We investigate the causal hierarchy in various modified theories of gravity. In general relativity the standard causal hierarchy, (key elements of which are chronology, causality, strong causality, stable causality, and global hyperbolicity), is well-established. In modified theories of gravity there is typically considerable extra structure, (such as: multiple metrics, aether fields, modified dispersion relations, Horava-like gravity, parabolic propagation, etcetera), requiring a reassessment and rephrasing of the usual causal hierarchy. We shall show that in this extended framework suitable causal hierarchies can indeed be established, and discuss the implications for the interplay between "superluminal" propagation and causality. The key distinguishing feature is whether the signal velocity is finite or infinite. Preserving even minimal notions of causality in the presence of infinite signal velocity requires the aether field to be both unique and hypersurface orthogonal, leading us to introduce the notion of global parabolicity.
In this work we provide the full description of the upper levels of the classical causal ladder for spacetimes in the context of Lorenztian length spaces, thus establishing the hierarchy between them. We also show that global hyperbolicity, causal simplicity, causal continuity, stable causality and strong causality are preserved under distance homothetic maps.
In this paper, we address the problem of causality violation in the solutions of Einstein equations and seek possible causality restoration mechanisms in modifed theories of gravity. We choose for the above problem, the causality violation due to the existence of closed time-like curves in the context of Kerr-Newman black hole. We first revisit and quantify the details of the causality violation in the Kerr-Newman spacetime. We then show that the issue is also existent in two of the modified solutions to the Kerr Newman spacetime: The Non-Commutativity inspired solution and the f(R)-Gravity mo…
Cone hierarchy and the screening of matter by gravity
SISSA（的里雅斯特国际高等研究学校）；INFN (Sez. Trieste)（意大利国家核物理研究所（的里雅斯特分部））；IFPU（弗里乌利理论物理研究所）；Instituto de Astrofísica de Andalucía (IAA-CSIC)（安达卢西亚天体物理学研究所（西班牙国家科研委员会））；Universidad Complutense de Madrid（马德里康普顿斯大学）
The full causal ladder of spacetimes is constructed, and their updated main properties are developed. Old concepts and alternative definitions of each level of the ladder are revisited, with emphasis in minimum hypotheses. The implications of the recently solved ``folk questions on smoothability'', and alternative proposals (as recent isocausality), are also summarized.
In this paper, we use Statefinder hierarchy method to distinguish between bimetric theory of massive gravity, galileon modified gravity and DGP models applied to late time expansion of the universe. We also carry out comparison between bimetric and DGP models using Statefinder pairs {r, s} and {r, q}. We show that statefinder diagnostic can differentiate between ΛCDM and above mentioned cosmological models of dark energy, and finally show that Statefinder S2 is an excellent discriminant of ΛCDM and modified gravity models.
In this paper, we will examine the problem of violation of causality in $f(R,T)$ modified gravity, where $R$ is the Ricci scalar and $T$ is the trace of the energy-momentum tensor $T_{μν}$. We investigate the causality problem in two special cases, in the first we consider the matter content of the universe as a perfect fluid and in the second case, the matter content is a perfect fluid plus a scalar field.
A unifying framework for the study of causal relations is presented. The causal relations are regarded as subsets of M x M and the role of the corresponding antisymmetry conditions in the construction of the causal ladder is stressed. The causal hierarchy of spacetime is built from chronology up to K-causality and new characterizations of the distinction and strong causality properties are obtained. The closure of the causal future is not transitive, as a consequence its repeated composition leads to an infinite causal subladder between strong causality and K-causality - the A-causality sublad…
In the present paper, we discuss gravitational relaxation models for the electroweak hierarchy problem. We show that modified gravity can naturally relax the electroweak hierarchy problem where conformal transformation provides a crucial rule about what modified gravity theories are favored to relax the electroweak hierarchy. The conformal transformation connects different gravitational theories and rescaling the metric changes the dimensional parameters like the Higgs mass or the cosmological constant in different frames drastically. When the electroweak scale is naturally realized by dynamic…
The $k$-essence modified $f(R)$ gravity model, i.e., $f(R,ϕ,X)$ theory is studied. The question of violation of causality, in the framework of Gödel-type universes, is investigated in this gravitational model. Causal and non-causal solutions are allowed. A critical radius for non-causal solution is calculated. It is shown that the violation of causality depends on the content of matter.
