We solve Einstein's equation with Robertson-Walker metric as an initial-value problem, using as the source of gravity a Halpern-Huang real scalar field, which was derived from renormalization-group analysis, with a potential that exhibits asymptotic freedom and spontaneous symmetry breaking. Both properties are crucial to the formulation of the problem. Numerical solutions show that the universe expands at an accelerated rate, with the radius increasing like the exponential of a power of the time. This is relevant to "dark energy" and "cosmic inflation". Extension to the complex scalar field will make the universe a superfluid. The vortex dynamics that emerges offers explanations for other cosmological problems, namely, matter creation, galactic voids, and the "dark mass".
Using the semi-classical approximation to the Wheeler-DeWitt equation obtained via Arnowitt-Deser-Misner (ADM) formalism in the Friedmann-Lemaitre-Robertson-Walker (FLRW) model coupled to a scalar field and positive cosmological constant, and in the Kantowski-Sachs (KS) Universe, we introduced a deformation on the commutation relation for the minisuperspace variables and find an explicit semiclassical expression equivalent, in an adequate limit, to the solution with the aid of asymptotically equal functions and the theory of Ultrafilters, offering a suggestive alternative to sketch the behavio…
Critical phenomenon inside asymptotically flat black holes with spontaneous scalarization
Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院，中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；International Centre for Theoretical Physics Asia-Pacific, University of Chinese Academy of Sciences（亚洲太平洋理论物理中心，中国科学院大学）
Simple interpolation formulas are proposed for the description of the renormalization group (RG) scale dependences of the gravitational couplings in the framework of the 2-parameters Einstein-Hilbert (EH) theory of gravity and applied to a simple, analytically solvable, spatially homogeneous and isotropic, spatially flat model universe. The analytical solution is found in two schemes incorporating different methods of the determination of the conversion rule $k(t)$ of the RG scale $k$ to the cosmological time $t$. In the case of the discussed model these schemes turn out to yield identical cos…
Interest in cosmological singularities has remarkably grown in recent times, particularly on future singularities with the discovery of late-time acceleration of the universe and dark energy. While such explorations have previously been done in various modified gravity and quantum gravitationally inspired cosmologies (besides standard general relativistic cosmology), no such an endeavour has been taken up till now in the realms of renormalization group approaches to cosmology and we have hence took up on this journey. In this work, we consider the formation of cosmological singularities in an …
A recently proposed Asymptotically Safe cosmology provides an elegant mechanism towards understanding the nature of dark energy and its associated cosmic coincidence problem. The underlying idea is that the accelerated expansion of the universe can occur due to infrared quantum gravity modifications at intermediate astrophysical scales (galaxies or galaxy clusters) which produce local anti-gravity sources. In this cosmological model no extra unproven energy scales or fine-tuning are used. In this study the Asymptotically Safe model is confronted with the most recent observational data from low…
We study FLRW cosmology, taking into account quantum gravitational corrections in the formalism of the exact renormalization group flow of the effective action for gravity. We calculate the quantum corrected scale factor, energy density, and entropy production at late times, taking different cut-off functions. Our approach differs from previous ones in the way energy-momentum conservation is imposed -- we include the running Newton constant $G(k)$ in the definition of energy-momentum tensor, keeping in mind the covariant conservation identity of the Einstein tensor. The quantum corrections obt…
The Standard Model Extension (SME) is a generic parametrization for Lorentz violation and the phenomenological consequences of the minimal gravity sector of the SME are usually studied using a post-Newtonian expansion that requires spacetime to be asymptotically flat. However, there is a term in this sector for which these approximations are unable to make predictions; this is known as the $t$ puzzle. The present paper studies a model of spontaneous Lorentz violation in the minimal gravity sector of the SME in a static and spherically symmetric situation, when no additional matter fields are p…
Institut für Theoretische Physik, Universität Heidelberg（海德堡大学理论物理研究所）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所跨学科理论与数学科学中心（iTHEMS））；ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung mbH（重离子研究亥姆霍兹中心极端物质研究所EMMI）；Department of Physics and Astronomy, University of Sussex（萨塞克斯大学物理与天文学系）
