This work was mainly driven by the desire to explore, to what extent embedding some given geometry in a higher dimensional flat one is useful for understanding the causal structure of classical fields traveling in the former, in terms of that in the latter. We point out, in the 4D spatially flat FLRW universe, that the causal structure of transverse-traceless (TT) gravitational waves can be elucidated by first reducing the problem to a 2D Minkowski wave equation with a time dependent potential, where the relevant Green's function is pure tail -- waves produced by a physical source propagate strictly within the null cone. By viewing this 2D world as embedded in a 4D one, the 2D Green's function can also be seen to be sourced by a cylindrically symmetric scalar field in 3D. From both the 2D wave equation as well as the 3D scalar perspective, we recover the exact solution of the 4D graviton tail, for the case where the scale factor written in conformal time is a power law. There are no TT gravitational wave tails when the universe is radiation dominated because the background Ricci scalar is zero. In a matter dominated one, we estimate the amplitude of the tail to be suppressed relative to its null counterpart by both the ratio of the duration of the source to the age of the universe $η_0$, and the ratio of the observer-source spatial distance (at the observer's time) to the same $η_0$. In a universe driven primarily by a cosmological constant, the tail contribution to the background FLRW geometry after the source has ceased, is the conformal factor $a^2$ times a spacetime-constant symmetric matrix proportional to the spacetime volume integral of the TT part of the source's stress-energy-momentum tensor. In other words, massless spin-2 gravitational waves exhibit a tail-induced memory effect in 4D de Sitter spacetime.
We show, through an explicit calculation of the relevant Green's functions, that the transverse-traceless (TT) portion of the gravitational perturbations of Minkowski spacetime and of spatially flat cosmologies with a constant equation-of-state $w$ receive contributions from their isolated matter source(s) outside the past null cone of the observer. This implies the TT gravitational wave (GW) cannot be a standalone observable -- despite widespread (apparent) claims in the gravitational wave literature to the contrary. About a Minkowski background, all 4 of the gauge-invariant variables -- the …
Thermal channels of scalar and tensor waves in Jordan-frame scalar--tensor gravity
Faculdade de Ciências da Universidade de Lisboa（里斯本大学理学院）；Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências da Universidade de Lisboa（里斯本大学理学院空间天体物理研究所）
利用类爱因斯坦有效流体分解，研究 Jordan 框架标量-张量引力在空间平坦 FLRW 背景上的一阶标量和张量扰动，推导出有效密度、压力、热流和各向异性应力，并证明它们在标量梯度框架中满足精确的 Eckart 型本构关系，进而揭示引力波阻尼的 Jordan 框架修正与标量扇区的横向无迹各向异性应力相关。
It has been argued that there are no islands in FLRW cosmologies with $Λ>0$ and $k=0$ arXiv:2008.01022. We argue that there is a timelike separated island at the initial singularity, and it will resolve the cosmological information paradox. The information about the particles that went beyond the horizon is not lost for our observer. By measuring Hawking radiation, we can get that information from the past when those particles were near the initial singularity. Similar to how islands inside black holes violate locality, we observe a violation of causality or noncausality but only at the initia…
We use phase space method to study possible consequences of fixed points in flat FLRW models. One of these consequences is that a fluid with a finite sound speed, or a differentiable pressure, reaches a fixed point in an infinite time and has no finite-time singularities of types I, II and III described in hep-th/0501025. It is impossible for such a fluid to cross the phantom divide in a finite time. We show that a divergent $dp/dH$, or a speed of sound is necessary but not sufficient condition for phantom crossing. We use pressure properties, such as asymptotic behavior and fixed points, to q…
I present a {\em general relativistic} model with a compactified second time coordinate that {\em a priori} allows for causal, yet faster than light travel in the background of a FLRW geometry, by local modification of a higher dimensional background geometry, specifically with respect to the radius of the compactified time coordinate. The modification can be induced via the fields of the model. I show that one cannot convert (as possible in special relativistic models, or simple general relativistic models) the super-luminality into closed time-like loops violating causality, due to a novel c…
In this work we take moves from the debate triggered by Melia et al [9]. and followed by opposite comments by Lewis and Oirschot [10,11]. The point in question regards the role of the Hubble horizon as a limit for observability in a cosmological setting. We propose to take the issue in a broader way by relating it to the causal character of the Hubble surface and to the tracing of null trajectories, focusing on both three-fluids and generalized Chaplygin gas models. The results should make clear that light rays reaching a comoving observer at R(t_0)=0 have never travelled a distance greater th…
