비만아 부모의 돌봄 경험: q 방법론

Over recent decades, the role of torsion in gravity has been extensively investigated along the main direction of bringing gravity closer to its gauge formulation and incorporating spin in a geometric description. Here we review various torsional constructions, from teleparallel, to Einstein-Cartan, and metric-affine gauge theories, resulting in extending torsional gravity in the paradigm of f (T) gravity, where f (T) is an arbitrary function of the torsion scalar. Based on this theory, we further review the corresponding cosmological and astrophysical applications. In particular, we study cosmological solutions arising from f (T) gravity, both at the background and perturbation levels, in different eras along the cosmic expansion. The f (T) gravity construction can provide a theoretical interpretation of the late-time universe acceleration, alternative to a cosmological constant, and it can easily accommodate with the regular thermal expanding history including the radiation and cold dark matter dominated phases. Furthermore, if one traces back to very early times, for a certain class of f (T) models, a sufficiently long period of inflation can be achieved and hence can be investigated by cosmic microwave background observations-or, alternatively, the Big Bang singularity can be avoided at even earlier moments due to the appearance of non-singular bounces. Various observational constraints, especially the bounds coming from the large-scale structure data in the case of f (T) cosmology, as well as the behavior of gravitational waves, are described in detail. Moreover, the spherically symmetric and black hole solutions of the theory are reviewed. Additionally, we discuss various extensions of the f (T) paradigm. Finally, we consider the relation with other modified gravitational theories, such as those based on curvature, like f (R) gravity, trying to illuminate the subject of which formulation, or combination of formulations, might be more suitable for quantization ventures and cosmological applications.

f(T) teleparallel gravity and cosmology

Over the past decades, the role of torsion in gravity has been extensively investigated along the main direction of bringing gravity closer to its gauge formulation and incorporating spin in a geometric description. Here we review various torsional constructions, from teleparallel, to Einstein-Cartan, and metric-affine gauge theories, resulting in extending torsional gravity in the paradigm of f(T) gravity, where f(T) is an arbitrary function of the torsion scalar. Based on this theory, we further review the corresponding cosmological and astrophysical applications. In particular, we study cosmological solutions arising from f(T) gravity, both at the background and perturbation levels, in different eras along the cosmic expansion. The f(T) gravity construction can provide a theoretical interpretation of the late-time universe acceleration, and it can easily accommodate with the regular thermal expanding history including the radiation and cold dark matter dominated phases. Furthermore, if one traces back to very early times, a sufficiently long period of inflation can be achieved and hence can be investigated by cosmic microwave background observations, or alternatively, the Big Bang singularity can be avoided due to the appearance of non-singular bounces. Various observational constraints, especially the bounds coming from the large-scale structure data in the case of f(T) cosmology, as well as the behavior of gravitational waves, are described in detail. Moreover, the spherically symmetric and black hole solutions of the theory are reviewed. Additionally, we discuss various extensions of the f(T) paradigm. Finally, we consider the relation with other modified gravitational theories, such as those based on curvature, like f(R) gravity, trying to enlighten the subject of which formulation might be more suitable for quantization ventures and cosmological applications.

