Schedule

We investigate gravitational waves in theories of gravity described by a non-metric compatible connection, free from torsion and curvature, known as symmetric-teleparallel gravity. We show that these theories exhibit only two massless and tensor modes. Their polarizations are transverse with helicity equal to two, exactly reproducing the plus and cross tensor modes typical of General Relativity. In order to analyze these gravitational waves, we first obtain the deviation equation of two trajectories followed by nearby freely falling point-like particles and we find it to coincide with the geodesic deviation of General Relativity. This is because the energy-momentum tensor of matter and field equations are Levi-Civita covariantly conserved and, therefore, free structure-less particles follow, also in non-metric gravity, the General Relativity geodesics. Equivalently, it is possible to show that the curves are solutions of a force equation, where an extra force term of geometric origin, due to non-metricity, modifies the autoparallel curves with respect to the non-metric connection. In summary, gravitational waves produced in non-metric theories of gravity behave as those in torsion-based gravity and it is not possible to distinguish them from those of General Relativity only by wave polarization measurements. This shows that the situation is different with respect to the curvature-based theories of gravity where additional scalar modes emerge for extensions and are rigorously two only for the Einstein-Hilbert theory.

I will explore possible ways to test the non-metricity from observations, particularly from cosmology observations. Linear non-metricity scalar produces the equivalent equation of motions as of GR. A function of nonmetricity (f(Q)) potentially changes the Friedmann equation in the background, as well as perturbation equations such as the Poisson equation, lensing equation, and propagation of gravitational waves (GW). Therefore we can put observational constraints on the observables and model parameters. I will discuss some observational bounds on the model parameters of some specific f(Q) models on the modified Newtonian constant (G_N) of the Poisson equation, and the amplitude damping parameter of the GW propagation ().

The Kerr (exterior) solution of General Relativity (GR) is one of the most relevant results of such theory since it is compatible with the current observational results. But GR has some shortcomings as, for example, unavoidable singularities in the inner part of the Kerr solution which entail a lack of predictability of our theory. This suggests to extend GR in order to get rid of them. A proposal to do it is by considering Ricci Based gravities. We will see that we can find non-singular solutions within these theories.

The finite Euclidean action solutions known as instantons played an important role in non-perturbative understanding of Yang-Mills theory. In 1970s, a similar idea was being developed in the case of gravity but the self-duality caused serious limitations in this attempt. In this talk, I will show how teleparallel gravity avoids these limitations and we can obtain gravitational instantons that resembles those found in the standard Yang-Mills theory. I will then discuss some consequences of this construction for our understanding the structure of the gravitational vacuum.

Standard modelo extension accordingly to Bluhm fam be show to be used to look for beyond Riemann geometries such as Riemann Cartan and Finsler. In this presentation we show that the SME action already contains a Holst term were the torsion Tracey vector and axial torsionare mixed. in this way we May show how condensates dark massive torsion ones can be given by magneto genesis and the massive torsion like magnetico field like the electroweak condensate.

In the conventional formulation of general relativity, gravity is represented by the metric curvature of Riemannian geometry. There are also alternative formulations in flat affine geometries, wherein the gravitational dynamics is instead described by torsion and nonmetricity. These so called general teleparallel geometries may also have applications in material physics, such as the study of crystal defects. In this work, we explore the general teleparallel geometry in the language of differential forms. We discuss the special cases of metric and symmetric teleparallelisms, clarify the relations between formulations with different gauge fixings and without gauge fixing, and develop a method of recasting Riemannian into teleparallel geometries. As illustrations of the method, exact solutions are presented for the generic quadratic theory in 2, 3 and 4 dimensions.

We are interested in the static spherically symmetric geometries in F(T) teleparallel gravity with physical importance. We have found the general forms of the spherically symmetric frame with zero curvature, metric compatible and non-zero spin connection. We then analyse the antisymmetric field equations (the solutions splitting into two separate cases), and derive and analyse the resulting symmetric field equations. For studying the applications of spherically symmetric teleparallel models, we have studied the static spherical symmetric by solving the antisymmetric field equations and by setting the final static symmetric field equations to solve. Then, we solved these field equations for vacuum spacetimes and obtain a number of new F(T) solutions. Finally, we have proposed some insights and aims for fluids new possible F(T) solutions in some future works.

