Hamed Barzegar
It is shown that the generalized Collins--Stewart radiation and Milne solutions are attractors of the massless Einstein--Vlasov system for Bianchi types II and V spacetimes, respectively. The proof is based on an energy method and bootstrap argument which are used to determine the decay rates of the perturbations away from the attractors.
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Future of Bianchi I magnetic cosmologies with kinetic matter
本文在小数据假设下证明，带纯磁场的 Bianchi I Einstein–Vlasov 系统未来会各向同性化并趋于尘埃解，同时给出主要变量衰减率，将既有理想流体结果推广至 Vlasov 情形。
Quiescence for the exceptional Bianchi cosmologies
本文研究例外 Bianchi 宇宙学的静止性，通过引入正交刚性流体，证明类型 VI_{-1/9} 的通用宇宙学与类型 VIII/IX 具有相似渐近行为，仅在极化或正交传递条件下特征值极限可为负。
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…
The solvable Bianchi I-VII groups which arise as homogeneity groups in cosmological models are analyzed in a uniform manner. The dual spaces (the equivalence classes of unitary irreducible representations) of these groups are computed explicitly. It is shown how parameterizations of the dual spaces can be chosen to obtain explicit Plancherel formulas. The Laplace operator $Δ$ arising from an arbitrary left invariant Riemannian metric on the group is considered, and its spectrum and eigenfunctions are given explicitly in terms of that metric. The spectral Fourier transform is given by means of …
Averaging generalized scalar field cosmologies IV: locally rotationally symmetric Bianchi V model
本研究针对广义谐波势的标量场宇宙学，聚焦LRS Bianchi I、III及Bianchi V度规，发现哈勃参数作为时间依赖微扰参数控制误差，使全系统与时间平均系统渐近一致，简化问题。
It is well known that the so called Bianchi IX spacetimes with SO(3)-symmetry in a neighbourhood of the Big Bang exhibit a chaotic behaviour of typical trajectories in the backward movement of time. This behaviour (Mixmaster Model of the Universe) can be encoded by the shift of two-sided continued fractions. Exactly the same shift encodes the sequences of intersections of hyperbolic geodesics with purely imaginary axis in the upper complex half-plane, that is geodesic flow on an appropriate modular surface. A physical interpretation of this coincidence was suggested in arXiv:1402.2158: namely,…
Description of the magnetic Bianchi VI$_0$ cosmologies of LeBlanc, Kerr, and Wainwright in the formalisms both of Belinskii, Khalatnikov, and Lifshitz, and of Misner allows qualitative understanding of the Mixmaster-like singularity in those models.
We consider the asymptotic dynamics of the Einstein-Maxwell field equations for the class of non-tilted Bianchi cosmologies with a barotropic perfect fluid and a pure homogeneous source-free magnetic field, with emphasis on models of Bianchi type VII_{0}, which have not been previously studied. Using the orthonormal frame formalism and Hubble-normalized variables, we show that, as is the case for the previously studied class A magnetic Bianchi models, the magnetic Bianchi VII_{0} cosmologies also exhibit an oscillatory approach to the initial singularity. However, in contrast to the other magn…
Anisotropic Spacetimes in $f(G)$-gravity: Bianchi I, Bianchi III and Kantowski-Sachs Cosmologies
本文研究了$f(G)$引力中Bianchi I、III和Kantowski-Sachs宇宙的各向异性演化，发现存在两个有限吸引子，并揭示了理论中的不稳定解和Big Rip奇点问题。
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…
Bianchi cosmologies in a Thurston-based theory of gravity
本文研究了基于Thurston几何的引力理论中Bianchi-Kantowski-Sachs时空的非倾斜解，证明了在正宇宙学常数下所有拓扑结构均能等向化，且弱能量条件下不可能塌缩，与广义相对论不同。
In this paper we give, for the first time, a qualitative description of the asymptotic dynamics of a class of non-tilted spatially homogeneous (SH) cosmologies, the so-called exceptional Bianchi cosmologies, which are of Bianchi type VI$_{-1/9}$. This class is of interest for two reasons. Firstly, it is generic within the class of non-tilted SH cosmologies, being of the same generality as the models of Bianchi types VIII and IX. Secondly, it is the SH limit of a generic class of spatially inhomogeneous $G_{2}$ cosmologies. Using the orthonormal frame formalism and Hubble-normalized variables, …
An invariant description of Bianchi Homogeneous (B.H.) 3-spaces is presented, by considering the action of the Automorphism Group on the configuration space of the real, symmetric, positive definite, $3\times 3$ matrices. Thus, the gauge degrees of freedom are removed and the remaining (gauge invariant) degrees, are the --up to 3-- curvature invariants. An apparent discrepancy between this Kinematics and the Quantum Hamiltonian Dynamics of the lower Class A Bianchi Types, occurs due to the existence of the Outer Automorphism Subgroup. This discrepancy is satisfactorily removed by exploiting th…
Using the methods developed for different Bianchi class A cosmological models we treat the simplest Bianchi class B model, namely Bianchi type V. The future non-linear stability for solutions of the Einstein-Vlasov system is demonstrated and it is shown that these solutions are asymptotically stable to the Milne solution. Within the isotropic solutions of the Einstein-Vlasov system the spatially flat Friedmann solution is unstable within this class, and expanding models tend also to the Milne solution.
