In this paper we mainly focus on the curvature perturbation generated at the end of multi-field inflation, such as the multi-brid inflation. Since the curvature perturbation is produced on the super-horizon scale, the bispectrum and trispectrum have a local shape. The size of bispectrum is measured by $f_{NL}$ and the trispectrum is characterized by two parameters $τ_{NL}$ and $g_{NL}$. For simplicity, the trajectory of inflaton is assumed to be a straight line in the field space and then the entropic perturbations do not contribute to the curvature perturbation during inflation. As long as the background inflaton path is not orthogonal to the hyper-surface for inflation to end, the entropic perturbation can make a contribution to the curvature perturbation at the end of inflation and a large local-type non-Gaussiantiy is expected. An interesting thing is that the non-Gaussianity parameters are completely determined by the geometric properties of the hyper-surface of the end of inflation. For example, $f_{NL}$ is proportional to the curvature of the curve on this hyper-surface along the adiabatic direction and $g_{NL}$ is related to the change of the curvature radius per unit arc-length of this curve. Both $f_{NL}$ and $g_{NL}$ can be positive or negative respectively, but $τ_{NL}$ must be positive and not less than $({6\over 5}f_{NL})^2$.
We extend the δN formalism so that it gives all of the stochastic properties of the primordial curvature perturbation ζif the initial field perturbations are gaussian. The calculation requires only the knowledge of some family of unperturbed universes. A formula is given for the normalisation \fnl of the bispectrum of ζ, which is the main signal of non-gaussianity. Examples of the use of the formula are given, and its relation to cosmological perturbation theory is explained.
We consider a member of the family of scalar-tensor theories of Inflation - the so-called Horndeski model for Inflation, for which we calculate the non-Gaussianity (NG) and the power spectrum of curvature perturbations. We concentrate on the determination of the power spectrum, and the bi-spectrum along with the associated $f_\mathrm{NL}$ parameter and the Spectral Index. We follow the methodology outlined within the Quantum field theory framework (S-matrix approach and Weinberg's 'in-in' formalism) and compare - whenever necessary - our findings with those obtained via the traditional $δ$N fo…
We study the non-Gaussianity and secondary Gravitational Waves (GWs) in the process of the Primordial Black Holes (PBHs) production from inflation. In our work, we focus on the $α$-attractor inflation model in which a tiny bump in the inflaton potential enhances the amplitude of the curvature perturbations at some scales and consequently leads to the PBHs production with different mass scales. We implement the computational code BINGO which calculates the non-Gaussianity parameter in different triangle configurations. Our examination implies that in this setup, the non-Gaussianity gets amplifi…
Inflationary dynamics driven by multiple fields, especially with nonminimal couplings, allow for highly interesting features such as isocurvature, non-Gaussianity, and preheating. In this paper, we study two-field inflation in the context of purely affine gravity, where the metrical structure results from the dynamics of the spacetime affine connection. We introduce a covariant formulation in the new framework and show that it leads to a curved field space which can produce conspicuous departure from the purely metric gravity. In the case where the fields are canonical, the field manifold gain…
Separable and non-separable multi-field inflation and large non-Gaussianity
在本文中，我们提供了一个一般的框架，$δN$形式主义的基础上，估计宇宙微波背景辐射的不可分的潜力，并为通用的\emph{end of inflation}边界条件的宇宙学观测值。我们提供了相关的观测值的解析和数值解分解的曲率和等曲率方向，\emph{instead of adiabatic and entropy directions}的宇宙学扰动。然后我们研究了在什么条件下通过相变可以产生大的双谱和三谱，从而结束暴胀。在一个说明性的例子中，我们表明，大的$f_{NL}\sim {\cal O}(80)$和$τ_{NL}\sim {\cal O}(20000)$可以得到的情况下，可分离和不可分离的通货膨胀潜力。
Sphaleron heating has been recently proposed as a mechanism to realize warm inflation when inflaton is an axion coupled to pure Yang-Mills. As a result of heating, there is a friction coefficient $γ\propto T^3$ in the equation of motion for the inflaton, and a thermal contribution to cosmological fluctuations. Without the knowledge of the inflaton potential, non-Gaussianity is the most promising way of searching for the signatures of this model. Building on an earlier work by Bastero-Gil, Berera, Moss and Ramos, we compute the scalar three-point correlation function and point out some distinct…
