We analyze the evolution of the mass density contrast in spherical perturbations of flat Friedman-Lemaitre-Robertson-Walker cosmologies. Both dark matter and dark energy are included. In the absence of dark energy the evolution equation coincides with that obtained by Bonnor within the ``Newtonian cosmology''.
Friedmann-Lemaître-Robertson-Walker cosmology is examined from the point of view of gravitoelectromagnetism, in the approximation of spacetime regions small in comparison with the Hubble radius. The usual Lorentz gauge is not appropriate for this situation, while the Painlevé-Gullstrand gauge is rather natural. Several non-trivial features and differences with respect to "standard" asymptotically flat gravitoelectromagnetism are discussed.
A regularization procedure has been recently suggested for regularizing Big Bang singularities in Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetimes. We argue that this procedure is only appliable to one case of Big Bang singularities and does not affect other types of singularities.
Hawking's proposal that the Universe has no temporal boundary and hence no beginning depends on the notion of imaginary time and is usually referred to as the "no-boundary proposal." This paper discusses a simple alternative approach by means of the five-dimensional Friedmann-Lemaitre-Robertson-Walker model.
We investigate toroidal Marginally Outer Trapped Surfaces (MOTS) and Marginally Outer Trapped Tubes (MOTT) in closed Friedmann-Lemaitre-Robertson-Walker (FLRW) geometries. They are constructed by embedding Constant Mean Curvature (CMC) Clifford tori in a FLRW spacetime. This construction is used to assess the quality of certain isoperimetric inequalities, recently proved in axial symmetry. Similarly to spherically symmetric MOTS existing in FLRW spacetimes, the toroidal ones are also unstable.
We completely classify the Friedmann-Lemaître-Robertson-Walker solutions with spatial curvature $K=0,\pm 1$ for perfect fluids with linear equation of state $p=wρ$, where $ρ$ and $p$ are the energy density and pressure, without assuming any energy conditions. We extend our previous work to include all geodesics and parallelly propagated curvature singularities, showing that no non-null geodesic emanates from or terminates at the null portion of conformal infinity and that the initial singularity for $K=0,-1$ and $-5/3<w<-1$ is a null non-scalar polynomial curvature singularity. We thus obtain …
Recent updated results of quasar spectra suggested a 3.9$σ$ significance of spatial variation of the fine-structure constant. Theoretically, it is important to examine whether the fine-structure constant, as a fundamental constant in quantum theory, is possible varying with space and time. In this paper, we explore the possibility that spatial variation of the fine-structure constant could be compatible with Einstein's general relativity. Namely, the spatially dependent fine-structure constant in the Universe could be originated in different values of the speed of light in separate local frame…
Blowing-up solutions of Klein-Gordon equations with gauge variant semilinear terms in Friedmann-Lemaítre-Robertson-Walker spacetimes under finite speed of propagation
The existence of self-similar solutions is discussed in symmetric teleparallel $f(Q)$-theory for a Friedmann-Lemaître-Robertson-Walker background geometry with zero and non-zero spatial curvature. For the four distinct families of connections which describe the specific cosmology in symmetric teleparallel gravity, the functional form of $f(Q)$ is reconstructed. Finally, to see if the analogy with General Relativity holds, we discuss the relation of the self-similar solutions with the asymptotic behaviour of more general $f(Q)$ functions.
We analyze propagation equations for the polar modes of gravitational waves in cosmological space-times. We prove that polar gravitational waves must perturb the density and non-azimuthal components of the velocity of material medium of the Friedman-Lemaitre-Robertson-Walker spacetimes. Axial gravitational waves can influence only the azimuthal velocity, leading to local cosmological rotation. The whole gravitational dynamics reduces to the single "master equation" that has the same form for polar and axial modes. That allows us to conclude that the status of the Huygens principle is the same …
Motivated by the models of geometry with discrete spaces as additional dimensions we investigate the stability of cosmological solutions in models with two metrics of the Friedmann-Lemaître-Robertson-Walker type. We propose an effective gravity action that couples the two metrics in a similar manner as in the bimetric theory of gravity and analyse whether standard solutions with identical metrics are stable under small perturbations.