In this talk, I will present a formulation of cosmological perturbation theory around a spatially curved FLRW background within the framework of metric-affine gauge theory of gravity, which incorporates both torsion and nonmetricity. Through a scalar-vector-tensor decomposition of the spatial perturbations, we discover that the theory exhibits a rich perturbation spectrum featuring helicities 0, 1, 2, and 3, alongside the standard scalar, vector, and tensor metric perturbations typical of Riemannian geometry. This leads to diverse phenomenological implications. For instance, the helicity-2 modes of the torsion and/or nonmetricity tensors can source helicity-2 metric tensor perturbations at the linear level, resulting in the generation of gravitational waves. As an immediate application, I will illustrate an example involving the helicity-3 modes of the spin-3 field manifesting in nonmetricity.

The Equivalence Principle is considered in the framework of metric-affine gravity. We show that it naturally emerges as a Noether symmetry starting from a general non-metric theory. In particular, we discuss the Einstein Equivalence Principle and the Strong Equivalence Principle showing their relations with the non-metricity tensor. Possible violations are also discussed pointing out the role of non-metricity in this debate.

The multisymplectic formalism provides a covariant, geometric approach to field theory in such a way that enables one to deal directly with higher order theories just as one treats ordinary mechanics. Yet, for various reasons, it is often necessary to break manifest covariance through a space + time decomposition. However, the canonical way of obtaining the instantaneous hamiltonian formalism by defining the instantaneous momenta in the Ostrogradsky prescription is no longer valid when the symplectic form is not in Darboux coordinates, which is likely to have been underseen by the community and which might be leading to hiding issues with generalised theories of gravity.

In this talk, I will show how this multisymplectic structure on the covariant level “descends” to a symplectic structure on the instantaneous level once a Cauchy surface is chosen in the context of cubic Horndeski’s theory.

Over the past few years, gauge theories of gravity with the khronon field, a gauge field that spontaneously breaks the Lorentz symmetry and accounts for the emergence of the time, have developed new formulations of gravity. Such formulations based on gauge symmetry enable us to consider the unification of gravity and electromagnetism. With the most recent formulation, which is constructed from a gauge field and Lorentz covariant derivative, I present the derivation of black hole solutions, examine their consistency with general relativity and how electromagnetic effects can be integrated in this theory.

General Relativity is a quite successful theory of gravity, but it is not in agreement with several cosmological observations and quantum field theory. One way to address this issue is by modifying the gravitational theory. An interesting modification arises when we consider gravity as the result of torsion rather than the curvature of the spacetime. This class of theories correspond to teleparallel gravity and in this case, we consider the tetrad as the fundamental variable instead of the metric. In this presentation, we focus on New General Relativity (NGR) which is constructed from the three possible quadratic torsion scalars [1]. We present the spherically symmetric field equations in one-parameter NGR for the most general tetrad and we discuss the three branches of solutions that we found in vacuum for this theory [2].

[1] K. Hayashi and T. Shirafuji, “New general relativity”, Phys. Rev. D 19 (1979) 3524–3553.

[2] H. Asuküla, S. Bahamonde, M. Hohmann, V. Karanasou, C. Pfeifer, J. L. Rosa, “Spherically symmetric vacuum solutions in one-parameter new general relativity and their phenomenology”, Phys. Rev. D 109, 064027 (2024)

White dwarfs are the final evolutionary stage of stars with a mass lower than approximately ten solar masses, thus about 97% of the stars in the Milky Way, and in particular our Sun. Even though their evolution is simple in comparison to other astrophysical objects, it involves several different physical processes under extreme conditions. With newer ground- and space based gravitational wave detectors, we will soon be able to study these stars in a multi-messenger approach. Hence, they present a possibility to discover new phenomena and test current physical models, including gravity theories. In this talk I will first give a brief introduction of white dwarfs’ properties, followed by a discussion of their structure in Newtonian gravity, general relativity and scalar-tensor theory. The main part of the talk will focus on a toy model describing the cooling process that determines a white dwarf’s age, again comparing the results for each gravity theory. Finally, I will give an outlook on possible future work and improvements.