We discuss the Damour--Esposito-Farèse model of gravity, which predicts the spontaneous scalarization of neutron stars in a certain range of parameter space. In the cosmological setup, the scalar field responsible for scalarization is subject to a tachyonic instability during inflation and the matter domination stage, resulting in a large value of the field today. This value feeds into the PPN parameters, which turn out to be in gross conflict with the Solar system measurements. We modify the original Damour--Esposito-Farèse model by coupling the scalar to the inflaton field. This coupling act…
Bianchi-I Cosmology with Radiation in Asymptotically Safe Gravity
National Central University（中央大学）；Center for High Energy and High Field Physics (CHiP), National Central University（国立中央大学高能高场物理中心）；Kobayashi-Maskawa Institute, Nagoya University（名古屋大学小林-益川研究所）；Department of Physics, Rikkyo University（立教大学物理学系）；Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University（大阪公立大学南部阳一郎理论实验物理研究所）；Department of Physics and Astronomy, Kwansei Gakuin University（关西学院大学物理学与天文学系）
A scalar field non-minimally coupled to certain geometric [or matter] invariants which are sourced by [electro]vacuum black holes (BHs) may spontaneously grow around the latter, due to a tachyonic instability. This process is expected to lead to a new, dynamically preferred, equilibrium state: a scalarised BH. The most studied geometric [matter] source term for such spontaneous BH scalarisation is the Gauss-Bonnet quadratic curvature [Maxwell invariant]. This phenomenon has been mostly analysed for asymptotically flat spacetimes. Here we consider the impact of a positive cosmological constant,…
In a model of spontaneous scalarization of neutron stars proposed by Damour and Esposite-Farese, a general relativistic branch becomes unstable to trigger tachyonic growth of a scalar field $ϕ$ toward a scalarized branch. Applying this scenario to cosmology, there is fatal tachyonic instability of $ϕ$ during inflation and matter dominance being incompatible with solar-system constraints on today's field value $ϕ_0$. In the presence of a four-point coupling $g^2 ϕ^2 χ^2/2$ between $ϕ$ and an inflaton field $χ$, it was argued by Anson et al. that a positive mass squared heavier than the square o…
We present a short review of possible applications of the Wheeler-De Witt equation to cosmological models based on the low-energy string effective action, and characterised by an initial regime of asymptotically flat, low energy, weak coupling evolution. Considering in particular a class of duality-related (but classically disconnected) background solutions, we shall discuss the possibility of quantum transitions between the phases of pre-big bang and post-big bang evolution. We will show that it is possible, in such a context, to represent the birth of our Universe as a quantum process of tun…
We consider the problem of matching two spacetimes, the previous and present aeons, in the Conformal Cyclic Cosmology model. The common boundary between them inherits two sets of constraints -- one for each solution of the Einstein field equations extended to the conformal boundaries. The previous aeon is assumed to be an asymptotically de Sitter spacetime, so the standard conformal formulation of the Einstein field equations suffice to derive the constraints on the future null infinity. For the future aeon, which is supposed to evolve from an initial singularity, they are obtained with the us…
We review the construction of holography for cosmologies with an emphasis on asymptotically de Sitter cosmologies. We do this by composition of the AdS/CFT correspondence and domain-wall/cosmology (DW/C) correspondence with the novel added benefit of keeping track of the DW/C marker $η$. This allows us to build explicitly the holographic dual of the DW/C correspondence. We then test this framework on a toy model: the GPPZ flow. We find the scalar one-point function for this flow to be invariant under the domain-wall/cosmology correspondence. Moreover, our construction seems to agree with previ…
Comparative Quantum Cosmology: Causality, Singularity, and Boundary Conditions
在这篇评论文章中，我们比较了彼得·林德最近的工作，“关于一个没有开始或结束的有限宇宙”，与斯蒂芬·霍金的工作，主要是“量子宇宙学，M理论和人择原理”，以及肖恩·M的两项基础性工作。Carroll和Jennifer Chen，“Does Inflation Provide Natural Conditions for the Universe”和“Spontaneous Inflation and the Origin of the Arrow of Time”，以评估他们对早期宇宙形成中的因果关系、时间顺序、热力学可逆性、奇点和边界条件的性质和作用的比较处理。我们简要地参考了斯莫林和考夫曼最近的论点，关于早期宇宙形成中可能的“进化选择”过程，作为对霍金早期“M理论”及其伴随的人存原理的关键要素的另一种解释。我们还简要摘录了一小部分斯莫林最近的工作拓扑量子圈引力，只是作为一个说明性的例子类型的复杂的量子拓扑变换，他提供了一个理论替代弦论在量子宇宙学。
The phenomenon of spontaneous scalarization of charged black holes has attracted a lot of attention. In this work, we study the dynamical process of the spontaneous scalarization of charged black hole in asymptotically anti-de Sitter spacetimes in Einstein-Maxwell-scalar models. Including various non-minimal couplings between the scalar field and Maxwell field, we observe that an initial scalar-free configuration suffers tachyonic instability and both the scalar field and the black hole irreducible mass grow exponentially at early times and saturate exponentially at late times. For fractional …
