Search

We introduce a new class of two dimensional gravity models using ideas motivated by the Teleparallel Equivalent of General Relativity. This leads to a rather natural formulation of a theory that has close links with Jackiw-Teitelboim gravity. After introducing the theory and discussing its vacuum solutions, we present the Hamiltonian analysis. This implies the presence of a single dynamical degree of freedom, which is in sharp contrast to General Relativity, where there are no degrees of freedom in two spacetime dimensions. Our approach can be extended to various other lower-dimensional gravity theories and thus could be of wider interest., Comment: 22 pages

We study azimuthal geodesics in closed Friedmann-Lem\^aitre-Robertson-Walker (FLRW) cosmological models and give the angular distance travelled by a test particle moving along such a geodesic during one cycle of expansion and re-collapse of the universe. We extend previous results regarding the path followed by light rays to the two-fluid case, also including a cosmological constant, as well as to massive test particles., Comment: 19 pages, 9 figures

Cosmological models can be studied effectively using dynamical systems techniques. Starting from Brown's formulation of the variational principle for relativistic fluids, we introduce new types of couplings involving a perfect fluid, a scalar field, and boundary terms. We describe three different coupling models, one of which turns out to be particularly relevant for cosmology. Its behaviour is similar to that of models in which dark matter decays into dark energy. In particular, for a constant coupling, the model mimics well-known dynamical dark energy models while the non-constant couplings offer a rich dynamical structure, unseen before. We are able to achieve this richness whilst working in a two-dimensional phase space. This is a significant advantage which allows us to provide a clear physical interpretation of the key features and draw analogies with previously studied models., Comment: 27 pages, 10 figures, 5 tables

The trace-free Einstein equations contain one equation less than the complete field equations. In a static and spherically symmetric spacetime, the number of field equations is thus reduced to two. The equation of pressure isotropy of general relativity, however, is preserved thus showing that any known perfect fluid spacetime is a suitable candidate for the trace-free scenario. The extra freedom in imposing two constraints may now be exploited to include polytopes, something that is difficult in general relativity. The point here is that using any known exact solution one can find a polytropic star for various values of the polytropic index. One arrives at Tolman-Oppenheimer-Volkoff type equations and can study their solutions explicitly. Two examples of well-known stellar distributions that generate polytropes with physically reasonable behaviour are discussed. These models are regular, exhibit a sound speed that is never superluminal and are adiabatically stable in the sense of Chandrasekhar. We investigate a compactness measure confirming that our results are consistent with some observational data., Comment: 14 pages, 2 figures

Modern cosmology is closely linked to our understanding of radial null geodesics as these model the propagation of light signals through an expanding universe. Azimuthal geodesics, on the other hand, are perhaps best known for their relevance within closed cosmological models. Such models typically have a finite lifetime: the universe expands up to a maximum size after which it recollapses during the so-called big crunch. An azimuthal geodesic starting at the beginning of the universe will travel a finite angular distance during the expansion and recollapse. It is well-known that this angle is $2\pi$ for a matter-dominated universe and $\pi$ for a radiation-dominated solution. Here we derive the simple formula $$\Delta \varphi = \frac{2\pi}{1+3w}$$ for an arbitrary linear equation of state parameter $w$. To the best of our knowledge this result has not been reported elsewhere and fills a small gap in the literature., Comment: 7 pages

It is well known that the Einstein-Hilbert action in two dimensions is topological and yields an identically vanishing Einstein tensor. Consequently one is faced with difficulties when formulating a non-trivial gravity model. We present a new, intrinsically two-dimensional, approach to this problem based on the Einstein action. This yields a well defined variational approach which results in new field equations that break diffeomorphism invariance. Our proposed approach does not require the introduction of additional scalar fields, nor the use of conformal transformations. However, we can show how including conformal counter terms leads to equivalent results. In doing so, we can provide an explanation for why previous approaches worked. Solutions to the field equations are briefly discussed., Comment: 8 pages. Final version accepted for publication