The title immediately brings to mind a standard reference of almost the same title [1]. The authors are quick to point out the relationship between these two works: they are complementary. The purpose of this work is to explain what is known about a selection of exact solutions. As the authors state, it is often much easier to find a new solution of Einstein's equations than it is to understand it. Even at first glance it is very clear that great effort went into the production of this reference. The book is replete with beautifully detailed diagrams that reflect deep geometric intuition. In many parts of the text there are detailed calculations that are not readily available elsewhere. The book begins with a review of basic tools that allows the authors to set the notation. Then follows a discussion of Minkowski space with an emphasis on the conformal structure and applications such as simple cosmic strings. The next two chapters give an in-depth review of de Sitter space and then anti-de Sitter space. Both chapters contain a remarkable collection of useful diagrams. The standard model in cosmology these days is the ICDM model and whereas the chapter on the Friedmann-Lema?tre?Robertson?Walker space-times contains much useful information, I found the discussion of the currently popular a representation rather too brief. After a brief but interesting excursion into electrovacuum, the authors consider the Schwarzschild space-time. This chapter does mention the Swiss cheese model but the discussion is too brief and certainly dated. Space-times related to Schwarzschild are covered in some detail and include not only the addition of charge and the cosmological constant but also the addition of radiation (the Vaidya solution). Just prior to a discussion of the Kerr space-time, static axially symmetric space-times are reviewed. Here one can find a very interesting discussion of the Curzon?Chazy space-time. The chapter on rotating black holes is rather brief and, for example, does not contain reference to the insights found by Pretorius and Israel [2]. This is perhaps justifiable in view of the many specialized texts devoted to the Kerr space-time (e.g. [3]). The large clear diagrams that one becomes accustomed to in this book show off the Taub-NUT (and related) space-times in the next chapter. After perhaps a somewhat standard discussion of stationary axially symmetric space-times, there is a very informative discussion of accelerating black holes. For example, the global structure of the C-metric is considered in detail. This is followed by a brief discussion of solutions for uniformly accelerating particles. The discussion of the Pleba?ski-Demia?ski solutions contains two very useful flow charts that help to systematize two rather complex families of solutions. After a somewhat brief discussion of plane and pp-waves, the authors give an extensive discussion of the Kunt solutions. I note here that after this text was in production the importance of the Kunt space-times as regards the characterization of space-times by scalar curvature invariants was made clear [4]. The discussion of the Robinson-Trautman solutions that follows is extensive, containing, for example, details of the singularity structure and of the global structure. The final formal chapter in this text covers colliding plane waves. This contains, for example, discussions of the Khan?Penrose, Ferrari?Iba?ez and Chandrasekhar?Xanthopoulos solutions. The text ends with a `final miscellany'. This covers a number of interesting topics, but I found the discussion of the Lema?tre?Tolman solutions rather weak (compare e.g. [5]). The book has two quite useful appendices covering 2-spaces and 3-spaces of constant curvature. To conclude, I will quote from the dust jacket: `The book is an invaluable resource for both graduate students and academic researchers working in gravitational physics'. I highly recommend it. References [1] Stephani H, Kramer D, MacCallum M, Hoenselaers C and Herlt E 2003 Exact Solutions of Einstein's Field Equations (Second Edition) (Cambridge: Cambridge University Press) [2] Pretorius F and Israel W 1998 Class. Quantum Grav.15 2289 [3] Wiltshire D, Visser M and Scott S (ed) 2008 The Kerr Spacetime: Rotating Black Holes in General Relativity (Cambridge: Cambridge University Press) [4] Coley A, Hervik S and Pelavas N 2009 Class. Quantum Grav. 26 025013 [5] Pleba?ski J and Krasi?ski A 2006 An Introduction to General Relativity and Cosmology (Cambridge: Cambridge University Press)

Exact Space-Times in Einstein's General Relativity

https://pure.mpg.de/pubman/item/item_2533988_4/component/file_2533987/1712.03107.pdf

Dynamical systems applied to cosmology: dark energy and modified gravity

To find more deliberate f ( R , T ) cosmological solutions, we take our previous paper further by studying some new aspects of the considered models via investigation of some new cosmological parameters/quantities to attain the most acceptable cosmological results. Our investigations are performed by applying the dynamical system approach. We obtain the cosmological parameters/quantities in terms of some defined dimensionless parameters that are used in constructing the dynamical equations of motion. The investigated parameters/quantities are the evolution of the Hubble parameter and its inverse, the “weight function”; the ratio of the matter density to the dark energy density and its time variation; the deceleration; the jerk and the snap parameters; and the equation-of-state parameter of the dark energy. We numerically examine these quantities for two general models R + α R - n + - T and R log [ α R ] q + - T . All considered models have some inconsistent quantities (with respect to the available observational data), except the model with n = - 0.9 , which has more consistent quantities than the other ones. By considering the ratio of the matter density to the dark energy density, we find that the coincidence problem does not refer to a unique cosmological event; rather, this coincidence also occurred in the early Universe. We also present the cosmological solutions for an interesting model R + c 1 - T in the nonflat Friedmann–Lemaitre–Robertson–Walker metric. We show that this model has an attractor solution for the late times, though with w ( DE ) = - 1 / 2 . This model indicates that the spatial curvature density parameter gets negligible values until the present era, in which it acquires the values of the order 10 - 4 or 10 - 3 . As the second part of this work, we consider the weak-field limit of f ( R , T ) gravity models outside a spherical mass immersed in the cosmological fluid. We have found that the corresponding field equations depend on the both background values of the Ricci scalar and the background cosmological fluid density. As a result, we attain the parametrized post-Newtonian parameter for f ( R , T ) gravity and show that this theory can admit the experimentally acceptable values of this parameter. As a sample, we present the post-Newtonian gamma parameter for general minimal power law models, in particular, the model R + c 1 - T .

