We study the cosmological dynamics of a class of symmetric teleparallel gravity theories known as “newer general relativity” using the methods of dynamical systems, restricted to the case of vacuum solutions with a spatially flat Friedmann–Lemaître–Robertson–Walker metric. For the most general class of theories, we study generic properties of the solutions, in particular their fixed points, asymptotic behavior and effective dark energy. We then apply this approach to two phenomenologically motivated subclasses of theories, which we study in full detail. For these theories, we derive the complete space of solutions and cosmological attractors, which we display in a number of phase diagram. Depending on the particular theory at hand, we find different possible scenarios, including a turnaround followed by a big crunch, a big rip and an eternally expanding universe whose Hubble parameter asymptotically approaches zero. It turns that this different behavior can be explained by the effective dark energy barotropic index, which shows either phantom or non-phantom behavior, depending on the theory, but does not change dynamically between these two possibilities.

Estonia

Kazakhstan

Manuel Hohmann

Ulbossyn Ualikhanova

Dynamical systems approach and cosmological attractors in newer general relativity

We study tensor perturbations around the most general cosmologically symmetric backgrounds in a class of teleparallel gravity theories known as New General Relativity. These theories comprise a one-parameter class, which is fully consistent with observations at the post-Newtonian level, and which contains the teleparallel equivalent of General Relativity as a special case. We find that for a particular class of cosmological background geometries these theories exhibit gravitational wave birefringence and dispersion, i.e., the dispersion relation for gravitational waves depends on their polarization and wave number. The strength of this effect is directly related to the spatial curvature of the cosmological background and the parameter describing the deviation of the theory from General Relativity. We discuss the possibility of observing this effect in gravitational wave experiments.

Germany

Christian Pfeifer

Gravitational wave birefringence in spatially curved teleparallel cosmology

We study linear cosmological perturbations in the most general teleparallel gravity setting, where gravity is mediated by the torsion and nonmetricity of a flat connection alongside the metric. For a general linear perturbation of this geometry around a homogeneous and isotropic background geometry, we derive the irreducible decomposition of the perturbation variables, as well as their behavior under gauge transformations, i.e., infinitesimal diffeomorphisms generated by a vector field. In addition, we also study these properties for the most general set of matter variables and gravitational field equations. We then make use of these result to construct gauge-invariant perturbation variables, using a general approach based on gauge conditions. We further calculate these quantities also in the metric and symmetric teleparallel geometries, where nonmetricity or torsion is imposed to vanish. To illustrate our results, we derive the energy-momentum–hypermomentum conservation equations for both the cosmological background and the linear perturbations. As another example, we study the propagation of tensor perturbations in the f(G), f(T) and f(Q) class of theories.

Lavinia Heisenberg

Gauge-invariant cosmological perturbations in general teleparallel gravity

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.

Italy

Daniel Blixt

Tomi Koivisto

Luca Marzola

Teleparallel bigravity

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.

Switzerland

Canada

Simon Kuhn

Homogeneous and isotropic cosmology in general teleparallel gravity

The study of cosmological perturbation theory in f(T) gravity is a topic of great interest in teleparallel gravity since this is one of the simplest generalizations of the theory that modifies the teleparallel equivalent of general relativity. In this work, we explore the possibility of a non-flat FLRW background solution and perform perturbations for positively as well as negatively curved spatial geometries, together with a comparison to the flat case. We determine the generalized behaviour of the perturbative modes for this non-flat FLRW setting for arbitrary f(T) models, when the most general homogeneous and isotropic background tetrads are used. We also identify propagating modes in this setup, and relate this with the case of a flat cosmology.

Japan

Sebastian Bahamonde

Greece

Konstantinos Dialektopoulos

Malta

Jackson Said

China

Emmanuel Saridakis

Perturbations in non-flat cosmology for f(T) gravity

We present a package for the computer algebra system Mathematica, which implements the parametrized post-Newtonian (PPN) formalism. This package, named xPPN, is built upon the widely used tensor algebra package suite xAct, and in particular the package xTensor therein. The main feature of xPPN is to provide functions to perform a proper  $$3+1$$  <math> <mrow> <mn>3</mn> <mo>+</mo> <mn>1</mn> </mrow> </math>   decomposition of tensors, as well as a perturbative expansion in so-called velocity orders, which are central tasks in the PPN formalism. Further, xPPN implements various rules for quantities appearing in the PPN formalism, which aid in perturbatively solving the field equations of any metric theory of gravity. Besides Riemannian geometry, also teleparallel and symmetric teleparallel geometry are implemented.

xPPN: an implementation of the parametrized post-Newtonian formalism using xAct for Mathematica

We consider the most general teleparallel theory of gravity whose action is a linear combination of the five scalar invariants which are quadratic in the torsion tensor. Since two of these invariants possess odd parity, they naturally allow for a coupling to pseudo-scalar fields, thus yielding a Lagrangian which is even under parity transformations. In analogy to similar fields in gauge theories, we call these pseudo-scalar fields teleparallel axions. For the most general coupling of a single axion field, we derive the cosmological field equations. We find that for a family of cosmologically symmetric teleparallel geometries, which possess non-vanishing axial torsion, the axion coupling contributes to the cosmological dynamics in the early universe. Most remarkably, this contribution is also present when the axion is coupled to the teleparallel equivalent of general relativity, hence allowing for a canonical coupling of a pseudo-scalar to general relativity. For this case we schematically present the influence of the axion coupling on the fixed points in the cosmological dynamics understood as dynamical system. Finally, we display possible generalizations and similar extensions in other geometric frameworks to model gravity.

Teleparallel axions and cosmology

A description of many-particle systems, which is more fundamental than the fluid approach, is to consider them as a kinetic gas. In this approach the dynamical variable in which the properties of the system are encoded, is the distribution of the gas particles in position and velocity space, called 1-particle distribution function (1PDF). However, when the gravitational field of a kinetic gas is derived via the Einstein-Vlasov equations, the information about the velocity distribution of the gas particles is averaged out and therefore lost. We propose to derive the gravitational field of a kinetic gas directly from its 1PDF, taking the velocity distribution fully into account. We conjecture that this refined approach could possibly account for the observed dark energy phenomenology.