A cosmological time variable is emerged from the Hamiltonian formulation of Friedmann model to measure the evolution of dynamical observables in the theory. A set of observables has been identified for the theory on the null hypersurfaces that its evolution is with respect to the volume clock introduced by the cosmological time variable.
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。
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。
We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lemaître cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we costruct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on a Hilbert space.
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…
In this work a series of methods are developed for understanding the Friedmann equation when it is beyond the reach of the Chebyshev theorem. First it will be demonstrated that every solution of the Friedmann equation admits a representation as a roulette such that information on the latter may be used to obtain that for the former. Next the Friedmann equation is integrated for a quadratic equation of state and for the Randall--Sundrum II universe, leading to a harvest of a rich collection of new interesting phenomena. Finally an analytic method is used to isolate the asymptotic behavior of th…
We present a reconstruction algorithm for cosmological models based on $f(\mathcal{Q})$ gravity. We specifically focus on obtaining exact Bianchi Type-I and Friedmann-Lema\^ıtre-Robertson-Walker solutions, finding solutions that might have application in a variety of scenarios such as spontaneous isotropization of Bianchi Type-I models, dark energy, inflation as well as pre-Big Bang cosmologies.
An effective Lagrangian approach based on an extended Einstein-Aether (EA) model is presented and formulated in a generic non flat Fridman-Lemaitre-Robertson-Walker (FLRW) space-time. For a flat FLRW space-time, a Friedmann equation similar to the one obtained in Quantum Loop Cosmology (QLC) is reproduced, with related non singular bounce solution. Finally, the Static Spherically Symmetric (SSS) solutions are investigated.
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…
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…
In this work we consider perturbations of homogeneous and hypersurface orthogonal cosmological backgrounds with local rotational symmetry (LRS), using a method based on the 1 + 1 + 2 covariant split of spacetime. The backgrounds, of LRS class II, are characterised by that the vorticity, the twist of the 2-sheets, and the magnetic part of the Weyl tensor all vanish. They include the flat Friedmann universe as a special case. The matter contents of the perturbed spacetimes are given by vorticity-free perfect fluids, but otherwise the perturbations are arbitrary and describe gravitational, shear,…
When using Einstein's equations, there exist a number of techniques for embedding non-linear structures in cosmological backgrounds. These include Swiss cheese models, in which spherically symmetric vacua are patched onto Friedmann solutions, and lattice models, in which weak-field regions are joined together directly. In this talk we will consider how these methods work in f(R) theories of gravity. We will show that their existence places constraints on the large-scale expansion of the universe, and that it may not always be possible to consider the Friedmann solutions and weak-field solution…
In a universe where, according to the standard cosmological models, some 97% of the total mass-energy is still "missing in action" it behooves us to spend at least a little effort critically assessing and exploring radical alternatives. Among possible, (dare we say plausible), nonstandard but superficially viable models, those spacetimes conformal to the standard Friedmann-Lemaitre-Robertson-Walker class of cosmological models play a very special role --- these models have the unique and important property of permitting large non-perturbative geometric deviations from Friedmann-Lemaitre-Robert…
The Asymptotically Safe Gravity provides a framework for the description of gravity from the trans-Planckian regime to cosmological scales. According to this scenario, the cosmological constant and Newton's coupling are functions of the energy scale whose evolution is dictated by the renormalization group equations. The formulation of the renormalization group equations on foliated spacetimes, based on the Arnowitt-Deser-Misner (ADM) formalism, furnishes a natural way to construct the RG energy scale from the spectrum of the laplacian operator on the spatial slices. Combining this idea with a …
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 show that bouncing open or flat Friedmann-Robertson-Walker cosmologies are inconsistent with worldsheet string theory to first approximation. Specifically, the Virasoro constraint translates to the null energy condition in spacetime at leading order in the alpha-prime expansion. Thus one must go beyond minimally-coupled Einstein gravity in order to find bounce solutions.
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 v…
We show how the large-scale cosmological dynamics can be obtained from the hydrodynamics of isotropic group field theory condensate states in the Gross-Pitaevskii approximation. The correct Friedmann equations are recovered in the semi-classical limit for some choices of the parameters in the action for the group field theory, and quantum gravity corrections arise in the high-curvature regime causing a bounce which generically resolves the big-bang and big-crunch singularities.