Modified gravity theories can be used for the description of homogeneous and isotropic cosmological models through the corresponding field equations. These can be cast into systems of autonomous differential equations because of their sole dependence on a well chosen time variable, be it the cosmological time, or an alternative. For that reason a dynamical systems approach offers a reliable route to study those equations. Through a model independent set of variables we are able to study all $f(Q)$ modified gravity models. The drawback of the procedure is a more complicated constraint equation. However, it allows the dynamical system to be formulated in fewer dimensions than using other approaches. We focus on a recent model of interest, the power-exponential model, and generalise the fluid content of the model., Comment: 12 pages, 3 figures. Accepted for publication in Universe special issue Modified Gravity Approaches to the Tensions of $\Lambda$CDM

The starting point of this work is the original Einstein action, sometimes called the Gamma squared action. Continuing from our previous results, we study various modified theories of gravity following the Palatini approach. The metric and the connection will be treated as independent variables leading to generalised theories which may contain torsion or non-metricity or both. Due to our particular approach involving the Einstein action, our setup allows us to formulate a substantial number of new theories not previously studied. Our results can be linked back to well-known models like Einstein-Cartan theory and metric-affine theories and also links to many recently studied modified gravity models. In particular we propose an Einstein-Cartan type modified theory of gravity which contains propagating torsion provided our function depends non-linearly on a boundary term. We also can state precise conditions for the existence of propagating torsion. Our work concludes with a brief discussion of cosmology and the role of cosmological torsion in our model. We find solutions with early-time inflation and late-time matter dominated behaviour. No matter sources are required to drive inflation and it becomes a purely geometrical effect., Comment: Final version published in JMP

The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundamental physics where LISA observations of GWs can be expected to provide key input. We provide the briefest of reviews to then delineate avenues for future research directions and to discuss connections between this working group, other working groups and the consortium work package teams. These connections must be developed for LISA to live up to its science potential in these areas., Comment: Accepted in: Living Reviews in Relativity

The field equations of modified gravity theories, when considering a homogeneous and isotropic cosmological model, always become autonomous differential equations. This relies on the fact that in such models all variables only depend on cosmological time, or another suitably chosen time parameter. Consequently, the field equations can always be cast into the form of a dynamical system, a successful approach to study such models. We propose a perspective that is applicable to many different modified gravity models and relies on the standard cosmological density parameters only, making our choice of variables model independent. The drawback of our approach is a more complicated constraint equation. We demonstrate our procedure studying various modified gravity models and show how much generic information can be extracted before a specific model is considered., Comment: 19 pages, 6 figures; v2 minor changes, updated references

General Relativity and the $\Lambda$CDM framework are currently the standard lore and constitute the concordance paradigm. Nevertheless, long-standing open theoretical issues, as well as possible new observational ones arising from the explosive development of cosmology the last two decades, offer the motivation and lead a large amount of research to be devoted in constructing various extensions and modifications. All extended theories and scenarios are first examined under the light of theoretical consistency, and then are applied to various geometrical backgrounds, such as the cosmological and the spherical symmetric ones. Their predictions at both the background and perturbation levels, and concerning cosmology at early, intermediate and late times, are then confronted with the huge amount of observational data that astrophysics and cosmology are able to offer recently. Theories, scenarios and models that successfully and efficiently pass the above steps are classified as viable and are candidates for the description of Nature. This work is a Review of the recent developments in the fields of gravity and cosmology, presenting the state of the art, high-lighting the open problems, and outlining the directions of future research. Its realization was performed in the framework of the COST European Action ``Cosmology and Astrophysics Network for Theoretical Advances and Training Actions''., Comment: 543 pages

Starting from the original Einstein action, sometimes called the Gamma squared action, we propose a new setup to formulate modified theories of gravity. This can yield a theory with second order field equations similar to those found in other popular modified gravity models. Using a more general setting the theory gives fourth order equations. This model is based on the metric alone and does not require more general geometries. It is possible to show that our new theory and the recently proposed $f(Q)$ gravity models are equivalent at the level of the action and at the level of the field equations, provided that appropriate boundary terms are taken into account. Our theory can also match up with $f(R)$ gravity which is an expected result. Perhaps more surprisingly, we can also show that this equivalence extends to $f(T)$ gravity at the level of the action and its field equations, provided that appropriate boundary terms are taken in account. While these three theories are conceptually different and are based on different geometrical settings, we can establish the necessary conditions under which their field equations are indistinguishable. The final part requires matter to couple minimally to gravity. Through this work we emphasise the importance played by boundary terms which are at the heart of our approach., Comment: 34 pages, 2 figures; v2 minor changes, references added; v3 final changes, published version

