Gravitational Tensor and Acoustic Waves in A Radiation Dominated Universe: Weyl Curvature and Polarization Patterns

Cosmological perturbations on the Phantom brane

We obtain a closed system of equations for scalar perturbations in a multi-component braneworld. Our braneworld possesses a phantom-like equation of state at late times, $w_{\rm eff} < -1$, but no big-rip future singularity. In addition to matter and radiation, the braneworld possesses a new effective degree of freedom - the 'Weyl fluid' or 'dark radiation'. Setting initial conditions on super-Hubble spatial scales at the epoch of radiation domination, we evolve perturbations of radiation, pressureless matter and the Weyl fluid until the present epoch. We observe a gradual decrease in the ampl…

Acoustics of early universe. II. Lifshitz vs. gauge-invariant theories

Appealing to classical methods of order reduction, we reduce the Lifshitz system to a second order differential equation. We demonstrate its equivalence to well known gauge-invariant results. For a radiation dominated universe we express the metric and density corrections in their exact forms and discuss their acoustic character.

Is Asymptotically Weyl-Invariant Gravity Viable?

We explore the cosmological viability of a theory of gravity defined by the Lagrangian $f(\mathcal{R})=\mathcal{R}^{n\left(\mathcal{R}\right)}$ in the Palatini formalism, where $n\left(\mathcal{R}\right)$ is a dimensionless function of the Palatini scalar curvature $\mathcal{R}$ that interpolates between general relativity when $n\left(\mathcal{R}\right)=1$ and a locally scale-invariant and superficially renormalizable theory when $n\left(\mathcal{R}\right)=2$. We refer to this model as asymptotically Weyl-invariant gravity (AWIG). We analyse perhaps the simplest possible implementation of AWI…

Analytic Results for a Flat Universe Dominated by Dust and Dark Energy

We find the solution for the scale factor in a flat Universe driven by dust plus a component characterized by a constant parameter of state which dominates in the asymptotic future. We also present an analytic formula (in terms of hypergeometric functions) for the past light cone in such a universe. As applications of this result, we give analytic expressions for the Luminosity Distance and for the Acoustic Scale, where the latter determines the peaks positions in the pattern of CMB anisotropies.

Acoustics of early universe. I. Flat versus open universe models

A simple perturbation description unique for all signs of curvature, and based on the gauge-invariant formalisms is proposed to demonstrate that: (1) The density perturbations propagate in the flat radiation-dominated universe in exactly the same way as electromagnetic or gravitational waves propagate in the epoch of the matter domination. (2) In the open universe, sounds are dispersed by curvature. The space curvature defines the minimal frequency $ω_{\rm c}$ below which the propagation of perturbations is forbidden. Gaussian acoustic fields are considered and the curvature imprint in the per…

1-圈阶宇宙引力波背景产生外尔费米子

Weyl Fermion Creation by Cosmological Gravitational Wave Background at 1-loop

本文研究发现，4维时空中与爱因斯坦引力最小耦合的自旋1/2外尔费米子虽无法在树图级纯引力产生，但在1-圈阶有引力波背景时会因共形不变性破缺而被诱导产生，该机制可解释暗物质丰度且在参数空间中主导树图级过程。

On the Friedmann Equation in Brane-World Scenarios

The Friedmann law on the brane generically depends quadratically on the brane energy density and involves a ``dark radiation'' term due to the bulk Weyl tensor. Despite its unfamiliar form, we show how it can be derived from a standard four-dimensional Brans-Dicke theory at low energy. In particular, the dark radiation term is found to depend linearly on the brane energy densities. For any equation of state on the branes, the radion evolves such as to generate radiation-dominated cosmology. The radiation-dominated era is conventional and consistent with nucleosynthesis.

旋子 cobordism 中的插值拓扑变化及手性 Weyl 曲率诊断

Interpolated Topology Change in a Spin Cobordism and the Chiral Weyl Curvature Diagnostic

该研究提出了一种基于旋 cobordism 的拓扑变化调节框架，并引入手性 Weyl 曲率诊断，通过 braids 描述虫洞喉部动力学。

Third-Order Density Perturbation and One-Loop Power Spectrum in Dark-Energy-Dominated Universe

We investigate the third-order density perturbation and the one-loop correction to the linear power spectrum in the dark-energy cosmological model. Our main interest is to understand the dark-energy effect on baryon acoustic oscillations in a quasi-nonlinear regime ($k \approx 0.1h$/Mpc). Analytical solutions and simple fitting formulae are presented for the dark-energy model with the general time-varying equation of state $w(a)$. It turns out that the power spectrum coincides with the approximate result based on the EdS (Einstein de-Sitter) model within 1% for $k<0.4h/$Mpc at $z=0$ in the WMA…