We introduce a new matter action principle, with a wide range of applicability, for the Vlasov equation in terms of a conjugate pair of functions. Here we apply this action principle to the study of matter in Bianchi cosmological models in general relativity. The Bianchi models are spatially-homogeneous solutions to the Einstein field equations, classified by the three-dimensional Lie algebra that describes the symmetry group of the model. The Einstein equations for these models reduce to a set of coupled ordinary differential equations. The class A Bianchi models admit a Hamiltonian formulati…
We apply the scale factor duality transformations introduced in the context of the effective string theory to the anisotropic Bianchi-type models. We find dual models for all the Bianchi-types [except for types $VIII$ and $IX$] and construct for each of them its explicit form starting from the exact original solution of the field equations. It is emphasized that the dual Bianchi class $B$ models require the loss of the initial homogeneity symmetry of the dilatonic scalar field.
Using the methods developed for the Bianchi I case we have shown that a boostrap argument is also suitable to treat the future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI$_0$. These solutions are asymptotic to the Collins-Stewart solution with dust and the Ellis-MacCallum solution respectively. We have thus generalized the results obtained by Rendall and Uggla in the case of locally rotationally symmetric Bianchi II spacetimes to the reflection symmetric case. However we needed to assume small data. For Bianchi VI$_0$ there i…
The asymptotic properties of the Bianchi type II cosmological model in the Brane-world scenario are investigated. The matter content is assumed to be a combination of a perfect fluid and a minimimally coupled scalar field that is restricted to the Brane. The isotropic braneworld solution is determined to represent the initial singularity in all brane-world cosmologies. Additionally, it is shown that it is the kinetic energy of the scalar field which dominates the initial dynamics in these brane-world cosmologies. It is important to note that, the dynamics of these brane-world cosmologies is no…
We investigate a special class of Poisson--Lie T-plurality transformations of Bianchi cosmologies invariant with respect to non-semisimple Bianchi groups. For six-dimensional semi-Abelian Manin triples $\mathfrak{b}\bowtie \mathfrak{a}$ containing Bianchi algebras $\mathfrak{b}$ we identify general forms of Poisson--Lie identities and dualities. We show that these can be decomposed into simple factors, namely automorphisms of Manin triples, B-shifts, $β$-shifts, and "full" or "factorized" dualities. Further, we study effects of these transformations and utilize the decompositions to obtain new…
We consider the case of $R^n$-gravity and perform a detailed analysis of the dynamics in Bianchi I cosmologies which exhibit {\it local rotational symmetry} (LRS). We find exact solutions and study their behaviour and stability in terms of the values of the parameter $n$. In particular, we found a set of cosmic histories in which the universe is initially isotropic, then develops shear anisotropies which approaches a constant value.
Bianchi models are posited by the BKL picture to be essential building blocks towards an understanding of generic cosmological singularities. We study the behaviour of spatially homogeneous anisotropic vacuum spacetimes of Bianchi type VIII and IX, as they approach the big bang singularity. It is known since 2001 that generic Bianchi IX spacetimes converge towards the so-called Mixmaster attractor as time goes towards the singularity. We extend this result to the case of Bianchi VIII vacuum. The BKL picture suggests that particle horizons should form, i.e. spatially separate regions should cau…
In this paper we study the future asymptotics of spatially homogeneous Bianchi type II cosmologies with a tilted perfect fluid with a linear equation of state. By means of Hamiltonian methods we first find a monotone function for a special tilted case, which subsequently allows us to construct a new set of monotone functions for the general tilted type II cosmologies. In the context of a new partially gauge invariant dynamical system, this then leads to a proof for a theorem that for the first time gives a complete description of the future asymptotic states of the general tilted Bianchi type …
The late-time behaviour of the Einstein-dust system is well understood for homogeneous spacetimes. For the case of Bianchi I we have been able to show that the late-time behaviour of the Einstein-Vlasov system is well approximated by the Einstein-dust system assuming that one is close to the unique stationary solution which is the attractor of the Einstein-dust system.
