We discuss the dynamical system approach applied to Higher Order Theories of Gravity. We show that once the theory of gravity has been specified, the cosmological equations can be written as a first-order autonomous system and we give several examples which illustrate the utility of our method. We also discuss a number of results which have appeared recently in the literature.
We consider the fourth-order differential theory of gravitation to treat the problem of singularity avoidance: studying the short-distance behaviour in the case of black-holes and the big-bang we are going to see a way to attack the issue from a general perspective.
The existence of black holes is a central prediction of general relativity and thus serves as a basic consistency test for modified theories of gravity. In spherical symmetry, only two classes of dynamic solutions are compatible with the formation of an apparent horizon in finite time of a distant observer. Moreover, the formation of black holes follows a unique scenario involving both types of solutions. To be compatible with their existence, any self-consistent theory of modified gravity must satisfy several constraints. We derive properties of the modified gravity terms of f(R) and generic …
Fourth order gravity: equations, history, and applications to cosmology
由拉格朗日量L（R）导出的场方程将在特殊情况下得到求解。如果L是曲率标量的非线性函数，则这些方程在度量中是四阶的。在引言中，我们介绍了这些方程的历史开始的文件H。Weyl于1918年首次将它们作为爱因斯坦理论的替代品进行讨论。在第三部分中，我们详细介绍了宇宙无毛定理，即，在四阶引力L = R + R^2的情况下，宇宙演化的暴胀阶段是如何变成一个瞬态吸引子的细节。最后，将简要介绍比克内尔定理，即从四阶引力到标量张量理论的共形关系。
We study a class of almost scale-invariant modified gravity theories, using a particular form of $f(R, G) = αR^2 + βG \log G$ where $R$ and $G$ are the Ricci and Gauss-Bonnet scalars, respectively and $α$, $β$ are arbitrary constants. We derive the Einstein-like field equations to first order in cosmological perturbation theory in longitudinal gauge.
Einstein field equations are second-order differential equations. In this paper, we propose a new gravity theory with pure fourth-order field equations, which we call 4G for brevity. We discuss the applications of 4G in cosmology, gravitational waves, and local gravitational systems. 4G predicts the scale factor $a\propto t^{4/3}$ for the matter-dominated universe, and $a\propto t$ for the radiation-dominated universe. The former can explain the late-time acceleration without suffering from the coincidence and fine-tuning problems, while the latter can solve the horizon problem. 4G is a massle…
The Big Bang initial singularity problem can be solved by means of bouncing solutions. In the context of extended theories of gravity, we will look for covariant effective actions whose field equations contain up to fourth-order derivatives of the metric tensor. In finding such bouncing solutions, we will make use of an order reduction technique based on a perturbative approach. Reducing the order of the field equations to second-order, we are able to find solutions which are perturbatively close to General Relativity. We will build the covariant effective actions of the resulting order reduce…
We review the history of the ghost problem in quantum field theory from the Pauli-Villars regulator theory to currently popular fourth-order derivative quantum gravity theories. While these theories all appear to have unitarity-violating ghost states with negative norm, we show that in fact these ghost states only appear because the theories are being formulated in the wrong Hilbert space. In these theories the Hamiltonians are not Hermitian but instead possess an antilinear symmetry. Consequently, one cannot use inner products that are built out of states and their Hermitian conjugates. Rathe…
We review the constraints modified theories of gravity must satisfy to be compatible with the spherically symmetric black hole solutions of semiclassical gravity that describe the formation of an apparent horizon in finite time of a distant observer. The constraints are satisfied in generic modified gravity theories with up to fourth-order derivatives in the metric, indicating that the semiclassical solutions correspond to zeroth-order terms in perturbative solutions of these models. From an observational point of view, this result implies that it may not be possible to distinguish between the…
The work is devoted to LRS Bianchi I domain walls cosmological models within the framework of teleparallel gravity using volumetric expansions laws for the depiction model. The physical and kinematical properties are discussed. The statefinder parameters are also analysed along with the jerk parameter and cosmological constraints.
We explore some cosmological features of the newly suggested 4D Gauss-Bonnet gravity through two different models assuming a varying cosmological constant. Observational constraints, such as the cosmic transit and the flat curvature, have been considered in constructing the models. The cosmology in the current work has been probed using a given scale factor derived from the desired cosmic behavior which is the inverse of the usual viewpoint. The stability and cosmography have been studied for the two models.