The compatibility conditions for generalised continua are studied in the framework of differential geometry, in particular Riemann-Cartan geometry. We show that Vall\'{e}e's compatibility condition in linear elasticity theory is equivalent to the vanishing of the three dimensional Einstein tensor. Moreover, we show that the compatibility condition satisfied by Nye's tensor also arises from the three dimensional Einstein tensor which appears to play a pivotal role in continuum mechanics not mentioned before. We discuss further compatibility conditions which can be obtained using our geometrical approach and apply it to the micro-continuum theories., Comment: 19 pages; v2 extended references and minor corrections

The regular black hole solution arising as a spherically symmetric vacuum solution of Born-Infeld gravity possesses an asymptotic interior structure which is very well described by a four dimensional generalization of the non-rotating BTZ metric. According to this picture no singularity exists, and instead, infalling observers experience a constant curvature manifold as they travel towards future null infinity. This is characterized by the BTZ event horizon. The exterior structure of the black hole is also studied, and it is shown that it corresponds to the Schwarzschild solution provided the black hole mass is not too small. In this way, the regular black hole state can be seen as a spacetime which connects two constant curvature asymptotic spaces, namely, the flat Minkowski spacetime in the outside region, and the locally AdS constant negative curvature one characterizing the BTZ-like asymptotic interior., Comment: 7 Pages. Final version published in CQG

Massless particles in General Relativity move with the speed of light, their trajectories in spacetime are described by null geodesics. This is independent of the electrical charge of the particle being considered, however, the charged light-like case is less well understood. Starting with the Maxwell field of a charged particle having a light-like geodesic world line in Minkowskian space-time we construct the Maxwell field of such a particle having a non-geodesic, light-like world line. The necessary geometry in the neighbourhood of an arbitrary null world line in Minkowskian space-time is described and properties of the resulting electromagnetic field are discussed. The electromagnetic field obtained represents a light-like analogue of the Lienard-Wiechert field, which generalises the Coulomb field of a charge having a time-like geodesic world line to the field of a charge having an accelerated world line., Comment: 11 pages, 1 figure

It is well-known that many three-dimensional chiral material models become non-chiral when reduced to two dimensions. Chiral properties of the two-dimensional model can then be restored by adding appropriate two-dimensional chiral terms. In this paper we show how to construct a three-dimensional chiral energy function which can achieve two-dimensional chirality induced already by a chiral three-dimensional model. The key ingredient to this approach is the consideration of a nonlinear chiral energy containing only rotational parts. After formulating an appropriate energy functional, we study the equations of motion and find explicit soliton solutions displaying two-dimensional chiral properties., Comment: 14 pages, 3 figures; v2 minor corrections

In the context of Born-Infeld gravity theories we report the existence of a regular black hole interior representing a spherically symmetric vacuum solution of the theory. It reduces to the Schwarzschild interior metric in the weak field region. In particular, there is a new length scale which is related to the Born-Infeld parameter. This endows the spacetime with an inner (i.e. well inside the event horizon) asymptotic region which is unattainable for observers. The central curvature singularity is replaced by an infinitely long cosmic string with constant curvature invariants related to the Born-Infeld constant. The presence of this limiting curvature spacetime renders the black hole timelike and null geodesically complete, free from the classical Schwarzschild singularity. The transition between the usual black hole interior and this maximum curvature space is achieved without introducing any kind of matter content nor topological changes., Comment: 6 pages, two figures; v2 minor additions and corrections