We investigate the dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations with Bianchi type I symmetry by using dynamical systems methods. All models are forever expanding and isotropize toward the future; toward the past there exists a singularity. We identify and describe all possible past asymptotic states; in particular, on the past attractor set we establish the existence of a heteroclinic network, which is a new type of feature in general relativity. This illustrates among other things that Vlasov matter can lead to quite different dynamics of cosmological models as…
We find a supersymmetrization of the Bianchi IX cosmology in terms of Ashtekar's new variables. This provides a framework for connecting the recent results of Graham and those of Ryan and Moncrief for quantum states of this model. These states are also related with the states obtained particularizing supergravity for a minisuperspace. Implications for the general theory are also briefly discussed.
We analyse spatially homogenous cosmological models of locally rotationally symmetric Bianchi type III with a massive scalar field as matter model. Our main result concerns the future asymptotics of these spacetimes and gives the dominant time behaviour of the metric and the scalar field for all solutions for late times. This metric is forever expanding in all directions, however in one spatial direction only at a logarithmic rate, while at a power-law rate in the other two. Although the energy density goes to zero, it is matter dominated in the sense that the metric components differ qualitat…
Exact models for Bianchi VI0 spacetimes with multiple scalar fields with exponential potentials have been derived and analysed. It has been shown that these solutions, when they exist, attract neighbouring solutions in the two cases corresponding to interacting and non-interacting fields. Unlike the results obtained in a previous work dealing with the late-time inflationary behaviour of Bianchi VI0 cosmologies, the knowledge of exact solutions has made possible to study in detail the occurrence of inflation before the asymptotic regime. As happened in preceding works, here as well inflation is…
Recent work on $N=2$ supersymmetric Bianchi type IX cosmologies coupled to a scalar field is extended to a general treatment of homogeneous quantum cosmologies with explicitely solvable momentum constraints, i.e. Bianchi types I, II, VII, VIII besides the Bianchi type IX, and special cases, namely the Friedmann universes, the Kantowski-Sachs space, and Taub-NUT space. Besides the earlier explicit solution of the Wheeler DeWitt equation for Bianchi type IX, describing a virtual wormhole fluctuation, an additional explicit solution is given and identified with the `no-boundary state'.
Solutions to the Einstein equations for Bianchi IX cosmologies are examined through the use of Ellis MacCallum Wainwright (expansion-normalized) variables. Using an iterative map derived from the Einstein equations one can construct an infinite number of periodic solutions. The simplest periodic solutions consist of 3-cycles. It is shown that for 3-cycles the time series of the logarithms of the expansion-normalized spatial curvature components vs normalized time (which is runs backwards towards the initial singularity), generates a set of self-similar golden rectangles. In addition the golden…
We reformulate the dynamics of homogeneous cosmologies with a scalar field matter source with an arbitrary self-interaction potential in the language of jet bundles and extensions of vector fields. In this framework, the Bianchi-scalar field equations become subsets of the second Bianchi jet bundle, $J^2$, and every Bianchi cosmology is naturally extended to live on a variety of $J^2$. We are interested in the existence and behaviour of extensions of arbitrary Bianchi-Lie and variational vector fields acting on the Bianchi variety and accordingly we classify all such vector fields correspondin…
Using the one-parameter internal symmetry group in the Bianchi type-I spacetime for cosmological models with a perfect fluid, we show that a system of coordinates exists in the associated internal space where two scale factors become equal. We find the general solution for an anisotropic model containing a perfect fluid with constant baryotropic index and investigate the asymptotic regimes. We obtain exact solutions for a set of anisotropic fluids which includes an anisotropic stiff fluid.