General K=-1 Friedman-Lemaître models and the averaging problem in cosmology
我们介绍了一般的K=-1弗里德曼-勒梅特（紧凑）宇宙学的概念和平均演化的概念，通过一个平均映射。然后，我们分析了弗里德曼-勒梅特方程和引力能在宇宙演化中的作用。我们区分两种渐近行为：辐射和质量间隙。我们通过精确的定义讨论了它们在宇宙学中的平均问题。然后，我们定量详细地描述了辐射的情况下，强调精确估计的引力能量的演变及其在宇宙的减速的影响。同样在辐射情况下，我们提出了一个平滑性质，它告诉我们平坦K=-1 FL模型的长时间H^{3} x H^{2}稳定性意味着H^{i+1} x H^{i}稳定性与H^{i+1} x H^{i}中的初始状态有多大无关，即存在时空的长时间平滑。最后，我们讨论了大引力能的初始“大爆炸”状态的存在，表明没有数学限制来假设它在时间开始时是低的。
We analyze the leading terms of the spectral action for a model of noncommutative geometry, which is a product of $4$-dimensional Riemannian manifold with a two-point space exploring the previously neglected case when the metrics over each sheet are different. Assuming the Friedmann-Lemaître-Robertson-Walker type of the metric for both sheets we obtain the action, which in addition to the the usual cosmological constant terms and the Einstein-Hilbert term involves a nonlinear interaction term. We study qualitative picture of potential consequences of such term in the basic cosmological models.
Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $γ$ for the Locally Rotationally Symmetric (LRS) Bianchi I and flat Friedmann-Lemaître-Robertson-Walker (FLRW) metrics are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, the simplest time-averaged system determines the future asymptotic behavior. Depending on the values of $γ$, th…
We study past-directed extendibility of Friedmann-Lemaître-Robertson-Walker (FLRW) and Bianchi type I spacetimes with a scale factor vanishing in the past. We give criteria for determining whether a boundary for past-directed incomplete geodesics is a parallelly propagated curvature singularity, which cannot necessarily be read off from scalar curvature invariants. It is clarified that, for incomplete FLRW spacetime to avoid the singularity, the spacetime necessarily reduces to the Milne universe or flat de Sitter universe toward the boundary. For incomplete Bianchi type I spacetime to be free…
We consider the wave equation, $\square_gψ=0$, in fixed flat Friedmann-Lemaître-Robertson-Walker and Kasner spacetimes with topology $\mathbb{R}_+\times\mathbb{T}^3$. We obtain generic blow up results for solutions to the wave equation towards the Big Bang singularity in both backgrounds. In particular, we characterize open sets of initial data prescribed at a spacelike hypersurface close to the singularity, which give rise to solutions that blow up in an open set of the Big Bang hypersurface $\{t=0\}$. The initial data sets are characterized by the condition that the Neumann data should domin…
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。
The cosmological Higgs vacuum stability has been an attractive research subject and it is crucial to accurately follow the development of the Higgs fluctuations. In this work, we thoroughly investigate how the vacuum fluctuations of the Higgs field affect the stability of the electroweak vacuum in Friedmann-Lemaitre-Robertson-Walker (FLRW) background. Adopting adiabatic (WKB) approximation or adiabatic regularization methods, we clearly show that vacuum fluctuations of the Higgs field in the FLRW background depend on the curvature and also masses of the Higgs or other scalar fields. The Higgs …
Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $γ$ for Locally Rotationally Symmetric (LRS) Bianchi III metric and open Friedmann-Lemaître-Robertson-Walker (FLRW) metric are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, simple time-averaged systems determine the future asymptotic behavior. Depending on values of barotropic in…