A new class of modified theory of gravity is introduced where the volume form becomes dynamical. This approach is motivated by unimodular gravity and can also be related to Brans-Dicke theory. On the level of the action, the only change made will be through the volume element which is used in the integration. This is achieved by the introduction of a fourth order tensor which connects the spacetime metric to the new volume form. Using dynamical systems techniques, this model is studied in the context of cosmology. The most interesting result is that there exist parameter ranges where this model starts undergoing an epoch of accelerated expansion, followed by a decelerating expansion which evolves to a final epoch of accelerated expansion., Comment: 13 pages, 3 figures, 2 tables; v2 two minor changes

We study the fully nonlinear dynamical Cosserat micropolar elasticity problem in space with three dimensionals with various energy functionals dependent on the microrotation $\overline{R}$ and the deformation gradient tensor $F$ . We derive a set of coupled nonlinear equations of motion from first principles by varying the complete energy functional. We obtain a double sine-Gordon equation and construct soliton solutions. We show how the solutions can determine the overall deformational behaviour and discuss the relations between wave numbers and wave velocities thereby identifying parameter values where the waves cannot propagate., Comment: 17 pages, 6 figures

The Nobel Prize winning confirmation in 1998 of the accelerated expansion of our Universe put into sharp focus the need of a consistent theoretical model to explain the origin of this acceleration. As a result over the past two decades there has been a huge theoretical and observational effort into improving our understanding of the Universe. The cosmological equations describing the dynamics of a homogeneous and isotropic Universe are systems of ordinary differential equations, and one of the most elegant ways these can be investigated is by casting them into the form of dynamical systems. This allows the use of powerful analytical and numerical methods to gain a quantitative understanding of the cosmological dynamics derived by the models under study. In this review we apply these techniques to cosmology. We begin with a brief introduction to dynamical systems, fixed points, linear stability theory, Lyapunov stability, centre manifold theory and more advanced topics relating to the global structure of the solutions. Using this machinery we then analyse a large number of cosmological models and show how the stability conditions allow them to be tightly constrained and even ruled out on purely theoretical grounds. We are also able to identify those models which deserve further in depth investigation through comparison with observational data. This review is a comprehensive and detailed study of dynamical systems applications to cosmological models focusing on the late-time behaviour of our Universe, and in particular on its accelerated expansion. In self contained sections we present a large number of models ranging from canonical and non-canonical scalar fields, interacting models and non-scalar field models through to modified gravity scenarios. Selected models are discussed in detail and interpreted in the context of late-time cosmology., Comment: 181 pages, 35 figures, 29 tables. Comments and suggestions for references are welcome, please note Section 1.4 `Note to the arXiv reader'; v2: revised version to take into account feedback by readers, references updated; v3: final version matches published version

The identification of a suitable gravitational energy in theories of gravity has a long history, and it is well known that a unique answer cannot be given. In the first part of this paper we present a streamlined version of the derivation of Freud's superpotential in general relativity. It is found if we once integrate the gravitational field equation by parts. This allows us to extend these results directly to the Einstein-Cartan theory. Interestingly, Freud's original expression, first stated in 1939, remains valid even when considering gravitational theories in Riemann-Cartan or, more generally, in metric-affine spacetimes., Comment: 14 pages in Latex

A new Vaidya-type generalisation of Kerr space-time is constructed by requiring the Kerr mass and angular momentum per unit mass to depend upon a variable which has a simple geometrical origin. The matter distribution introduced in this way radiates mass and angular momentum at future null infinity. The Vaidya generalisation of the Schwarzschild space-time is a special case of the newly found solution., Comment: 9 pages

We derive upper and lower limits for the mass-radius ratio of spin-fluid spheres in Einstein-Cartan theory, with matter satisfying a linear barotropic equation of state, and in the presence of a cosmological constant. Adopting a spherically symmetric interior geometry, we obtain the generalized continuity and Tolman-Oppenheimer-Volkoff equations for a Weyssenhoff spin-fluid in hydrostatic equilibrium, expressed in terms of the effective mass, density and pressure, all of which contain additional contributions from the spin. The generalized Buchdahl inequality, which remains valid at any point in the interior, is obtained, and general theoretical limits for the maximum and minimum mass-radius ratios are derived. As an application of our results we obtain gravitational red shift bounds for compact spin-fluid objects, which may (in principle) be used for observational tests of Einstein-Cartan theory in an astrophysical context. We also briefly consider applications of the torsion-induced minimum mass to the spin-generalized strong gravity model for baryons/mesons, and show that the existence of quantum spin imposes a lower bound for spinning particles, which almost exactly reproduces the electron mass., Comment: 21 pages, 3 figures; references added; minor revisions, accepted for publication in EPJC