We derive the late-time behaviour of tilted Bianchi VII_0 cosmologies with an irrotational radiation fluid as source, and give the asymptotic form of the general solution as $t \to +\infty$, making comparisons with the dust-filled models. At first sight the radiation-filled models appear to approximate the flat FL model at late times, since the Hubble-normalized shear and the tilt tend to zero and the density parameter tends to one. The Hubble-normalized Weyl curvature diverges, however, indicating that physically significant anisotropy remains. We also discuss the influence of a cosmological …
It was noted recently that the ADM-diffeomorphism-constraint does not generate all observed symmetries for several Bianchi-models. We will suggest not to use the ADM-constraint restricted to homogeneous variables, but some equivalent which is derived from a restricted action principle. This will generate all homogeneity preserving diffeomorphisms, which will be shown to be automorphism generating vector fields, in class A and class B models. Following Dirac's constraint formalism one will naturally be restricted to the unimodular part of the automorphism group.
The dynamics of solutions of the Einstein-Vlasov system with Bianchi I symmetry is discussed in the case of massive or massless particles. It is shown that in the case of massive particles the solutions are asymptotic to isotropic dust solutions at late times. The initial singularity is more difficult to analyse. It is shown that the asymptotic behaviour there must be one of a small set of possibilities but it is not clear whether all of these possibilities are realized. One solution is exhibited in the case of massless particles which behaves quite differently near the singularity from any Bi…
Introduction to Hamiltonian Formulation of General Relativity and Homogeneous Cosmologies
本文面向高年级本科生和研究生，系统介绍广义相对论的ADM哈密顿形式，并通过对Bianchi分类均匀宇宙在拉格朗日与哈密顿两种形式下的动力学分析及多种场耦合例子，展示两种方法的等价性。
We give the equations governing the shear evolution in Bianchi spacetimes for general f(R)-theories of gravity. We consider the case of R^n-gravity and perform a detailed analysis of the dynamics in Bianchi I cosmologies which exhibit local rotational symmetry. We find exact solutions and study their behaviour and stability in terms of the values of the parameter n. In particular, we found a set of cosmic histories in which the universe is initially isotropic, then develops shear anisotropies which approaches a constant value.
In this paper we give, for the first time, a complete description of the dynamics of tilted spatially homogeneous cosmologies of Bianchi type II. The source is assumed to be a perfect fluid with equation of state $p = (γ-1) μ$, where $γ$ is a constant. We show that unless the perfect fluid is stiff, the tilt destabilizes the Kasner solutions, leading to a Mixmaster-like initial singularity, with the tilt being dynamically significant. At late times the tilt becomes dynamically negligible unless the equation of state parameter satisfies $γ> {10/7}$. We also find that the tilt does not destabili…
The dynamics of cosmological models with isotropic matter sources (perfect fluids) is extensively studied in the literature; in comparison, the dynamics of cosmological models with anisotropic matter sources is not. In this paper we consider spatially homogeneous locally rotationally symmetric solutions of the Einstein equations with a large class of anisotropic matter models including collisionless matter (Vlasov), elastic matter, and magnetic fields. The dynamics of models of Bianchi types I, II, and IX are completely described; the two most striking results are the following: (i) There exis…
In this paper the dynamics of free gauge fields in Bianchi type I-VII$_{h}$ space-times is investigated. The general equations for a matter sector consisting of a $p$-form field strength ($p\,\in\,\{1,3\}$), a cosmological constant ($4$-form) and perfect fluid in Bianchi type I-VII$_{h}$ space-times are computed using the orthonormal frame method. The number of independent components of a $p$-form in all Bianchi types I-IX are derived and, by means of the dynamical systems approach, the behaviour of such fields in Bianchi type I and V are studied. Both a local and a global analysis are perform…
In a recent paper arXiv:1208.4231 we have treated the future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI$_0$. We have been able now to remove the reflection symmetry assumption, thus treating the non-diagonal case. Apart from the increasing complexity the methods have been essentially the same as in the diagonal case, showing that they are thus quite powerful. Here the challenge was to put the equations in a form that permits the use of the previous results. We are able to conclude that after a possible basis change the futur…
A class of exact solutions of the Wheeler-DeWitt equation for diagonal Bianchi type IX cosmologies with cosmological constant is derived in the metric representation. This class consists of all the ``topological solutions'' which are associated with the Bianchi type IX reduction of the Chern-Simons functional in Ashtekar variables. The different solutions within the class arise from the topologically inequivalent choices of the integration contours in the transformation from the Ashtekarrepresentation to the metric representation. We show how the saddle-points of the reduced Chern-Simons funct…
We analyse the Kantowski-Sachs cosmologies with Vlasov matter of massive and massless particles using dynamical systems analysis. We show that generic solutions are past and future asymptotic to the non-flat locally rotationally symmetric Kasner vacuum solution. Furthermore, we establish that solutions with massive Vlasov matter behave like solutions with massless Vlasov matter towards the singularities.