/pdf/cosmological-and-solar-system-consequences-of-f-r-t-gravity-1z7uuo0awh.pdf

Cosmological and Solar System Consequences of f(R,T) Gravity Models

We investigate the cosmological solutions of $f(R,T)$ modified theories of gravity for a perfect fluid in a spatially Friedmann-Lema\^{\i}tre-Robertson-Walker metric through the phase-space analysis, where $R$ is the Ricci scalar and $T$ denotes the trace of the energy-momentum tensor of the matter content. We explore and analyze the three general theories with the Lagrangians of minimal $g(R)+h(T)$, pure nonminimal $g(R)h(T)$, and nonminimal $g(R)(1+h(T))$ couplings through the dynamical systems approach. We introduce a few variables and dimensionless parameters to simplify the equations to more concise forms. The conservation of the energy-momentum tensor leads to a constraint equation that, in the minimal gravity, confines the functionality of $h(T)$ to a particular form, and hence relates the dynamical variables. In this case, acceptable cosmological solutions that contain a long enough matter-dominated era followed by a late-time accelerated expansion are found. To support the theoretical results, we also obtain numerical solutions for a few functions of $g(R)$, and the results of the corresponding models confirm the predictions. We separate the solutions into six classes which demonstrate more acceptable solutions and there is more freedom to have the matter-dominated era than in $f(R)$ gravity. In particular, there is a new fixed point which can represent the late-time acceleration. We draw different diagrams of the matter densities (consistent with the present values), the related scale factors, and the effective equation of state. The corresponding diagrams of the parameters illustrate that there is a saddle acceleration era which is a middle era before the final stable-acceleration de Sitter era for some models. All presented diagrams determine radiation, matter, and late-time acceleration eras very well. The pure nonminimal theory suffers from the absence of a standard matter era, though we illustrate that the nonminimal theory can have acceptable cosmological solutions.

/pdf/f-r-t-cosmological-models-in-phase-space-2vdraxfzlx.pdf

f ( R , T ) cosmological models in phase space

The Einstein static (ES) universe has played a major role in various emergent scenarios recently proposed in order to cure the problem of the initial singularity of the standard model of cosmology. In the model we address, we study the existence and stability of an ES universe in the context of f(R, T) modified theories of gravity. Considering specific forms of the f(R, T) function, we seek for the existence of solutions representing ES state. Using dynamical system techniques along with numerical analysis, we find two classes of solutions: the first one is always unstable of the saddle type, while the second is always stable so that its dynamical behavior corresponds to a center equilibrium point. The importance of the second class of solutions is due to the significant role they play in constructing non-singular emergent models in which the universe could have experienced past-eternally a series of infinite oscillations about such an initial static state after which it enters, through a suitable physical mechanism, to an inflationary era. Considering specific forms for the functionality of f(R, T), we show that this theory is capable of providing cosmological solutions which admit emergent universe (EU) scenarios. We also investigate homogeneous scalar perturbations for the mentioned models. The stability regions of the solutions are parametrized by a linear equation of state (EoS) parameter and other free parameters that will be introduced for the models. Our results suggest that modifications in f(R, T) gravity would lead to stable solutions which are unstable in f(R) gravity model.

