M. A. H. MacCallum
(There is no original abstract.) These are lecture notes from a 1971 summer school surveying the then known cosmological models in particular the properties of Bianchi cosmologies, and giving a pedagogical introduction to groups of isometries in spacetime and to the orthonormal tetrad method.
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Regarding axion electrodynamics in the background flat FRW universe, we show that cosmological birefringence arises from an adiabatic noncyclic geometric phase that appears in the quantum state of photons because of their interaction with the axion field. We also show that the axion electrodynamics is equivalent to standard electrodynamics in time-dependent bi-isotropic magnetoelectric Tellegen media, which serves as an analogue system that can simulate cosmological birefringence.
We investigate entanglement production by inhomogeneous perturbations over a homogeneous and isotropic cosmic background, demonstrating that the interplay between quantum and geometric effects can have relevant consequences on entanglement entropy, with respect to homogeneous scenarios. To do so, we focus on a conformally coupled scalar field and discuss how geometric production of scalar particles leads to entanglement. Perturbatively, at first order we find oscillations in entropy correction, whereas at second order the underlying geometry induces mode-mixing on entanglement production. We t…
Cosmologically Viable Solutions in Geometric Modified Gravity
本文研究基于挠率或非度量性的远平行引力扩展模型，发现部分模型虽能复现宇宙晚期加速，但常因爱丁顿参数偏差违反太阳系约束，强调需在宇宙学与局域尺度统一检验修正引力理论。
A two-component formulation of the Klein-Gordon equation is used to investigate the cyclic and noncyclic adiabatic geometric phases due to spatially homogeneous (Bianchi) cosmological models. It is shown that no adiabatic geometric phases arise for Bianchi type I models. For general Bianchi type IX models the problem of the adiabatic geometric phase is shown to be equivalent to the one for nuclear quadrupole interactions of a spin. For these models nontrivial non-Abelian adiabatic geometrical phases may occur in general.
We present a new approach to cosmological perturbations based on the theory of Lie groups and their representations. After re-deriving the standard covariant formalism from SO(3) considerations, we provide a new expansion of the perturbed Friedmann-Lemaitre-Robertson-Walker (FLRW) metric in terms of irreducible representations of the Lorentz group. The resulting decomposition splits into (scalar, scalar), (scalar, vector) and (vector, vector) terms. These equations directly correspond to the standard Lifshitz classification of cosmological perturbations using scalar, vector and tensor modes wh…
We present a cosmological model arising from a gravitational theory with an infinite tower of higher-order curvature invariants that can reproduce the entire evolution of the Universe: from inflation to late-time acceleration, without invoking an inflaton nor a cosmological constant. The theory is Einsteinian-like. The field equations for a Friedmann-Lemaître-Robertson-Walker metric are of second-order and can reproduce a late-time evolution that is consistent with the acceleration provided by the cosmological constant at low redshift. Our results force us to reinterpret the nature of dark ene…
This is a written version of the review talk given at the meeting on "Interface of Gravitational and Quantum Realms" at IUCAA, Pune during December 2001. The talk reviewed the recent work of Martin Bojowald on Loop Quantum Cosmology.
We detail a novel theoretical prediction that a geometric torsion model for scalar field dark matter could lead to oscillations, on readily probeable timescales, in the time evolution of cosmological redshifts of astronomical sources with qualitatively distinct behavior at different redshift scales (larger or smaller than z ~ 0.1). We present an analysis of extant spectroscopy data from the Australian Dark Energy Survey (OzDES) to assess whether such signals are present across a wide array of cosmological sources and baseline redshifts on the six-year timescale of OzDES. While a simple Fourier…
A gravity theory without masses can be constructed in Minkowski spaces using a geometric Minkowski potential. The related affine spacelike spheres can be seen as the regions of the Minkowski spacelike vectors characterized by a constant Minkowski gravitational potential. These spheres point out, for each dimension $n \geq 3$, spacetime models, the de Sitter ones, which satisfy Einstein's field equations in absence of matter. In other words, it is possible to generate geometrically the cosmological constant. Even if a lot of possible parameterizations have been proposed, each one highlighting s…
In this paper we study how to include the cosmological constant in geometric scalar theory of gravity (GSG). Firstly we show that the cosmological constant could not be modeled by a matter field, unlike in General Relativity. We also show that a spherically symmetric matter distribution, over the de Sitter vacuum, does not produce the Kottler solution and no black hole. To circumvent this problem we introduce an coupling term between the scalar field and the vacuum curvature in way to provide the Kottler solution. We also apply the original (GSGI) and the modified (GSGII) geometric scalar theo…
The averaging of the dynamic functions of the standard cosmological model (SCM) at its early stage with the dominance of the scalar field is carried out. It is shown that microscopic oscillations with Compton period provide the major contribution to the macroscopic energy density of the scalar field at large times at this stage. In this case, the effective equation of state of the scalar field oscillates between the inflationary and the extremely rigid ones, while the macroscopic equation of state is non-relativistic.