We investigate the set of spacetime general coordinate transformations (G.C.T.) which leave the line element of a generic Bianchi Type Geometry, quasi-form invariant; i.e. preserve manifest spatial Homogeneity. We find that these G.C.T.'s, induce special time-dependent automorphic changes, on the spatial scale factor matrix $γ_{αβ}(t)$ -along with corresponding changes on the lapse function $N(t)$ and the shift vector $N^α(t)$. These changes, which are Bianchi Type dependent, form a group and are, in general, different from those induced by the group SAut(G) -advocated in earlier investigation…
In this paper we give, for the first time, a complete description of the late-time evolution of non-tilted spatially homogeneous cosmologies of Bianchi type VIII. The source is assumed to be a perfect fluid with equation of state $p = (γ- 1)μ$, where $γ$ is a constant which satisfies $1 \leq γ\leq 2$. Using the orthonormal frame formalism and Hubble-normalized variables, we rigorously establish the limiting behaviour of the models at late times, and give asymptotic expansions for the key physical variables. The main result is that asymptotic self-similarity breaking occurs, and is accompanied …
On the future of solutions to the massless Einstein-Vlasov system in a Bianchi I cosmology
本文证明小各向异性Bianchi I时空中无质量Einstein-Vlasov系统的解未来趋向Einstein-de Sitter辐射流体，并给出各向异性量的$O(t^{-1/2})$衰减率。
We shall investigate the asymptotic properties of the Bianchi type IX cosmological model in the Brane-world scenario. The matter content is assumed to be a combination of a perfect fluid and a minimimally coupled scalar field that is restricted to the Brane. A detailed qualitative analysis of the Bianchi type IX braneworld containing a scalar field having an exponential potential is undertaken. It is found that the Brane-Robertson Walker solution is a local source for the expanding Bianchi IX models, and if $k^2<2$ the expanding Bianchi IX models asymptote to the power-law inflationary solutio…
This paper is a study of the effects of anisotropic matter sources on the qualitative evolution of spatially homogenous cosmologies of Bianchi type VIII. The analysis is based on a dynamical system approach and makes use of an anisotropic matter family developed by Calogero and Heinzle which generalises perfect fluids and provides a measure of deviation from isotropy. Thereby the role of perfect fluid solutions is put into a broader context. The results of this paper concern the past and future asymptotic dynamics of locally rotationally symmetric solutions of type VIII with anisotropic matter…
We are investigating the dynamics of a new Poincaré gauge theory of gravity model, which has cross coupling between the spin-0$^+$ and spin-0$^-$ modes. To this end we here consider a very appropriate situation---homogeneous-isotropic cosmologies---which is relatively simple, and yet all the modes have non-trivial dynamics which reveals physically interesting and possibly observable results. More specifically we consider manifestly isotropic Bianchi class A cosmologies; for this case we find an effective Lagrangian and Hamiltonian for the dynamical system. The Lagrange equations for these mode…
Poisson-Lie T-duality and plurality are important solution generating techniques in string theory and (generalized) supergravity. Since duality/plurality does not preserve conformal invariance, the usual beta function equations are replaced by Generalized Supergravity Equations containing vector $\mathcal{J}$. In this paper we apply Poisson-Lie T-plurality on Bianchi cosmologies. We present a formula for the vector $\mathcal{J}$ as well as transformation rule for dilaton, and show that plural backgrounds together with this dilaton and $\mathcal{J}$ satisfy the Generalized Supergravity Equation…
We study the low energy string effective action with an exponential type dilaton potential and vanishing torsion in a Bianchi type I space-time geometry. In the Einstein and string frames the general solution of the gravitational field equations can be expressed in an exact parametric form. Depending on the values of some parameters the obtained cosmological models can be generically divided into three classes, leading to both singular and nonsingular behaviors. The effect of the potential on the time evolution of the mean anisotropy parameter is also considered in detail, and it is shown that…
We analyze the dynamics of a class of cosmological solutions of the Einstein-Vlasov equations. These equations describe an ensemble of collisionless particles (which represent galaxies or clusters of galaxies) that interact gravitatively through Einstein's equations of general relativity. The cosmological models we consider are spatially homogeneous, of Bianchi type IX, and locally rotationally symmetric (LRS). We prove that generic solutions exhibit an oscillatory approach toward the singularities (the "big bang" in the past and the "big crunch" in the future); this is in contrast to the beha…