We explicitly prove the horizon-entropy increase law for both causal and quasi-locally defined horizons in scalar-tensor and $f(R)$ gravity theories. Contrary to causal event horizons, future outer trapping horizons are not conformally invariant and we provide a modification of trapping horizons to complete the proof, using the idea of generalised entropy. This modification means they are no longer foliated by marginally outer trapped surfaces but fixes the location of the horizon under a conformal transformation. We also discuss the behaviour of horizons in "veiled" general relativity and sho…
We simulate the evolution of a dust universe from $z=1089$ to $z=0$ by numerically integrating the Einstein's equation for a spatially flat Friedmann-Lemaire-Robertson-Walker (FLRW) background spacetime with scalar perturbations which are derived from the matter power spectrum produced with the Code for Anisotropies in the Microwave Background (CAMB). To investigate the effects of primordial gravitational waves (GWs) on the inhomogeneity of the universe, we add an additional decaying, divergenceless and traceless primordial tensor perturbation with its initial amplitude being $3\times 10^{-4}$…
In this paper we consider conformally flat perturbations on the Friedmann Lemaitre Robertson Walker (FLRW) spacetime containing a general matter field. Working with the linearised field equations, we unearth some important geometrical properties of matter shear and vorticity and how they interact with the thermodynamical quantities in the absence of any free gravity powered by the Weyl curvature. As there are hardly any physically realistic rotating exact conformally flat solutions in general relativity, these covariant and gauge invariant results bring out transparently the role of vorticity …
McVittie spacetimes embed the vacuum Schwarzschild(-(anti) de Sitter) spacetime in an isotropic FLRW background universe. We study the global structure of McVittie spacetimes with spatially non-flat FLRW backgrounds. This requires the extension of the definition of such spacetimes, previously given only for the flat and open cases, to the closed case. We revisit this definition and show how it gives rise to a unique spacetime (given the FLRW background, the mass parameter $M$ and the cosmological constant $Λ$) in the open and flat cases. In the closed case, an additional free function of the c…
We derive criteria for whether two cosmological events can have a shared causal past or a shared causal future, assuming a Friedmann-Lemaitre-Robertson-Walker universe with best-fit ΛCDM cosmological parameters from the Planck satellite. We further derive criteria for whether either cosmic event could have been in past causal contact with our own worldline since the time of the hot "big bang", which we take to be the end of early-universe inflation. We find that pairs of objects such as quasars on opposite sides of the sky with redshifts z >= 3.65 have no shared causal past with each other or …
Gravitational waves in a minimal gravitational SME
Universidade Federal da Paraíba（帕拉伊巴联邦大学）；Universidade Federal de Campina Grande（坎皮纳格兰德联邦大学）；Khazar University（哈扎尔大学）；Damghan University（达姆甘大学）；Federal University of Paraíba（帕拉伊巴联邦大学）
We extend recent theoretical results on the propagation of linear gravitational waves (GWs), including their associated memories, in spatially flat Friedmann--Lemaître--Robertson--Walker (FLRW) universes, for all spacetime dimensions higher than 3. By specializing to a cosmology driven by a perfect fluid with a constant equation-of-state $w$ -- conformal re-scaling, dimension-reduction and Nariai's ansatz may then be exploited to obtain analytic expressions for the graviton and photon Green's functions, allowing their causal structure to be elucidated. When $0 < w \leq 1$, the gauge-invariant …
Gravitational Wave Propagation in K-essence Cosmology: Theory and Observational Constraints
University of Calcutta（加尔各答大学）；Ben-Gurion University of the Negev（内盖夫本-古里安大学）；Frankfurt Institute for Advanced Studies (FIAS)（法兰克福高等研究所）；Bahamas Advanced Study Institute and Conferences（巴哈马高级研究院与会议）；Sister Nivedita University（尼维蒂达修女大学）；Pontificia Universidad Católica de Valparaíso（瓦爾帕萊索天主教大學）；Prabhat Kumar College（普拉巴特庫瑪學院）；Institute of Astronomy, Space and Earth Science（天文、太空與地球科學研究所）
Acoustic gravitational waves from primordial curvature perturbations
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study (HIAS), University of Chinese Academy of Sciences (UCAS)（杭州高等研究院基础物理与数学学院，中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences (CAS)（中国科学院理论物理研究所）；University of Chinese Academy of Sciences (UCAS)（中国科学院大学）；Asia Pacific Center for Theoretical Physics (APCTP)（亚太理论物理中心）；School of Physical Sciences, University of Chinese Academy of Sciences (UCAS)（中国科学院大学物理科学学院）；Institute of Fundamental Physics and Quantum Technology & School of Physical Science and Technology, Ningbo University（宁波大学基础物理与量子技术研究所及物理科学与技术学院）