Dark energy cosmology is considered in a modified Gauss-Bonnet (GB) model of gravity where an arbitrary function of the GB invariant, $f(G)$, is added to the General Relativity action. We show that such theory is endowed with a quite rich cosmological structure: it may naturally lead to an effective cosmological constant, quintessence or phantom cosmic acceleration, with a possible transition from deceleration to acceleration. It is demonstrated in the paper that this theory is perfectly viable, since it is compliant with Solar System constraints. Specific properties of $f(G)$ gravity in a de …
In this paper, the hybrid metric-Palatini gravity is an approach to modified gravity in which is added to the usual Einstein-Hilbert action a supplementary term containing a Palatini-type correction of the form $f({\cal R},T)$. Here, ${\cal R}$ is the Palatini curvature scalar, which is constructed from an independent connection and $T$ is the trace of the energy-momentum tensor. This theory describes a non-minimal coupling between matter and geometry. The modified Einstein field equations in this hybrid metric-Palatini approach are obtained. Then, it is investigated whether this modified theo…
We present a general description of the propagation properties of quantum gravity modified electrodynamics characterized by constitutive relations up to second order in the correction parameter. The effective description corresponds to an electrodynamics in a dispersive and absorptive non-local medium, where the Green functions and the refraction indices can be explicitly calculated. The reality of the electromagnetic field together with the requirement of causal propagation in a given referrence frame leads to restrictions in the form of such refraction indices. In particular, absorption must…
Some exact, nonlinear, vacuum gravitational wave solutions are derived for certain polynomial $f(R)$ gravities. We show that the boundaries of the gravitational domain of dependence, associated with events in polynomial $f(R)$ gravity, are not null as they are in general relativity. The implication is that electromagnetic and gravitational causality separate into distinct notions in modified gravity, which may have observable astrophysical consequences. The linear theory predicts that tachyonic instabilities occur, when the quadratic coefficient $a_{2}$ of the Taylor expansion of $f(R)$ is neg…
We verify the consistency of the Gödel-type solutions within the four-dimensional Chern-Simons modified gravity with the non-dynamical Chern-Simons coefficient, for different forms of matter including dust, fluid, scalar field and electromagnetic field, and the related causality issues. Unlike the general relativity, the vacuum solution turns out to be possible in our theory. Another essentially new result of our theory having no analogue in the general relativity consists in the existence of the hyperbolic causal solutions for the physically well-motivated matter.
We modify Randall-Sundrum model of brane-world (with two branes) by adding the scalar curvature squared term in five dimensions. We find that it does not destabilize Randall-Sundrum solution to the hierarchy problem of the Standard Model in particle physics.
We consider a model belonging to the class of gravities with dynamical torsion. The model is free of ghosts and gradient instabilities about Minkowski and torsionless Einstein backgrounds. We find that at zero cosmological constant, the model admits a self-accelerating solution with non-Riemannian connection. Small value of the effective cosmological constant is obtained at the expense of the hierarchy between the dimensionless couplings.
A quantum field theory formalism is reviewed that leads to a self-consistent, finite quantum gravity, Yang-Mills and Higgs theory, which is unitary and gauge invariant to all orders of perturbation theory. The gauge hierarchy problem is solved due to the exponential damping of the Higgs self-energy loop graph for energies greater than a scale $Λ_H\leq 1$ TeV. The cosmological constant problem is solved by introducing a fundamental quantum gravity scale, $Λ_G\leq 10^{-4}$ eV, above which the virtual contributions to the vacuum energy density coupled to gravity are exponentially suppressed, yiel…