/pdf/stability-of-the-einstein-static-universe-in-f-r-t-gravity-iqch14x2ly.pdf

Stability of the Einstein static universe in f ( R , T ) gravity

In this work we study classical bouncing solutions in the context of $$f(\mathsf{R},\mathsf{T})=\mathsf{R}+h(\mathsf{T})$$
 gravity in a flat FLRW background using a perfect fluid as the only matter content. Our investigation is based on introducing an effective fluid through defining effective energy density and pressure; we call this reformulation as the “effective picture”. These definitions have been already introduced to study the energy conditions in $$f(\mathsf{R},\mathsf{T})$$
 gravity. We examine various models to which different effective equations of state, corresponding to different $$h(\mathsf{T})$$
 functions, can be attributed. It is also discussed that one can link between an assumed $$f(\mathsf{R},\mathsf{T})$$
 model in the effective picture and the theories with generalized equation of state (EoS). We obtain cosmological scenarios exhibiting a nonsingular bounce before and after which the Universe lives within a de-Sitter phase. We then proceed to find general solutions for matter bounce and investigate their properties. We show that the properties of bouncing solution in the effective picture of $$f(\mathsf{R},\mathsf{T})$$
 gravity are as follows: for a specific form of the $$f(\mathsf{R,T})$$
 function, these solutions are without any future singularities. Moreover, stability analysis of the nonsingular solutions through matter density perturbations revealed that except two of the models, the parameters of scalar-type perturbations for the other ones have a slight transient fluctuation around the bounce point and damp to zero or a finite value at late times. Hence these bouncing solutions are stable against scalar-type perturbations. It is possible that all energy conditions be respected by the real perfect fluid, however, the null and the strong energy conditions can be violated by the effective fluid near the bounce event. These solutions always correspond to a maximum in the real matter energy density and a vanishing minimum in the effective density. The effective pressure varies between negative values and may show either a minimum or a maximum.

/pdf/bouncing-cosmological-solutions-from-f-mathsf-r-t-f-r-t-3ph9tg5xz6.pdf

Bouncing cosmological solutions from $$f(\mathsf{R,T})$$ f ( R , T ) gravity

Very recently, Josset and Perez (Phys. Rev. Lett. 118:021102, 2017) have shown that a violation of the energy-momentum tensor (EMT) could result in an accelerated expansion state via the appearance of an effective cosmological constant, in the context of unimodular gravity. Inspired by this outcome, in this paper we investigate cosmological consequences of a violation of the EMT conservation in a particular class of $$f(\mathsf{R},\mathsf{T})$$
 gravity when only the pressure-less fluid is present. In this respect, we focus on the late time solutions of models of the type $$f(\mathsf{R},\mathsf{T})=\mathsf{R}+\beta \Lambda (-\mathsf{T})$$
 . As the first task, we study the solutions when the conservation of EMT is respected, and then we proceed with those in which violation occurs. We have found, provided that the EMT conservation is violated, that there generally exist two accelerated expansion solutions of which the stability properties depend on the underlying model. More exactly, we obtain a dark energy solution for which the effective equation of state depends on the model parameters and a de Sitter solution. We present a method to parametrize the $$\Lambda (-\mathsf{T})$$
 function, which is useful in a dynamical system approach and has been employed in the model. Also, we discuss the cosmological solutions for models with $$\Lambda (-\mathsf{T})=8\pi G(-\mathsf{T})^{\alpha }$$
 in the presence of ultra-relativistic matter.

/pdf/consequences-of-energy-conservation-violation-late-time-gofh21g13a.pdf

Consequences of energy conservation violation: late time solutions of $\Lambda (\mathsf{T}) \mathsf{CDM}$ subclass of $f(\mathsf{R},\mathsf{T})$ gravity using dynamical system approach

Hamid Shabani

Papers

Cosmological and Solar System Consequences of f(R,T) Gravity Models

f ( R , T ) cosmological models in phase space

Stability of the Einstein static universe in f ( R , T ) gravity

Bouncing cosmological solutions from $$f(\mathsf{R,T})$$ f ( R , T ) gravity

Consequences of energy conservation violation: late time solutions of $\Lambda (\mathsf{T}) \mathsf{CDM}$ subclass of $f(\mathsf{R},\mathsf{T})$ gravity using dynamical system approach