The note presents a classification of the relevant distinct types of solutions of the general Friedmann equation without assuming a priori restrictions for the parameters occurring in this equation. The emphasis is on the case of a non-vanishing cosmological constant. The classification uses algebraic criteria. The result is: There are four distinct basic types of models. Explicit formulas for decisive terms are given. Characteristic mutual relations of cosmological constant, mass and radiation density to distinguish between the models are calculated.
The thermodynamics of the Kerr-AdS black hole is reformulated within the context of the formalism of geometrothermodynamics (GTD) and the cosmological constant is considered as a new thermodynamical parameter. We conclude that the mass of the black hole corresponds to the total enthalpy of this system. Choosing appropriately the metric in the equilibrium states manifold, we study the phase transitions as a divergence of the thermodynamical curvature scalar. This approach reproduces the Hawking-Page transition and shows that considering the cosmological constant as a thermodynamical parameter d…
A broader perspective is suggested for the study of higher dimensional cosmological models. [1986: Considerations involving the Einstein constraints and the Ricci form of the evolution equations for spatially homogeneous spacetimes in 4 or more dimensions in the Taub time gauge (constant densitized lapse) are used to show how many of the special exact solutions found at random fit together into a larger picture in which the Taub spacetime solution plays an instructive role. Concludes with some remarks on chaos.]
Loop Quantum Gravity is a background independent, nonperturbative approach to the quantization of General Relativity. Its application to models of interest in cosmology and astrophysics, known as Loop Quantum Cosmology, has led to new and exciting views of the gravitational phenomena that took place in the early universe, or that occur in spacetime regions where Einstein's theory predicts singularities. We provide a brief introduction to the bases of Loop Quantum Cosmology and summarize the most important results obtained in homogeneous scenarios. These results include a mechanism to avoid the…
Orbits of Massive Particles in a Spherically Symmetric Gravitational Field in View of Cosmological Constant
本文在考虑宇宙学常数Λ的Köttler度规中，通过将代数曲线展开为Puiseux级数得到轨迹方程解，分类正负Λ下massive粒子轨迹并提供特定类型轨迹，还基于星系旋转曲线估算了负Λ的上限
The cosmological perturbation theory is revisited from the holographic point of view. In the case of the single brane model, it turns out that the AdS/CFT correspondence plays an important role. In the case of the two-brane model, it is shown that the effective equations of motion becomes the quasi-scalar-tensor gravity. It is also demonstrated that the radion anisotropy gives the CMB fluctuations through the Sachs-Wolfe effect.
We construct a compact phase space for flat FLRW spacetimes with standard matter described by a perfect fluid with a barotropic equation of state for general f(R) theories of gravity, subject to certain conditions on the function f. We then use this framework to study the behaviour of the phase space of Universes with a non-negative Ricci scalar in R + αR^n gravity. We find a number of interesting cosmological evolutions which include the possibility of an initial unstable power-law inflationary point, followed by a curvature fluid dominated phase mimicking standard radiation, then passing thr…
The gravitation theory is modified on the base of geometric identity and equivalence principle. This makes it possible to generalize the geodesics and solve several problems of classical GRT such as flat rotation curves of the spiral galaxies, Tully-Fisher law and some others and reveal the fundamental (geometrical) origin of the cH acceleration value. The developed approach contains all the results of the classical GRT and has promising cosmological consequences.
In this paper, using the concept of Lewis Riesenfeld invariant quantum operator method for finding continuous eigenvalues of quantum mechanical wave functions we derive the analytical expressions for the cosmological geometric phase, which is commonly identified to be the Pancharatnam Berry phase from primordial cosmological perturbation scenario. We compute this cosmological geometric phase from two possible physical situations,(1) In the absence of Bell's inequality violation and (2) In the presence of Bell's inequality violation having the contributions in the sub Hubble region ($-kτ\gg 1$)…
The Baryon Acoustic Oscillations feature (BAO) imprinted in the clustering correlation function is known to furnish us cosmic distance determinations that are independent of the cosmological-background model and the primordial perturbation parameters. These measurements can be accomplished rigorously by means of the Purely Geometric BAO methods. To date two different Purely Geometric BAO approaches have been proposed. The first exploits the linear-point standard ruler. The second, called correlation-function model-fitting, exploits the sound-horizon standard ruler. A key difference between the…
F(R,..) theories from the point of view of the Hamiltonian approach: non-vacuum Anisotropic Bianchi type I cosmological model
本文通过各向异性比内型宇宙模型研究F(R)理论的经典方案，采用等压流体方程状态$P=γρ$，在N=1和N=6ABCD=6η^3D两种坐标系下求解经典解，并给出真空解以完善研究。
The thermodynamics of the Schwarzschild-AdS black hole is reformulated within the context of the recently developed formalism of geometrothermodynamics (GTD). Different choices of the metric in the equilibrium states manifold are used in order to reproduce the Hawking-Page phase transition as a divergence of the thermodynamical curvature scalar. We show that the enthalpy and total energy representations of GTD does not reproduce the transition while the entropy rep- resentation gives the expected behavior.
