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We write down the teleparallel equivalent to Hassan-Rosen bigravity, which is written using a torsionful but curvature-free connection. The theories only differ by a boundary term. The equivalence was proven, both by using perturbation theory and Hamiltonian analysis. It is further shown how one can construct novel bigravity theories within the teleparallel framework. Some of those are analyzed through perturbation theory, and it is found that all of the considered novel bigravity theories suffer from pathologies. In particular, it is found that a construction with two copies of new general relativity leads to ghostly degrees of freedom which are not present in the single tetrad teleparallel corresponding theory. We demonstrate how the teleparallel framework allows to easily create theories with derivative interaction. However, it is shown through perturbation theory that the simplest model is not viable. Furthermore, we demonstrate some steps in the Hamiltonian analysis of teleparallel bigravity with two copies of new general relativity and some toy models. The results rule out some of the novel teleparallel bigravity theories, but also demonstrate techniques in perturbation theory and Hamiltonian analysis which could be further used for more profound theories in the future., Comment: 34 pages, 1 figure, comments welcome

In this work we study diffeomorphism-invariant metric-affine theories of gravity from the point of view of self-interacting field theories on top of Minkowski spacetime (or other background). We revise how standard metric theories couple to their own energy-momentum tensor, and discuss the generalization of these ideas when torsion and nonmetricity are also present. We review the computation of the corresponding currents through the Hilbert and canonical (Noether) prescriptions, emphasizing the potential ambiguities arising from both. We also provide the extension of this consistent self-coupling procedure to the vielbein formalism, so that fermions can be included in the matter sector. In addition, we clarify some subtle issues regarding previous discussions on the self-coupling problem for metric theories, both General Relativity and its higher derivative generalizations. We also suggest a connection between Lovelock theorem and the ambiguities in the bootstrapping procedure arising from those in the definition of conserved currents., Comment: 31 pages, no figures, no tables

We derive the most general homogeneous and isotropic teleparallel geometries, defined by a metric and a flat, affine connection. We find that there are five branches of connection solutions, which are connected via several limits, and can further be restricted to the torsion-free and metric-compatible cases. We apply our results to several classes of general teleparallel gravity theories and derive their cosmological dynamics for all five branches. Our results show that for large subclasses of these theories the dynamics reduce to that of closely related metric or symmetric teleparallel gravity theories, while for other subclasses up to two new scalar degrees of freedom participate in the cosmological dynamics., The European Physical Journal C, 83 (4), ISSN:1434-6044, ISSN:1434-6052

Symmetric teleparallel gravity theories, in which the gravitational interaction is attributed to the nonmetricity of a flat, symmetric, but not metric-compatible affine connection, have been a topic of growing interest in recent studies. Numerous works study the cosmology of symmetric teleparallel gravity assuming a flat Friedmann-Lema\^itre-Robertson-Walker metric, while working in the so-called "coincident gauge", further assuming that the connection coefficients vanish. However, little attention has been paid to the fact that both of these assumptions rely on the freedom to choose a particular coordinate system in order to simplify the metric or the connection, and that they may, in general, not be achieved simultaneously. Here we construct the most general symmetric teleparallel geometry obeying the conditions of homogeneity and isotropy, without making any assumptions on the properties of the coordinates, and present our results in both the usual cosmological coordinates and in the coincident gauge. We find that in general these coordinates do not agree, and that assuming both to hold simultaneously allows only for a very restricted class of geometries. For the general case, we derive the energy-momentum-hypermomentum conservation relations and the cosmological dynamics of selected symmetric teleparallel gravity theories. Our results show that the symmetric teleparallel connection in general contributes another scalar quantity into the cosmological dynamics, which decouples only for a specific class of theories from the dynamics of the metric, and only if the most simple geometry is chosen, in which both assumed coordinate systems agree. Most notably, the $f(Q)$ class of theories falls into this class., Comment: 18 pages, no figures

We consider Lorentz invariant scalar-tensor teleparallel gravity theories with a Lagrangian built from the torsion scalar, a scalar field, its kinetic term and a derivative coupling between the torsion and the scalar field. The field equations of the theory are derived and the relation between the spin connection and the antisymmetric part of the tetrad field equations is found explicitly, which is an important consistency result for Lorentz invariant teleparallel theories of gravity. Afterwards we study the behaviour of this class of theories under conformal transformations and find that such transformations map different theories in this class onto each other., 14 pages, no figures

