In this methodological note we discuss several topics related to interpretation of some basic cosmological principles. We demonstrate that one of the key points is the usage of synchronous reference frames. The Friedmann-Robertson-Walker one is the most known example of them. We describe how different quantities behave in this frame. Special attention is paid to potentially observable parameters. We discuss different variants for choosing measures of velocity and acceleration representing the Hubble flow, and present illustrative calculations of apparent acceleration in flat $ΛCDM$ model for various epochs. We generalize description of the "tethered" galaxies problem for different velocity measures and equations of state, and illustrate time behavior of velocities and redshifts in the $ΛCDM$ model.
We employ recently developed approximation methods in the hybrid quantization of the Gowdy $T^3$ model with linear polarization and a massless scalar field to obtain physically interesting solutions of this inhomogeneous cosmology. More specifically, we propose approximate solutions of the quantum Gowdy model constructed in such a way that, for the Hamiltonian constraint, they effectively behave as those corresponding to a flat homogeneous and isotropic universe filled with a perfect fluid, even though these quantum states are far from being homogeneous and isotropic. We analyze how one can ge…
We construct approximate solutions of the hybrid quantum Gowdy cosmology with three-torus topology, linear polarization, and local rotational symmetry, in the presence of a massless scalar field. More specifically, we determine some families of states for which the complicated inhomogeneous and anisotropic Hamiltonian constraint operator of the Gowdy model is approximated by a much simpler one. Our quantum states follow the dynamics governed by this simpler constraint, while being at the same time also approximate solutions of the full Gowdy model. This is so thanks to the quantum correlations…
It is known that barotropic FRW equations written in the conformal time variable can be reduced to simple linear equations for an exponential function involving the conformal Hubble rate. Here, we show that an interesting class of barotropic universes can be obtained in the linear limit of a special type of nonlinear dissipative Ermakov-Pinney equations with the nonlinear dissipation built from Chiellini's integrability condition. These cosmologies, which evolutionary are similar to the standard ones, correspond to barotropic fluids with adiabatic indices rescaled by a particular factor and ha…
Shifted Riccati Procedure: Application to Conformal Barotropic FRW Cosmologies
在正压FRW宇宙学的情况下，共形时间的哈勃参数是一个简单的常系数Riccati方程的解。我们认为这些宇宙学的框架内的非相对论性超对称性，已在该地区的超对称量子力学的有效。回顾Faraoni [Amer. J. Phys. 67（1999），732-734]提出了如何将正压FRW微分方程组简化为简谐振子微分方程，我们将后者的方程组用超对称方法求解，并将其解分为两类“玻色子”（非奇异）和“费米子”（奇异）宇宙学零模解。费米子方程可以被认为是代表Stephani类型的宇宙学，即，在保形时间内，曲率变化。接下来，我们通过在这些超对称伙伴宇宙学的共同Riccati解中引入一个常数加性参数（用S表示）来应用所谓的移位Riccati过程。这导致正压Stephani宇宙学与周期性奇点在其空间曲率指数，我们称之为U和V宇宙学，第一个是玻色子型和费米子型后者。我们完全解决这些循环奇异宇宙学在其零模式的水平上，表明一个可接受的移位参数应该是纯粹的虚的，这反过来又引入了宇称时间（PT）属性的合作伙伴曲率指数。
It is well known that for spatially flat FRW cosmologies, the holographic dark energy disfavours the Hubble parameter as a candidate for the IR cutoff. For overcoming this problem, we explore the use of this cutoff in holographic ellipsoidal cosmological models, and derive the general ellipsoidal metric induced by a such holographic energy density. Despite the drawbacks that this cutoff presents in homogeneous and isotropic universes, based on this general metric, we developed a suitable ellipsoidal holographic cosmological model, filled with a dark matter and a dark energy components. At late…
We develop approximation methods in the hybrid quantization of the Gowdy model with linear polarization and a massless scalar field, for the case of three-torus spatial topology. The loop quantization of the homogeneous gravitational sector of the Gowdy model (according to the improved dynamics prescription) and the presence of inhomogeneities lead to a very complicated Hamiltonian constraint. Therefore, the extraction of physical results calls for the introduction of well justified approximations. We first show how to approximate the homogeneous part of the Hamiltonian constraint, correspondi…
We consider the field equations for a flat FRW cosmological model, in a generic $f(R)$ gravity model and cast them into a, completely normalized-dimensionless, system of O.D.Es for the scale factor and the function $f(R)$, with respect to the scalar curvature $R$. It is shown that under reasonable assumptions one can produce simple analytical and numerical solutions describing bouncing cosmological models where in addition there are late-time accelerating. Possibility of extending these results is briefly discussed.