New classes of modified teleparallel theories of gravity are introduced. The action of this theory is constructed to be a function of the irreducible parts of torsion $f(T_{\rm ax},T_{\rm ten},T_{\rm vec})$, where $T_{\rm ax},T_{\rm ten}$ and $T_{\rm vec}$ are squares of the axial, tensor and vector components of torsion, respectively. This is the most general (well-motivated) second order teleparallel theory of gravity that can be constructed from the torsion tensor. Different particular second order theories can be recovered from this theory such as new general relativity, conformal teleparallel gravity or $f(T)$ gravity. Additionally, the boundary term $B$ which connects the Ricci scalar with the torsion scalar via $R=-T+B$ can also be incorporated into the action. By performing a conformal transformation, it is shown that the two unique theories which have an Einstein frame are either the teleparallel equivalent of general relativity or $f(-T+B)=f(R)$ gravity, as expected., Comment: v2: 10 pages, accepted for publication in PLB; for a detailed derivation of the field equations see Appendix A in v1

Modelling two-dimensional chiral materials is a challenging problem in continuum mechanics because three-dimensional theories reduced to isotropic two-dimensional problems become non-chiral. Various approaches have been suggested to overcome this problem. We propose a new approach to this problem by formulating an intrinsically two-dimensional model which does not require references to a higher dimensional one. We are able to model planar chiral materials starting from a geometrically non-linear Cosserat type elasticity theory. Our results are in agreement with previously derived equations of motion but can contain additional terms due to our non-linear approach. Plane wave solutions are briefly discussed within this model., Comment: 22 pages, 1 figure; v2 updated version

We investigate modified theories of gravity in the context of teleparallel geometries with possible Gauss-Bonnet contributions. The possible coupling of gravity with the trace of the energy-momentum tensor is also taken into account. This is motivated by the various different theories formulated in the teleparallel approach and the metric approach without discussing the exact relationship between them. Our formulation clarifies the connections between different well known theories. For instance, we are able to formulate the correct teleparallel equivalent of Gauss-Bonnet modified general relativity, amongst other results. Finally, we are able to identify modified gravity models which have not been studied in the past. These appear naturally within our setup and would make a interesting starting point for further studies., Comment: 15 pages, 2 figures, 1 table; slightly revised version

A new Lagrangian framework has recently been proposed to describe interactions between relativistic perfect fluids and scalar fields. In this paper we investigate the Einstein static universe in this new class of theories, which have been named Scalar-Fluid theories. The stability of the static solutions to both homogeneous and inhomogeneous perturbations is analysed deriving the relevant cosmological perturbation equations at the linear order. We can find several configurations corresponding to an Einstein static universes which are stable against inhomogeneous perturbations, but unstable against homogeneous perturbations. This shows the possible applications of Scalar-Fluid theories to the inflationary emergent universe scenario., Comment: 16 pages, 4 figures

We investigate modified theories of gravity in the context of teleparallel geometries. It is well known that modified gravity models based on the torsion scalar are not invariant under local Lorentz transformations while modifications based on the Ricci scalar are. This motivates the study of a model depending on the torsion scalar and the divergence of the torsion vector. We derive the teleparallel equivalent of $f(R)$ gravity as a particular subset of these models and also show that this is the unique theory in this class that is invariant under local Lorentz transformation. Furthermore one can show that $f(T)$ gravity is the unique theory admitting second order field equations., Comment: 9 pages, 1 figure; some typos fixed, slightly improved notation