We consider a Weyl-Lorentz-\(U(1)\)-invariant gravity model written in terms of a scalar field, electromagnetic field and nonmetricity without torsion and curvature, the so-called symmetric teleparallel geometry, in three dimensions. Firstly, we obtain variational field equations from a Lagrangian. Then, we find some classes of circularly symmetric rotating solutions by making only a metric ansatz. The coincident gauge of symmetric teleparallel spacetime allows us for doing so.

SymPy is a Python library for symbolic mathematics. It contains a tensor package which offers necessary basic tools to carry out complicated component calculations ubiquitous in the theories of gravity. It is convenient to use in the Jupyter notebook or lab environments, that run on different platforms and have kernels for many programming languages. Sympy in combination with Numpy, Matplotlib and other libraries provides as a powerful toolbox that starts to rival the well established commercial program sets like Mathematica and Maple. But it is completely free. In the talk I give and overview of the basic techniques in general relativity, and show more elaborate computations in general teleparallel gravity.

In this study, we explore the structure of neutron stars within the framework of covariant \(f(Q)\) gravity, an extension of general relativity that incorporates non-metricity. By adopting a static and spherically symmetric metric, we derive the modified Tolman-Oppenheimer-Volkoff (TOV) equations specific to this gravitational theory. After successful testing in previous work [1] using polytropic model, we analyze the configurations of neutron stars by employing realistic equations of state (EoS) for nuclear matter. Our results indicate some deviations in the mass-radius relationship of neutron stars when compared to predictions from general relativity, suggesting potential observable consequences.

[1] R.Lin and X.Zhai. (2021). “Spherically symmetric configuration in \(f(Q)\) gravity”. Phys. Rev. D, 103 (12), 124001.

General relativity (GR) exists in different formulations. They are equivalent in pure gravity but generically lead to distinct predictions once matter is included. After a brief overview of various versions of GR, I will focus on metric-affine gravity, which avoids any assumption about the vanishing of curvature, torsion, or nonmetricity. With a view toward the Standard Model, we can construct a generic model of (complex) scalar, fermionic, and gauge fields coupled to GR and derive an equivalent metric theory, which features numerous new interaction terms. There are phenomenological consequences, which I will detail: an improved setting for Higgs inflation and an outlook on a new (purely gravitational) production channel for fermionic dark matter.

P-S: My proposed talk introduces some aspects presented in the contribution by Sebastian Zell. So if possible and if both abstracts are accepted, I’d like to ask to schedule my talk before the one by Sebastian Zell.

I will show that metric-affine gravity features a new extended projective (EP) symmetry that arises from the non-minimal kinetic term of fermions. EP transformations are generated by a pair of vectors, generalize the known projective symmetry, and effectively point to the Einstein-Cartan formulation of General Relativity. The most general EP-invariant theory (at most quadratic in field strengths) possesses a non-linearly consistent particle spectrum with only a single pseudoscalar field in addition to the massless graviton. Once coupled to the Standard Model, this theory can solve the strong CP-problem with an axion of purely gravitational origin. At the same time, it both leads to successful Higgs inflation with small controllable quantum corrections and provides a new channel for the production of fermionic dark matter.

Based on: C. Rigouzzo, S. Zell, Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions, Phys. Rev. D 108 (2023) 124067, arXiv:2306.13134. W. Barker, S. Zell, Consistent particle physics in metric-affine gravity from extended projective symmetry, arXiv:2402.14917. G. Karananas, M. Shaposhnikov, S. Zell, to appear.

[Note to the organizers: I have coordinated my talk with the contributions by Will Barker and Claire Rigouzzo. For maximal synergy, I’d like to ask to schedule my talk after the ones by Claire and Will, if this is possible and if our abstracts are accepted.]

In this work, we apply the formalism of dynamical systems to analyze the viability of the \(\Lambda\)CDM model in a generalized form of the hybrid metric-Palatini gravity theory written in terms of its dynamically equivalent scalar-tensor representation. Adopting a matter distribution composed of two relativistic fluids described by the equations of state of radiation and pressureless dust, one verifies that the cosmological phase space features the usual curvature-dominated, radiation-dominated, matter-dominated, and exponentially accelerated fixed points, even in the absence of a dark energy component. A numerical integration of the dynamical equations describing the system, subjected to initial conditions consistent with the cosmographic observations from the Planck satellite and weak-field solar system dynamics, shows that cosmological solutions with the same behavior as the \(\Lambda\)CDM model in General Relativity (GR) are attainable in this theory, with the deviations from GR being exponentially suppressed at early-times and the scalar-field potential effectively playing the role of dark energy at late times.