Friedmann-Robertson-Walker like cosmologies with spherical symmetry
我们重新考虑了金成元[Phys. Rev D 53，6889（1996）]在具有可穿越虫洞的弗里德曼-罗伯逊-沃克宇宙学的背景下讨论的宇宙学模型，其中假设物质内容分为两部分：仅依赖于时间的宇宙部分和仅依赖于空间的虫洞部分。宇宙部分服从正压状态方程$p_c=γρ_c$。完整的分析需要进一步的关注，并揭示了比作者以前所展示的更有趣的结果。它们可以很容易地应用到一大类宇宙学模型的演化，这是更普遍的比FRW模型。
Localization of gravity in brane world cosmologies
膜世界方案最显著和最有趣的特征是使用体曲率将引力定位在膜上，尽管需要对膜和体参数进行微调。对于膜上的FRW膨胀宇宙，它是Schwarzschild anti de Sitter体时空中的运动超曲面。我们证明了在适当的膜参数和体参数下，零质量引力子在膜上存在束缚态。在不同的情况下会产生不同的宇宙学模型，特别讨论了膜上具有正宇宙学常数的模型。
We obtain a constraint on cosmological scalars for the FRW metric with a pure radiation fluid source and positive cosmological constant. We demonstrate that this constraint is conformally invariant in the context of Penrose's Conformal Cyclic Cosmology proposal, where the metrics of the late stages of the previous aeon and the early stages of the present aeon are described by FRW cosmologies.
In earlier papers we showed that a frame dependent effective action motivated by the postulates of three-space general coordinate invariance and Weyl scaling invariance exactly mimics a cosmological constant in Friedmann-Robertson-Walker (FRW) spacetimes, but alters the linearized equations governing scalar perturbations around a spatially flat FRW background metric. Here we analyze the implications of a frame dependent dark energy for the spacetime cosmological metric within both a perturbative and a non-perturbative framework. Both methods of calculation give a one-parameter family of cosmol…
We study the stability of spatially flat FRW solutions which are geodesically complete, i.e. for which one can follow null (graviton) geodesics both in the past and in the future without ever encountering singularities. This is the case of NEC-violating cosmologies such as smooth bounces or solutions which approach Minkowski in the past. We study the EFT of linear perturbations around a solution of this kind, including the possibility of multiple fields and fluids. One generally faces a gradient instability which can be avoided only if the operator $~^{(3)}{R} δN~$ is present and its coefficie…
The problem of cosmological production of gravitational waves is discussed in the framework of an expanding, spatially homogeneous and isotropic FRW type Universe with time-evolving vacuum energy density. The gravitational wave equation is established and its modified time-dependent part is analytically resolved for different epochs in the case of a flat geometry. Unlike the standard $Λ$CDM cosmology (no interacting vacuum), we show that gravitational waves are produced in the radiation era even in the context of general relativity. We also show that for all values of the free parameter, the h…
本文研究了由两种理想流体$ρ_1$和$ρ_2$组成的Friedmann-Robertson-Walker宇宙模型，正压压力密度为$p_1/ ρ_1=ω_1=const$和$p_2/ ρ_2=ω_2=const$，其中一种能量密度为$ρ_1=C_1 a^α+ C_2 a^β$，$C_1$，$C_2$，$α$和$β$取常值.我们使用守恒方程求解场方程，而不需要借助耦合相互作用项$Q$将其分解为两个相互作用的部分。然而，与所发现的解决方案可能是相关的相互作用项PDMATHAMV，然后在文献中研究的一些宇宙相互作用模型对应于我们的宇宙模型的特定情况。特别是那些具有恒定耦合参数$\tildeα$、$\tildeβ$和由$Q=\tildeα H ρ_{_{DM}}$、$Q=\tildeα H ρ_{_{DE}}$、$Q=\tildeα H (ρ_{_{DM}}+ ρ_{_{DE}})$和$Q=\tildeα H ρ_{_{DM}}+\tildeβ H ρ_{_{DE}}$给出的相互作用项的模型，其中$ρ_{_{DM}}$和$ρ_{_{DE}}$分别是暗物质和暗能量的能量密度。所研究的一组解决方案包含一类宇宙模型，在早期和晚期呈现出标度行为。另一方面，本文考虑的双流体宇宙学模型也允许三流体解释，这也是讨论。在这种重新解释中，对于平坦的Friedmann-Robertson-Walker宇宙学，暗…
The time-evolution dynamics of two nonlinear cosmological real gas models has been reexamined in detail with methods from the theory of Hamiltonian dynamical systems. These examples are FRWL cosmologies, one based on a gas, satisfying the van der Waals equation and another one based on the virial expansion gas equation. The cosmological variables used are the expansion rate, given by the Hubble parameter, and the energy density. The analysis is aided by the existence of global first integral as well as several special (second) integrals in each case. In addition, the global first integral can …