We calculate the parameters $��$ and $��$ in the parametrized post-Newtonian (PPN) formalism for scalar-tensor gravity (STG) with an arbitrary potential, under the assumption that the source matter is given by a non-rotating sphere of constant density, pressure and internal energy. For our calculation we write the STG field equations in a form which is manifestly invariant under conformal transformations of the metric and redefinitions of the scalar field. This easily shows that also the obtained PPN parameters are invariant under such transformations. Our result is consistent with the expectation that STG is a fully conservative theory, i.e., only $��$ and $��$ differ from their general relativity values $��= ��= 1$, which indicates the absence of preferred frame and preferred location effects. We find that the values of the PPN parameters depend on both the radius of the gravitating mass source and the distance between the source and the observer. Most interestingly, we find that also at large distances from the source $��$ does not approach $��= 1$, but receives corrections due to a modified gravitational self-energy of the source. Finally, we compare our result to a number of measurements of $��$ and $��$ in the Solar System. We find that in particular measurements of $��$ improve the previously obtained bounds on the theory parameters, due to the aforementioned long-distance corrections., 35 pages, 5 figures

We consider the parametrized post-Newtonian (PPN) limit of ghost-free massive bimetric gravity with two mutually non-interacting matter sectors coupled to the two metrics. Making use of a gauge-invariant differential decomposition of the metric perturbations, we solve the field equations up to the linear PPN order for a static, point-like mass source. From the result we derive the PPN parameter $��$ for spherically symmetric systems, which describes the gravitational deflection of light by visible matter. By a comparison to its value measured in the solar system we obtain bounds on the parameters of the theory. We further discuss the deflection of light by dark matter and find an agreement with the observed light deflection by galaxies. We finally speculate about a possible explanation for the observed distribution of dark matter in galactic mergers such as Abell 520 and Abell 3827., 36 pages, 1 figure; journal version

We compute the parametrized post-Newtonian parameter $��$ in the case of a static point source for multiscalar-tensor gravity with completely general nonderivative couplings and potential in the Jordan frame. Similarly to the single massive field case $��$ depends exponentially on the distance from the source and is determined by the length of a vector of non-minimal coupling in the space of scalar fields and its orientation relative to the mass eigenvectors. Using data from the Cassini tracking experiment, we estimate bounds on a general theory with two scalar fields. Our formalism can be utilized for a wide range of models, which we illustrate by applying it to nonminimally coupled Higgs SU(2) doublet, general hybrid metric-Palatini gravity, linear ($\Box^{-1}$) and quadratic ($\Box^{-2}$) nonlocal gravity., some clarifications and references added, REVTex version submitted to PRD for publication, 31 pages, 3 figures

From general relativity we have learned the principles of general covariance and local Lorentz invariance, which follow from the fact that we consider observables as tensors on a spacetime manifold whose geometry is modeled by a Lorentzian metric. Approaches to quantum gravity, however, hint towards a breaking of these symmetries and the possible existence of more general, non-tensorial geometric structures. Possible implications of these approaches are non-tensorial transformation laws between different observers and an observer-dependent notion of geometry. In this work we review two different frameworks for observer dependent geometries, which may provide hints towards a quantization of gravity and possible explanations for so far unexplained phenomena: Finsler spacetimes and Cartan geometry on observer space. We discuss their definitions, properties and applications to observers, field theories and gravity., Comment: 43 pages, 2 figures; invited contribution to "Mathematical Structures of the Universe", Copernicus Center Press, Krakow, 2014, ISBN 978-83-7886-107-2; minor corrections to match published version

Recently we discussed a multimetric gravity theory containing several copies of standard model matter each of which couples to its own metric tensor. This construction contained dark matter sectors interacting repulsively with the visible matter sector, and was shown to lead to cosmological late-time acceleration. In order to test the theory with high-precision experiments within the solar system we here construct a simple extension of the parametrized post-Newtonian (PPN) formalism for multimetric gravitational backgrounds. We show that a simplified version of this extended formalism allows the computation of a subset of the PPN parameters from the linearized field equations. Applying the simplified formalism we find that the PPN parameters of our theory do not agree with the observed values, but we are able to improve the theory so that it becomes consistent with experiments of post-Newtonian gravity and still features its promising cosmological properties., Comment: 19 pages, no figures, journal version

We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and the manifold structure of spacetime. In this picture we demonstrate that classical spacetime emerges as a finite-dimensional manifold through the topological identification of all quantum points with identical position expectation value. We speculate on the possible relevance of this geometry to quantum field theory and gravity., Comment: 31 pages

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