Geometric Matching of Local Static Regions in Cosmological Spacetimes with an Evolving Lapse
通过Israel连接条件将静态Schwarzschild内部嵌入演化GCT-FLRW外部，推导出几何一致性条件，证明局部静态区域可与演化时移宇宙学背景兼容。
The LCDM cosmological model assumes the existence of a small cosmological constant in order to explain the observed accelerating cosmic expansion. Despite the dramatic improvement of the quality of cosmological data during the last decade it remains the simplest model that fits remarkably well (almost) all cosmological observations. In this talk I review the increasingly successful fits provided by LCDM on recent geometric probe data of the cosmic expansion. I also briefly discuss some emerging shortcomings of the model in attempting to fit specific classes of data (eg cosmic velocity dipole f…
Geometrical Reconstruction of Spinfoam Critical Points with A Cosmological Constant
本文通过建立SL(2,C)平坦联络模空间与常曲率4-单形几何的对应，利用Fock-Goncharov坐标和旋量重构了具有非零宇宙学常数的4维洛伦兹自旋泡沫振幅临界点，为量子引力修正计算及量子宇宙学和黑洞物理应用奠定算法基础。
The $α$-attractor inflationary models are nowadays favored by CMB Planck observations. Their similarity with canonical quintessence models motivates the exploration of a common framework that explains both inflation and dark energy. We study the expected constraints that next-generation cosmological experiments will be able to impose for the dark energy $α$-attractor model. We systematically account for the constraining power of SNIa from WFIRST, BAO from DESI and WFIRST, galaxy clustering and shear from LSST and Stage-4 CMB experiments. We assume a tensor-to-scalar ratio, $10^{-3} < r < 10^{-…
Recent cosmological and astrophysical observations point out that the Universe is in accelerating expansion and filled up with non-luminous matter. In order to explain the observed large scale structures and this accelerating behavior one needs a huge amounts of Dark Energy and Dark Matter. Although many attempts have been done, both at theoretical and experimental level, up to now there are several models proposed to explain such mysterious components. However, no final conclusion on the nature of dark components has been reached up to now so the question is completely open. In this paper, we…
Cosmological implications of the Weyl geometric gravity theory
本文研究了Weyl几何引力理论的宇宙学意义，通过引入辅助标量场和共形不变物质作用量导出场方程，并推导出推广的Friedmann宇宙演化方程，详细比较了真空和物质模型的预测与观测数据及标准ΛCDM模型，发现Weyl几何效应会使宇宙呈现各向异性特征。
Some theoretic results related to the cosmological constant, obtained in the 80's and 90's of last century, are reviewed. These results exhibit some interesting underlying pattern when viewed from a category-theoretic perspective. In doing this, we illustrate how Baez and Dolan's Periodic Table of $k$-tuply monoidal $n$-categories can serve as a basic framework of a quantum spacetime structure. Explicitly, we show how Einstein gravity (with the cosmological constant turned on) emerges when we de-categorify certain $2$-tuply monoidal $2$-categories properly, as Crane proposed a long time ago. I…
Exact formula for geometric quantum complexity of cosmological perturbations
本文通过生成元的有限维矩阵表示，推导出宇宙扰动几何量子复杂度的精确公式，并应用于de Sitter时空及渐近静态宇宙模型。
Solution to the Cosmological Constant Problem from Pre-geometric Gravity
预几何引力通过拓扑高斯-博内耦合与de Sitter熵的比例关系，动态解释了宇宙学常数的小性，统一了引力、拓扑和量子信息。
Minisuperspace Cosmology in Extended Geometric Trinity of Gravity
本文通过minisuperspace方法研究扩展几何三位一体引力的经典和量子宇宙学层面，利用Noether对称性选择可行模型，比较了广义相对论、Teleparallel等理论的等价性。
In this paper, we investigate the possibility that a geometric model of dark energy that assume \textquotedblleft lower dimensions\textquotedblright, could generates a repulsive pressure which cause the current accelerated expansion of the Universe. We show how this geometrical model resemble as quintessence, cosmological constant and phantom energy during the cosmological evolution of the Universe choosing the corresponding matter scale factor as well as the possible consequences of this model in the Universe fate. Finally we perform the dynamical evolution of the model with the other Univers…
This article proposes some cosmological reflections at the qualitative and conjectural level, suggested by the Fantappie & Arcidiacono projective relativity theory. The difference will firstly be discussed between two types of singularity in this theory: geometric (de Sitter horizon) and physical (big bang, big crunch). The reasons for the existence of geometric singularities are deeply rooted in the principle of inertia and in the principle of relativity, while physical singularities are associated with the creation or destruction of matter. In this framework, quantum mechanics is introduced …
The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit representation of information content, and also the value itself is a geometric signature of area. It is proposed that the fractal distribution of galaxies may thus be interpreted as a signature of holography (``fractal holography''), providing more support for current theories of holographic cosmologies. Implications for entropy bounds are addressed. In parti…
We consider the cosmological horizons in the expanding universe from the point of view of observer moving with respect to CMB frame. The deformation (non-sphericity) of cosmological horizons is demonstrated. Some principle consequences are discussed.