Methods of dynamical systems analysis are used to show rigorously that the presence of a magnetic field orthogonal to the two commuting Killing vector fields in any spatially homogeneous Bianchi type VI_0 vacuum solution to Einstein's equation changes the evolution toward the singularity from convergent to oscillatory. In particular, it is shown that the alpha-limit set (for time direction that puts the singularity in the past) of any of these magnetic solutions contains at least two sequential Kasner points of the BKL sequence and the orbit of the transition solution between them. One of the …
Many cosmological scenarios envisage either a bounce of the universe at early times, or collapse of matter locally to form a black hole which re-expands into a new expanding universe region. Energy conditions preclude this happening for ordinary matter in general relativistic universes, but scalar or dilatonic fields can violate some of these conditions, and so could possibly provide bounce behaviour. In this paper we show that such bounces cannot occur in Kantowski-Sachs models without violating the {\it reality condition} $\dotϕ^2\geq 0$. This also holds true for other isotropic spatially ho…
The scalar field degree of freedom in Einstein's plus Matter field equations is decoupled for Bianchi type I and V general cosmological models. The source, apart from the minimally coupled scalar field with arbitrary potential V(Phi), is provided by a perfect fluid obeying a general equation of state p =p(rho). The resulting ODE is, by an appropriate choice of final time gauge affiliated to the scalar field, reduced to 1st order, and then the system is completely integrated for arbitrary choices of the potential and the equation of state.
We investigate in detail the qualitative behaviour of the class of Bianchi type B spatially homogeneous cosmological models in which the matter content is composed of two non-interacting components; the first component is described by a barotropic fluid having a gamma-law equation of state, whilst the second is a non-interacting scalar field (phi) with an exponential potential V=Lambda exp(k phi). In particular, we study the asymptotic properties of the models both at early and late times, paying particular attention on whether the models isotropize (and inflate) to the future, and we discuss …
We analyze the phase space of Bianchi I cosmologies filled by a spin fluid in the framework of $f(R)$-gravity with torsion using a combination of the dynamical systems approach and the 1+3 covariant formalism. In the simple case of $f(R)=R^n$ our results allow a quantification of the role of torsion and the spin of the cosmic fluid in the evolution of the cosmology. While torsion is able to modify the cosmological dynamics with respect to the purely metric case, the spin has little influence on the cosmology. We argue that this is due to the different symmetries of the tensor characterizing th…
We derive exact solutions to the vacuum Einstein field equations in 5D, under the assumption that (i) the line element in 5D possesses self-similar symmetry, in the classical understanding of Sedov, Taub and Zeldovich, and that (ii) the metric tensor is diagonal and independent of the coordinates for ordinary 3D space. These assumptions lead to three different types of self-similarity in 5D: homothetic, conformal and "wave-like". In this work we present the most general wave-like solutions to the 5D field equations. Using the standard technique based on Campbell's theorem, they generate a larg…
We perform dynamical analysis of anisotropic Rastall cosmologies and, in particular Kantowski-Sachs, locally rotationally symmetric (LRS) Bianchi I and LRS Bianchi III cosmologies. Using dynamical system techniques, a qualitative analysis of cosmological equations yield physically interesting cases which are in agreement with observations such as de Sitter, accelerating, stable attractors are isotropic. Features such as isotropization and cosmological bounce are discussed in detail.
Constraining inflationary models via de-Sitterization of Bianchi Cosmologies
研究比安基宇宙通过均匀暴胀场实现特定状态，无需宇宙学常数，且此条件可约束暴胀模型并举例说明。
The concept of scale factor duality is considered within the context of the spatially homogeneous, vacuum Brans-Dicke cosmologies. In the Bianchi class A, it is found that duality symmetries exist for the types I, II, VI_0, VII_0, but not for types VIII and IX. The Kantowski-Sachs and locally rotationally symmetric Bianchi type III models also exhibit a scale factor duality, but no such symmetries are found for the Bianchi type V. In this way anisotropy and spatial curvature may have important effects on the nature of such dualities.
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