High-precision observational data have confirmed with startling evidence that the Universe is currently undergoing a phase of accelerated expansion. This phase, one of the most important and challenging current problems in cosmology, represents a new imbalance in the governing gravitational equations. Historically, physics has addressed such imbalances by either identifying sources that were previously unaccounted for, or by altering the gravitational theory. Several candidates, responsible for this expansion, have been proposed in the literature, in particular, dark energy models and modified gravity models, amongst others. Outstanding questions are related to the nature of this so-called "dark energy" that is driving this acceleration, and whether it is due to the vacuum energy or a dynamical field. On the other hand, the late-time cosmic acceleration may be due to modifications of General Relativity. In this work we explore a generalised modified gravity theory, namely $f(R,\phi,X)$ gravity, where $R$ is the Ricci scalar, $\phi$ is a scalar field, and $X$ is a kinetic term. This theory contains a wide range of dark energy and modified gravity models. We considered specific models and applications to the late-time cosmic acceleration., Comment: 13 pages, 1 figure; slightly revised version, displayed name corrected. arXiv admin note: text overlap with arXiv:1412.0867

The Cosserat model generalises an elastic material taking into account the possible microstructure of the elements of the material continuum. In particular, within the Cosserat model the structured material point is rigid and can only experience microrotation, which is also known as micropolar elasticity. We present the geometrically nonlinear theory taking into account all possible interaction terms between the elastic and microelastic structure. This is achieved by considering the irreducible pieces of the deformation gradient and of the dislocation curvature tensor. In addition we also consider the so-called Cosserat coupling term. In this setting we seek soliton type solutions assuming small elastic displacements, however, we allow the material points to experience full rotations which are not assumed to be small. By choosing a particular ansatz we are able to reduce the system of equations to a Sine-Gordon type equation which is known to have soliton solutions., Comment: 12 pages, 1 figure; minor revision, sine-Gordon-d'Alembert system discussed

We consider an original variational approach for building new models of quintessence interacting with dark or baryonic matter. The coupling is introduced at the Lagrangian level using a variational formulation for relativistic fluids, where the interacting term generally depends on both the dynamical degrees of freedom of the theory and their spacetime derivatives. After deriving the field equations from the action, we consider applications in the context of cosmology. Two simple models are studied using dynamical system techniques showing the interesting phenomenology arising in this framework. We find that these models contain dark energy dominated late time attractors with early time matter dominated epochs and also obtain a possible dynamical crossing of the phantom barrier. The formulation and results presented here complete and expand the analysis exposed in the first part of this work, where only algebraic couplings, without spacetime derivatives, were considered., Comment: 18 pages, 6 figures, Part II of arXiv:1501.06540; updated and slightly extended, matches published version

We present a new approach to build models of quintessence interacting with dark or baryonic matter. We use a variational approach for relativistic fluids to realize an effective description of matter fields at the Lagrangian level. The coupling is introduced directly in the action by considering a single function mixing the dynamical degrees of freedom of the theory. The resulting gravitational field equations are derived by variations with respect to the independent variables. New interesting phenomenology can be obtained at both small scales, where new screening mechanisms for scalar fields can be realized, and large scales, where one finds an original and rich class of interacting quintessence models. The background cosmology of two of these models is studied in detail using dynamical system techniques. We find a variety of interesting results: for instance, these models contain dark energy dominated late time attractors and scaling solutions, both with early time matter dominated epochs and a possible inflationary origin. In general this new approach provides the starting point for future in depth studies on new interacting quintessence models., Comment: 29 pages, 12 figures; updated and slightly extended, matches published version

Hartle's slow rotation formalism is developed in the presence of a cosmological constant. We find the generalisation of the Hartle-Thorne vacuum metric, the Hartle-Thorne-(anti)-de Sitter metric, and find that it is always asymptotically (anti)-de Sitter. Next we consider Wahlquist's rotating perfect fluid interior solution in Hartle's formalism and discuss its matching to the Hartle-Thorne-(anti)-de Sitter metric. It is known that the Wahlquist solution cannot be matched to an asymptotically flat region and therefore does not provide a model of an isolated rotating body in this context. However, in the presence of a cosmological term, we find that it can be matched to an asymptotic (anti)-de Sitter space and we are able to interpret the Wahlquist solution as a model of an isolated rotating body, to second order in the angular velocity., Comment: 19 pages, 2 figures

