarithmic expression has an equivalent dual expression, due to the second-order nature of the equation of motion for $\varphi$. We also clarify the condition under which $\mathcal{R}(\delta\varphi)$ reduces to a single logarithm, which yields either the renowned "exponential tail" of the probability distribution function of $\mathcal{R}$ or a Gumbel-distribution-like tail.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： In the curvaton scenario, the curvature perturbation is generated after inflation at the curvaton decay, which may have a prominent non-Gaussian effect. For a model with a non-trivial kinetic term, an enhanced curvature perturbation on a small scale can be realized, which can lead to copious production of primordial black holes (PBHs) and induce secondary gravitational waves (GWs). Using the probability distribution function which takes full nonlinear effects into account, we calculate the PBH formation. We find that under the assumption that thus formed PBHs would not overclose the universe, the non-Gaussianity of the curvature perturbation can be well approximated by the local quadratic form, which can be used to calculate the induced GWs. In this model the limit of large non-Gaussianity can be reached when the curvaton energy fraction $r$ is small at the moment of curvaton decay. We also show that the $r\to1$ limit of non-Gaussianity coincides with that of ultra-slow-roll inflation.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： We study the power spectrum of the comoving curvature perturbation $\cal R$ in the model that glues two linear potentials of different slopes, originally proposed by Starobinsky. We find that the enhanced power spectrum reaches its maximum at the wavenumber which is $\pi$ times the junction scale. The peak is $\sim2.61$ times larger than the ultraviolet plateau. We also show that its near-peak behavior can be well approximated by a constant-roll model, once we define the effective ultra-slow-roll $e$-folding number appropriately by considering the contribution from non-single-clock phase only. Such an abrupt transition to non-attractor phase can leave some interesting characteristic features in the energy spectrum of the scalar-induced gravitational waves, which are detectable in the space-borne interferometers if the primordial black holes generated at such a high peak are all the dark matter.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
Ligong Bian
Rong-Gen Cai
Shuo Cao
Zhoujian Cao
He Gao
Zong-Kuan Guo
Kejia Lee
Di Li
Jing Liu
Youjun Lu
Shi Pi
Jian-Min Wang
Shao-Jiang Wang
Yan Wang
Tao Yang
Xing-Yu Yang
Shenghua Yu
Xin Zhang
摘要： It has been a half-decade since the first direct detection of gravitational waves, which signifies the coming of the era of the gravitational-wave astronomy and gravitational-wave cosmology. The increasing number of the detected gravitational-wave events has revealed the promising capability of constraining various aspects of cosmology, astronomy, and gravity. Due to the limited space in this review article, we will briefly summarize the recent progress over the past five years, but with a special focus on some of our own work for the Key Project ``Physics associated with the gravitational waves'' supported by the National Natural Science Foundation of China. In particular, (1) we have presented the mechanism of the gravitational-wave production during some physical processes of the early Universe, such as inflation, preheating and phase transition, and the cosmological implications of gravitational-wave measurements; (2) we have put constraints on the neutron star maximum mass according to GW170817 observations; (3) we have developed a numerical relativity algorithm based on the finite element method and a waveform model for the binary black hole coalescence along an eccentric orbit.
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