We study the detector's response when moving along an ingoing null geodesic. The backgrounds are chosen to be black hole spacetimes ($(1+1)$ dimensional Schwarzschild metric and near horizon effective metric for any stationary black hole in arbitrary dimensions) as well as Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe. For black holes the trajectories are defined in Schwarzschild coordinates and the field modes are corresponding to {\it Boulware vacuum}. Whereas for FLRW case, the detector is moving along the path defined in original {\it cosmic time} and the field modes are related to {…
Phase-plane analysis of Friedmann-Robertson-Walker cosmologies in Brans-Dicke gravity
我们提出了一个自治的相平面描述的Friedmann-Robertson-Walker模型包含一个完美的流体（正压指数γ）在Brans-Dicke引力（Brans-Dicke参数ω）的演变。我们发现自相似不动点对应于纳里埃的幂律解决方案的空间平坦的模型和曲率缩放的解决方案弯曲的模型。在无限值的相平面变量，我们恢复O 'Hanlon和Tupper的真空解决方案的空间平坦的模型和米尔恩宇宙的负空间曲率。我们发现这些临界点的存在性和稳定性的条件，并描述在所有区域的（Ω，伽马）参数空间0<伽马-3/2的定性演变<2 and omega>。我们证明了在Brans-Dicke引力中暴胀的条件总是强于广义相对论的条件，γ <2/3。
Scalar field cosmologies with a generalized harmonic potential and matter with energy density $ρ_m$, pressure $p_m$, and barotropic equation of state (EoS) $p_m=(γ-1)ρ_m, \; γ\in[0,2]$ in Kantowski-Sachs (KS) and closed Friedmann--Lemaître--Robertson--Walker (FLRW) metrics are investigated. We use methods from non--linear dynamical systems theory and averaging theory considering a time--dependent perturbation function $D$. We define a regular dynamical system over a compact phase space, obtaining global results. That is, for KS metric the global late--time attractors of full and time--averaged…
We completely classify Friedmann-Lemaître-Robertson-Walker solutions with spatial curvature $K=0,\pm 1$ and equation of state $p=wρ$, according to their conformal structure, singularities and trapping horizons. We do not assume any energy conditions and allow $ρ< 0$, thereby going beyond the usual well-known solutions. For each spatial curvature, there is an initial spacelike big-bang singularity for $w>-1/3$ and $ρ>0$, while no big-bang singularity for $w<-1$ and $ρ>0$. For $K=0$ or $-1$, $-1<w<-1/3$ and $ρ>0$, there is an initial null big-bang singularity. For each spatial curvature, there i…
The pseudo-complex Friedmann Lemaitre Robertson Walker model and the time dependence of the Hubble constant
University of Mentouri, Constantine 1（孔蒂纳一世门图里大学）；Mathematical and Subatomic Physics Laboratory (LPMPS) University of Mentouri, Constantine 1（孔蒂纳一世门图里大学数学与亚原子物理实验室）；Instituto de Ciencias Nucleares, UNAM（墨西哥国立自治大学核科学研究所）；Frankfurt Institute for Advanced Studies, J. W. von Goethe University（法兰克福高等研究院，约翰·沃尔夫冈·冯·歌德大学）；Department of Physics, San Diego State University（圣地亚哥州立大学物理系）；Department of Physics, University of California at SanDiego (UCSD)（加州大学圣地亚哥分校物理系）；International Center for Relativistic AstrophysicsNetwork (ICRANet)（相对论天体物理学国际网络中心）；Instituto de Física, Universidade Federal do Rio Grandedo Sul (UFRGS)（南里奥格兰德联邦大学物理研究所）
The dissipative dynamics of an expanding massless gas with constant cross section in a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe is studied. The mathematical problem of solving the full nonlinear relativistic Boltzmann equation is recast into an infinite set of nonlinear ordinary differential equations for the moments of the one-particle distribution function. Momentum-space resolution is determined by the number of non-hydrodynamic modes included in the moment hierarchy, i.e., by the truncation order. We show that in the FLRW spacetime the non-hydrodynamic modes decou…