Cosmology is a well established research area in physics while dynamical systems are well established in mathematics. It turns out that dynamical system techniques are very well suited to study many aspects of cosmology. The aim of this book chapter is to provide the reader with a concise introduction to both cosmology and dynamical system. The material is self-contained with references to more detailed work. It is aimed at applied mathematics and theoretical physics graduate level students who have an interest in this exciting topic., Comment: 29 pages, 9 figures, lecture notes; v2 reference added and some typos fixed

Using ideas from continuum mechanics we construct a theory of gravity. We show that this theory is equivalent to Einstein's theory of general relativity; it is also a much faster way of reaching general relativity than the conventional route. Our approach is simple and natural: we form a very general model and then apply two physical assumptions supported by experimental evidence. This easily reduces our construction to a model equivalent to general relativity. Finally, we suggest a simple way of modifying our theory to investigate non-standard space-time symmetries., Comment: 7 pages, this essay received a honorable mention in the 2014 essay competition of the Gravity Research Foundation

We consider a modification of General Relativity motivated by the treatment of anisotropies in Continuum Mechanics. The Newtonian limit of the theory is formulated and applied to galactic rotation curves. By assuming that the additional structure of spacetime behaves like a Newtonian gravitational potential for small deviations from isotropy, we are able to recover the Navarro-Frenk-White profile of dark matter halos by a suitable identification of constants. We consider the Burkert profile in the context of our model and also discuss rotation curves more generally., Comment: 8 pages; v2 11 pages, heavily revised version, new title; v3 13 pages final version

Hybrid metric-Palatini gravity is a recent and novel approach to modified theories of gravity, which consists of adding to the metric Einstein-Hilbert Lagrangian an f(R) term constructed a la Palatini. It was shown that the theory passes local tests even if the scalar field is very light, and thus implies the existence of a long-range scalar field, which is able to modify the dynamics in galactic and cosmological scales, but leaves the Solar System unaffected. In this work, motivated by the possibility that the Universe may have started out in an asymptotically Einstein static state in the inflationary universe context, we analyse the stability of the Einstein static Universe by considering linear homogeneous perturbations in the respective dynamically equivalent scalar-tensor representation of hybrid metric-Palatini gravity. Considering linear homogeneous perturbations, the stability regions of the Einstein static universe are parametrized by the first and second derivatives of the scalar potential, and it is explicitly shown that a large class of stable solutions exists in the respective parameter space, in the context of hybrid metric-Palatini gravity., Comment: 10 pages, 6 figures; v2 added inhomogeneous perturbations

The importance of choosing suitable tetrads for the study of exact solutions in f(T) gravity is discussed. For any given metric, we define the concept of good tetrads as the tetrads satisfying the field equations without constrainig the function f(T). Employing local Lorentz transformations, good tetrads in the context of spherical symmetry are found for Schwarzschild-de Sitter solutions., Comment: Prepared for the proceedings of the 13th Marcel Grossmann Meeting

We introduce a new approach to modified gravity which generalizes the recently proposed hybrid metric-Palatini gravity. The gravitational action is taken to depend on a general function of both the metric and Palatini curvature scalars. The dynamical equivalence with a non-minimally coupled bi-scalar field gravitational theory is proved. The evolution of cosmological solutions is studied using dynamical systems techniques., Comment: 11 pages, 12 figures

We propose a new point of view for interpreting Newton's and Einstein's theories of gravity. By taking inspiration from Continuum Mechanics and its treatment of anisotropies, we formulate new gravitational actions for modified theories of gravity. These models are simple and natural generalisations with many interesting properties. Above all, their precise form can, in principle, be determined experimentally., Comment: 9 pages, conservation equation discussion revised, Kasner type solutions included

We investigate the importance of choosing good tetrads for the study of the field equations of $f(T)$ gravity. It is well known that this theory is not invariant under local Lorentz transformations, and therefore the choice of tetrad plays a crucial role in such models. Different tetrads will lead to different field equations which in turn have different solutions. We suggest to speak of a good tetrad if it imposes no restrictions on the form of $f(T)$. Employing local rotations, we construct good tetrads in the context of homogeneity and isotropy, and spherical symmetry, where we show how to find Schwarzschild-de Sitter solutions in vacuum. Our principal approach should be applicable to other symmetries as well., Comment: 25 pages