\(f(R)\) theories of gravity are amongst the most successful generalisations of GR, being a simple, versatile alternative thereto which remains observationally viable in a wide variety of scenarios, such as Cosmology. It is widely thought that, at linear level, all \(f(R)\) theories propagate an extra scalar field in addition to the usual massless and traceless graviton of GR, thus being compatible with gravitational-wave observations. However, it has been recently noticed that some particular \(f(R)\) models, such as \(f(R)\propto R^2\), do not feature all expected degrees of freedom in their linearised spectrum atop a Minkowski background. In this talk, we will see that these oddities affect a wide class of \(f(R)\) models, which we dub ‘degenerate models.’ In particular, we will prove that there are no propagating linear degrees of freedom atop maximally-symmetric backgrounds in degenerate \(f(R)\) models, either due to a strong-coupling instability or other reasons. We shall compare this situation to the case of ‘healthy’ \(f(R)\) models, whose linearised spectrum atop maximally-symmetric backgrounds contains the expected 2 + 1 stable degrees of freedom. We will also discuss other pathological traits of degenerate \(f(R)\) models further questioning their physical viability.

We derive the equations of motion of a test particle with intrinsic hypermomentum in spacetimes with both torsion S and nonmetricity Q (along with curvature R). Accordingly, S and Q can be measured by tracing out the trajectory followed by a hypermomentum-charged test particle in such a non-Riemannian background. The test particle is approximated by means of a Dirac δ-function. Thus we find a tangible way to observe and measure the effects of torsion and nonmetricity.

In this talk, I’ll discuss our recently defined generalized horizon entropy(Phys.Rev.D 109 (2024) 8, 084075) and how it applies to entropic force cosmological models, in which the entropic force terms are thought to be responsible for the universe’s current accelerated phase. Our generalized entropic force models are completely equivalent to the standard ΛCDM model, providing new support for the origin and nature of the cosmological constant from an entropic perspective.Overall, we show excellent agreement with the cosmological data that is comparable to ΛCDM and from which our models are indistinguishable in terms of Bayesian analysis.

Teleparallel theories of gravity have gained a lot of attention in the context of cosmology. However, all theories that have been investigated either contain ghosts, or strongly coupled fields. The latter is not necessarily a problem, and can on the contrary introduce screening mechanisms which gives rise to predictions that are very interesting observationally. In order to address these features it is useful to perform both a linear and nonlinear analysis. This talk focuses on the nonlinear (Hamiltonian) analysis which gives information on what symmetries are present at the nonlinear level. (Non)presence of symmetries is important to take into consideration because it gives a first classification of theories where there is an abrupt change in the number of degrees of freedom. In this talk I present classifications of general quadratic teleparallel theories and their nonlinear extensions f(T), f(Q), and f(G).

I will briefly explore the connection between modified theories of gravity (here Palatini gravity) and models based on the generalized uncertainty principle. This connection enables the examination of gravity proposals through tabletop experiments. Using the Landau model of liquid helium as an illustrative example, we will delve into the details.

In this work, we study cosmological spacetime configurations in \(f(Q)\) gravity with a nonvanishing symmetric teleparallel connection. It is known that the spatially homogeneous and isotropic connections that solve the equations of motion paired with a flat Friedmann-Lema^itre-Robertson-Walker (FLRW) metric can be classified into three sets. We explore the stability of \(f(Q)\) cosmology across radiation, matter, dark energy, and geometric dark energy eras by utilizing a perturbative approach around FLRW background solutions of the metric field equation. Our results show that connection set I exhibits stable behavior throughout all evolutionary eras. Conversely, connection set II exhibits stability during the radiation era and marginal stability in the matter era, while for the dark energy and geometric dark energy eras our results are inconclusive. Furthermore, we discuss the general conditions on the function \(f(Q)\) that physically viable models should obey, and point out that for a generic \(f(Q)\) the cosmological connection sets II and III are prone to trigger a rip or crunch singularity, hence these configurations could be problematic already on the background level.