Cosmological boundary conditions for particles and fields are often discussed as a Cauchy problem, in which configurations and conjugate momenta are specified on an "initial" time slice. But this is not the only way to specify boundary conditions, and indeed in action-principle formulations we often specify configurations at two times and consider trajectories joining them. Here, we consider a classical system of particles interacting with short range two body interactions, with boundary conditions on the particles' positions for an initial and a final time. For a large number of particles tha…
Geometric measure of quantum complexity in cosmological systems
基于Nielsen量子复杂性几何方法，通过Lie群结构常数展开取领头阶，推导了时变频率谐振子Hamiltonian复杂性上限公式，发现在de Sitter背景无质量标量场中复杂性随尺度因子在超Hubble尺度对数增长。
Effective supergravity inflationary models induced by anti-D3 brane interaction with the moduli fields in the bulk geometry have a geometric description. The Kähler function carries the complete geometric information on the theory. The non-vanishing bisectional curvature plays an important role in the construction. The new geometric formalism, with the nilpotent superfield representing the anti-D3 brane, allows a powerful generalization of the existing inflationary models based on supergravity. They can easily incorporate arbitrary values of the Hubble parameter, cosmological constant and grav…
Basic geometric and kinematic features of the Standard Cosmological Model
本文研究了标准宇宙模型（ΛCDM）的几何和运动学特性，推导了描述当前观测数据的模型方程，并探讨了宇宙早期和晚期的简化公式、关键演化时刻及距离与红移的关系。
We propose an accurate method for counting states of close to zero and positive cosmological constant in the Bousso-Polchinski Landscape. This method is based on simple geometrical considerations on the high-dimensional lattice of quantized fluxes and on a probabilistic model (the "random hyperplane" model) that provides a distribution of the values of the cosmological constant. Justification of the assumptions made in this model are given by means of numerical experiments.
Geometric origin of the cosmological constant from Einstein-Chern-Simons gravity compactified to four dimensions
该研究通过五维爱因斯坦-切连-西蒙斯引力压缩到四维，将宇宙学常数作为几何效应产生，无需引入自由参数，且保持与广义相对论的结构相似性，推导出克托勒黑洞解。
Robertson-Walker spacetimes within a large class are geometrically extended to larger cosmologies that include spacetime points with zero and negative cosmological times. In the extended cosmologies, the big bang is lightlike, and though singular, it inherits some geometric structure from the original spacetime. Spacelike geodesics are continuous across the cosmological time zero submanifold which is parameterized by the radius of Fermi space slices, i.e, by the proper distances along spacelike geodesics from a comoving observer to the big bang. The continuous extension of the metric, and the …
It is shown that the Born--Infeld nonlinear electrodynamics with a polynomial type nonlinearity accommodates finite-energy electric point charges but rejects finite-energy magnetic point charges, or monopoles, thereby spelling out an electromagnetic asymmetry. Moreover, it is demonstrated, in a systematic way, that the curvature singularities of finite-energy charged black holes in the context of the Born--Infeld theory may effectively be relegated or in some cases removed under a critical mass-energy condition, which has been employed successfully in earlier concrete studies. Furthermore, it …
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,…
Natural observables and dynamical approximations in multifield cosmological models
本文针对任意目标空间拓扑的多场宇宙学模型，几何构造一阶自然动力学可观测量，并讨论相关动力学近似及适用机制。
The \SN (SN) equation is recast on purely geometrical grounds, namely in terms of Bargmann structures over $(\d+1)$-dimensional Newton-Cartan (NC) spacetimes. Its maximal group of invariance, which we call the SN group, is determined as the group of conformal Bargmann automorphisms that preserve the coupled Schrödinger and NC gravitational field equations. Canonical unitary representations of the SN group are worked out, helping us recover, in particular, a very specific occurrence of dilations with dynamical exponent $z=(\d+2)/3$.
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