We investigate two seemingly disjoint definitions of helicity, one commonly used in particle physics, the other one used when studying bilinear covariants of Clifford algebras. We can prove that the `mathematical' definition of helicity implies its `physical' counterpart. As an unexpected application of our result we show that the Hamiltonian describing the one-layer superconductor Graphene is proportional to the trace of an operator that is used in the `mathematical' definition of helicity., Comment: 13 pages

We consider charged spherically symmetric static solutions of the Einstein-Maxwell equations with a positive cosmological constant $\Lambda$. If $r$ denotes the area radius, $m_g$ and $q$ the gravitational mass and charge of a sphere with area radius $r$ respectively, we find that for any solution which satisfies the condition $p+2p_{\perp}\leq \rho,$ where $p\geq 0$ and $p_{\perp}$ are the radial and tangential pressures respectively, $\rho\geq 0$ is the energy density, and for which $0\leq \frac{q^2}{r^2}+\Lambda r^2\leq 1,$ the inequality $\frac{m_g}{r} \leq 2/9+\frac{q^2}{3r^2}-\frac{\Lambda r^2}{3}+2/9\sqrt{1+\frac{3q^2}{r^2}+3\Lambda r^2}$ holds. We also investigate the issue of sharpness, and we show that the inequality is sharp in a few cases but generally this question is open., Comment: 12 pages. Revised version to appear in Class. Quant. Grav

We analyse dark energy models where self-interacting three-forms or phantom fields drive the accelerated expansion of the Universe. The dynamics of such models is often studied by rewriting the cosmological field equations in the form of a system of autonomous differential equations, or simply a dynamical system. Properties of these systems are usually studied via linear stability theory. In situations where this method fails, for instance due to the presence of zero eigenvalues in the Jacobian, centre manifold theory can be applied. We present a concise introduction and show explicitly how to use this theory in two concrete examples., Comment: 11 pages, 1 figure

In this work, we explore the possibility that static and spherically symmetric traversable wormhole geometries are supported by modified teleparallel gravity or f(T) gravity, where T is the torsion scalar. Considering the field equations with an off-diagonal tetrad, a plethora of asymptotically flat exact solutions are found, that satisfy the weak and the null energy conditions throughout the spacetime. More specifically, considering T=0, we find the general conditions for a wormhole satisfying the energy conditions at the throat and present specific examples. Secondly, considering specific choices for the f(T) form and for the redshift and shape functions, several solutions of wormhole geometries are found that satisfy the energy conditions throughout the spacetime. As in their general relativistic counterparts, these f(T) wormhole geometries present far-reaching physical and cosmological implications, such as being theoretically useful as shortcuts in spacetime and for inducing closed timelike curves, possibly violating causality., Comment: 8 pages, 4 figures. V2: major revision, discussion added; to appear in PRD

We examine the existence of relativistic stars in f(T) modified gravity and explicitly construct several classes of static perfect fluid solutions. We derive the conservation equation from the complete f(T) gravity field equations and present the differences with its teleparallel counterpart. Firstly, we choose the tetrad field in the diagonal gauge and study the resulting field equations. Some exact solutions are explicitly constructed and it is noted that these solutions have to give a constant torsion scalar. Next, we choose a non diagonal tetrad field which results in field equations similar to those of general relativity. For specific models we are able to construct exact solutions of these field equations. Among those new classes of solutions, we find negative pressure solutions, and an interesting class of polynomial solutions., Comment: 19 pages; substantially revised and extended version, off diagonal tetrad discussion added

We formulate elasticity theory with microrotations using the framework of gauge theories, which has been developed and successfully applied in various areas of gravitation and cosmology. Following this approach, we demonstrate the existence of particle-like solutions. Mathematically this is due to the fact that our equations of motion are of Sine-Gordon type and thus have soliton type solutions. Similar to Skyrmions and Kinks in classical field theory, we can show explicitly that these solutions have a topological origin., Comment: 15 pages, 1 figure; revised and extended version, one extra page; revised and extended version