The stress energy tensor we all know is related to the existence of a metric. But the metric is not the only character we have to take into account when studying a theory of gravity. We can also consider an independent connection and we will have also the hypermomentum tensor in the game. How it is related to quantities such as torsion and non metricity? What is its role in cosmology? Can it explains some kind of accelerated expansion? These are questions will be addressed in this talk.

Physical evolution of cosmological models can be tested by using expansion data, while growth history of these models is capable of testing dynamics of the inhomogeneous parts of energy density. The growth factor, as well as its growth index and \(f\sigma_8\), gives a clear indication of the performance of cosmological models in the regime of structure formation of early Universe. In this work, we explore the growth index in several cosmological models, based on a specific class of teleparallel gravity theories. These have become prominent in the literature and lead to other formulations of teleparallel gravity. By taking a generalized approach in obtaining the Meszaros equation without immediately imposing the subhorizon limit, because this assumption could lead to over-simplification. This approach gives avenue to study at which \(k\) modes the subhorizon limit starts to apply.

In this work we study the properties of a congruence of timelike curves in an n-dimensional manifold in the presence of torsion. We generalise the geodesic deviation equation to the “deviation equation” describing the relative acceleration of nearby timelike curves. The result is used to obtain an alternative way of deriving the Raychaudhuri equation with torsion. Torsion is further incorporated into the notions of conjugate points and hypersurface orthogonality. Together with the Raychaudhuri equation, we then proceed to predict appearances of focal points, which are vital for the formulation of Singularity theorems.

We consider Chern-Simons gravity coupled to a dynamical scalar inflaton in the full metric-affine formalism. We also calculate the effective action for the Einstein-Cartan and Palatini formalisms, and show that all the cases are qualitatively equivalent. We show that, for general monomial potentials, the theory can flatten the inflaton potential, allowing for the spectral index to be consistent with observations. We further consider tensor perturbations and show that there is no significant deviation from GR.

I will present a modification of General Relativity (GR), named topo-GR, in which a non-dynamical term depending on the topology of the Universe is added in the Einstein equation. The action of the theory is formally equivalent to the Symmetric Teleparallel Equivalent GR, with the fundamental difference that the non-metric connection is, in general, non-flat and chosen as a function of the topology. I will present the three main motivations for this theory, which correspond to the requirement that, in any topology, a non-relativistic limit, a first order action for gravitation, and a simple inflationary scenario are all well-posed. The simplicity of the theory, i.e. no additional degrees of freedom are introduced compared to GR, and the full independence of the motivations are strong indicators that, for non-asymptotically flat spacetimes, topo-GR should be considered over GR.

In this study, the f(G,T) theory of gravity is recast in terms of the ϕ and ψ fields within the scalar-tensor formulation, where G is the Gauss–Bonnet term and T denotes the trace of the energy–momentum tensor. The general aspects of the introduced reformulation are discussed and the reconstruction of the cosmological scenarios is presented, focusing on the so-called hybrid evolution. As a result, the scalar-tensor f(G,T) theory is successfully reconstructed for the early and late time approximations with the corresponding potentials. The procedure of recovering the f (G,T) theory in the original formulation is performed for the late time evolution and a specific quadratic potential. The scalar-tensor formulation introduced herein not only facilitates the description of various cosmic phases but also serves as a viable alternative portrayal of the f(G,T) gravity which can be viewed as an extension of the well-established scalar Einstein–Gauss–Bonnet gravity.

The main goal of this presentation is to explore the gravitational action of a Schwarzschild black hole and its subsequent regularisation from the perspective of general relativity and teleparallel gravity. As these two contrasting approaches result in a disagreement, we investigate this problem by testing various frames, including the so-called proper and canonical frames, to identify the root of this inconsistency. Finally, we explore the role of singular points in the action and their contributions to the surface terms structure as a possible remedy to this problem.

This talk will be composed of two parts. First, I will briefly introduce the foundations of numerical relativity and our work on generating 1+1 numerical codes for general relativity. Our motivation is to apply this knowledge to recent progress on the 3+1 foundations of the symmetric teleparallel equivalent of general relativity that offers a new perspective on traditional numerical relativity. The second part of the talk will be devoted to f(Q) gravity and how it is possible to significantly simplify the search for cosmological solutions when dropping the assumption of imposing symmetries on the connection through the Killing equation. We will also discuss the hypothesized existence of remnant symmetries in f(Q) gravity. Both parts are work in progress in collaboration with Marie Jaarma and Bert Siimon, respectively.

1. The relativistic completion of General Relativity can be formulated as the teleparallelisation of the original theory (Einstein 1916). This completion is the breakthrough that resolves the relativistic observables the epitome of which is energy.

2. Extensively considered teleparallel modified gravity models are ruled out, since they are now established to contain ghosts. The extra degrees of freedom are strongly coupled in typical solutions which has lead many unjustified claims in the literature.

3. We can present viable, ghost-free classes of teleparallel modified gravity models. Such models are discussed in view of their phenomenologies, relations to previously considered theories, and interpretations from the perspective of General Relativity.

The stability of linear perturbations around the Minkowski background is revisited in all the different types of NGR, according to the primary constraint classification. In particular, I will show in a gauge invarinat manner that, unless they vanish, all the vector modes will contribute ghosts. In addition, I will present two new branches of the classification that are ghost free and propagate two tensor modes plus a massless scalar field. This shows that, unlike what was thought up to now, there exist three possible realizations of ghost-free cases in the NGR family of theories instead of one.

We study transformations of the dynamical fields - a metric, a flat affine connection and a scalar field - in scalar-teleparallel gravity theories. The theories we study belong either to the general teleparallel setting, where no further condition besides vanishing curvature is imposed on the affine connection, or the symmetric or metric teleparallel gravity, where one also imposes vanishing torsion or nonmetricity, respectively. For each of these three settings, we find a general class of scalar-teleparallel action functionals which retain their form under the aforementioned field transformations. This is achieved by generalizing the constraint of vanishing torsion or nonmetricity to non-vanishing, but algebraically constrained torsion or nonmetricity. We find a number of invariant quantities which characterize these theories independently of the choice of field variables, and relate these invariants to analogues of the conformal frames known from scalar-curvature gravity. Using these invariants, we are able to identify a number of physically relevant subclasses of scalar-teleparallel theories. We also generalize our results to multiple scalar fields, and speculate on further extended theories with non-vanishing, but algebraically constrained curvature.

This talk is based on arXiv:2312.17609.

(based on joint work with L. Ducobu)

The method of variational completion allows one to transform an (in principle, arbitrary) system of partial differential equations – based on an intuitive “educated guess” – into the Euler-Lagrange one attached to a Lagrangian, by adding a canonical correction term. Here, we extend this technique to theories that involve at least two sets of dynamical variables: we show that an educated guess of the field equations with respect to one of these sets of variables only, is sufficient to variationally complete these equations and recover a Lagrangian for the full theory, up to boundary terms and to terms that do not involve the respective variables. Applying this idea to natural metric-affine theories of gravity, we prove that, starting from an educated guess of the metric equations only, one can find the full metric equations, together with a generally covariant Lagrangian, up to metric-independent terms. The latter terms (which can only involve the distortion of the connection) are then completely classified over 4-dimensional spacetimes,by techniques pertaining to differential invariants.

The method of variational bootstrapping, based on canonical variational completion, allows one to construct a Lagrangian for a physical theory depending on two sets of field variables starting from a guess of the field equations for only one such set of field variables. Such a setup is particularly appealing for the construction of modified theories of gravity, in general, since one can apply this procedure by taking lessons from GR for the “educated guess” of the metric field equations; the field equations for the other fields being fixed by the obtained Lagrangian (up to terms completely independent from the metric tensor).

Following the talk by N. Voicu, presenting the method mathematically, in this talk, I explore its applications in the context of metric-affine theories of gravity with the aim of finding those metric-affine models which are, in a variational sense, closest to the ΛCDM model of cosmology.

This presentation is based on the work done in [arXiv:2403.15564] (https://arxiv.org/abs/2403.15564) in collaboration with Nicoleta Voicu.

Eliminating ghosts and tachyons from the linear spectrum has long been a crucial criterion for establishing viable theories within the metric-affine paradigm. However, this necessary step must be complemented by additional measures to ensure the development of a predictive quantum model. In this talk, we explore the one-loop structure for some ghost and tachyon-free vector theories, highlighting the significance of structural constraints in their interactions, even in the absence of gauge symmetries. Despite the presence of soft-breaking terms, we demonstrate that achieving a predictive framework for vector models within the realm of effective field theory depends critically on adopting a gauge-like approach to their interactions. Our findings provide a deeper understanding of the theoretical and practical challenges in advancing metric-affine gravity as a credible effective field theory.

The MAG framework admits torsion and non-metricity into the spacetime alongside curvature: in this geometric sense it constitutes a very general starting point for model-building. Initially, the MAG theory-space seems too big: the many possible models dilute its predictive power. But looking more closely, there are theoretical self-consistency requirements (ghosts, tachyons and strongly-coupled modes) which threaten to over-constrain MAG and leave us with nothing beyond GR. We navigate this dichotomy with the new extended projective (EP) symmetry. As diff symmetry leads to GR, so too EP symmetry leads to one unique, consistent MAG, with little room to maneuver. We argue that the non-linearity of the EP inflaton potential is a smoking-gun for non-Riemannian geometry. We show that non-geometric attempts to introduce non-linearity lead instead to inconsistent models with non-canonical kinetic terms. We explore the space of higher-order EP-invariant operators. We review new software tools for automatically finding novel non-linear symmetries in MAG Lagrangia with higher powers of curvature, and for responsible model-building in general.

Based on: W. Barker, S. Zell, Consistent particle physics in metric-affine gravity from extended projective symmetry, arXiv:2402.14917. W. Barker, C. Marzo, S. Zell, to appear.

Note to the organizers: This talk focusses on some formal aspects of EP, it is coordinated with the contribution by Sebastian Zell, who will address the phenomenological aspects of EP.

We analyse the stability of the vector and axial sectors of Poincaré gauge theory around general backgrounds in the presence of cubic order invariants defined from the curvature and torsion tensors, showing how the latter can in fact cancel out well-known instabilities arising from the quadratic curvature invariants of the theory and accordingly help in the construction of healthy models with both curvature and torsion. For this task, we introduce the most general parity preserving cubic Lagrangian with mixing terms of the curvature and torsion tensors, and find the relations of its coefficients to avoid a pathological behaviour from the vector and axial modes of torsion. As a result, on top of the gravitational constant of General Relativity and the mass parameters of torsion, our action contains 23 additional coupling constants controlling the dynamics of this field. As in the quadratic Poincaré gauge theory, we show that a further restriction on the cubic part of the action allows the existence of Reissner-Nordström-like black hole solutions with dynamical torsion.

A first viability test of theories of gravity beyond general relativity is often performed in their non-relativistic, post-Newtonian regime. In this talk I will present how we can test modified gravity theories in the complementary ultra-relativistic regime, by predicting the gravitational field of ultra-relativistic particle beams, which can in principle be measured by the acceleration of test particles in the vicinity of such particle beams. Such a setup can for example be realised with test particles placed around particle accelerators such as the LHC.

As an example I will explicitly discuss how the ultra-relativistic regime of scalar-tensor theories can be tested.

Palatini \(F(R)\) gravity proved to be a powerful tool in order to realize asymptotically flat inflaton potentials. Unfortunately, it also inevitably implies higher-order inflaton kinetic terms in the Einstein frame that might jeopardize the evolution of the system out of the slow-roll regime. We prove that a \(F(R+X)\) gravity, where X is the inflaton kinetic term, solves the issue. Moreover, when F is a quadratic function such a choice easily leads to a new class of inflationary attractors, fractional attractors, that generalizes the already well-known polynomial α-attractors

This paper presents an analysis of a cosmological model that is based on F(R, G) gravity, where R represents the Ricci scalar, and G represents the Gauss-Bonnet invariant. The model parameter has been constrained using observational data sets and shows a viable era with early deceleration and late-time acceleration in the dark energy-dominated era. The study has also explored the stability of the model through phase-space analysis, which reveals the behavior of critical points and the current values of density parameters for matter and dark energy. These values align with cosmological observations.