arXiv subjects
Publications and source records attributed to Tomi S. Koivisto.
A novel first order action principle has been proposed as the possible foundation for a more fundamental theory of General Relativity and the Standard Model. It is shown in this article that the proposal consistently incorporates gravity and matter fields, and guides to a new and robust path towards unification of fundamental interactions.
We show the known pathological character of $f(\mathbb{Q})$ gravity in its scalar-tensor representation.
The parallel theory of relativity predicts conserved energy-momentum currents for an arbitrary metric, without invoking Killing symmetries. By treating the reference frame as an independent variational field and requiring it to carry no energy, the theory naturally unifies Einstein's two formulations of gravity and yields uniquely defined covariant charges. In isotropic and homogeneous cosmology, the canonical time direction selected by the reference frame coincides with the Kodama vector, and the associated Noether energy reproduces the Misner-Sharp mass.
The Euclidean path integral approach to quantum gravity is conventionally formulated in terms of the Einstein-Hilbert-York-Gibbons-Hawking action, which requires suitable subtractions to produce the correct black hole partition function. However, there is a unique, canonical teleparallel reformulation which reproduces the same results without subtractions or other ambiguities. This is verified in the case of a black hole with or without an electric or a magnetic charge and in a background with or without a cosmological constant. Moreover, a new quasilocal prescription is proposed and tested, where the black hole partition function is determined solely by the horizon boundary term, yielding the correct Helmholtz free energy without the need for counterterms.
Motivated by cosmological applications for interacting matters, an extension of the action functional for relativistic fluids is proposed to incorporate the physics of non-adiabatic processes and chemical reactions. The former are characterised by entropy growth, while the latter violate particle number conservation. The relevance of these physics is demonstrated in the contexts of self-interacting fluids, fluids interacting with scalar fields, and hyperhydrodynamical interactions with geometry. The possible cosmological applications range from early-universe phase transitions to astrophysical phenomena, and from matter creation inflationary alternatives to interacting dark sector alternatives to the $Λ$CDM model that aim to address its tensions. As an example of the latter, a single fluid model of a unified dark sector is presented. The simple action of the model features one field and one parameter, yet it can both reproduce the $Λ$CDM cosmology and predict new phenomenology.
Theories formulated in the arena of teleparallel geometries are generically plagued by ghost-like instabilities or other pathologies that are ultimately caused by the breaking of some symmetries. In this work, we construct a class of ghost-free theories based on a symmetry under Transverse Diffeomorphisms that is naturally realised in symmetric teleparallelism. We explicitly show their equivalence to a family of theories with an extra scalar field plus a global degree of freedom and how Horndeski theories and healthy couplings to matter fields can be readily accommodated.
Black hole solutions are explored in the Lorentz gauge theory of gravity. The fields of the theory are the gauge potential in the adjoint and a scalar in the fundamental representation of the Lorentz group, a metric tensor then emerging as a composite field in a symmetry-broken phase. Three distinct such phases of the theory are considered. In an SO(3) phase, the fundamental field is identified with a generalised Painlevé-Gullstrand-Lemaître coordinate time. In the static spherically symmetric case it is a stealth scalar, and the general vacuum solution is then parameterised by two constants, one related to the black hole mass and the other to an observer. Also, formulations of pregeometric first order electromagnetism are considered in order to construct a consistent realisation of a charged black hole. In an SO(1,2) phase of the theory, the Schwarzschild solution is realised as a configuration wherein the fundamental field is real outside and imaginary inside the horizon. In this phase the field can be associated with an effective radial pressure resulting in additional singularities and asymptotic non-flatness. Finally, a symmetry-broken phase which would correspond to solutions in an alternative attempt at a Lorentz gauge theory is shown to be incompatible with black holes.
We explore a new action formulation of hyperfluids, fluids with intrinsic hypermomentum. Brown's Lagrangian for a relativistic perfect fluid is generalised by incorporating the degrees of freedom encoded in the hypermomentum tensor, namely by including connection-matter couplings. Quite interestingly, generic hyperfluids are imperfect, since hypermomentum induces such effects as bulk and shear viscosities as well as heat fluxes. The various coefficients that appear in the first order expansion of hydrodynamics can now be deduced from a Lagrangian formulation, given a geometrical interpretation and a suggested microscopic description in terms of hypermomentum. This connection between hypermomentum and dissipative fluids could shed new light on the physics of relativistic hydrodynamics. The applicability of the new formalism is demonstrated by exact cosmological solutions.
The intrinsic presence of ghosts in the symmetric teleparallel framework is elucidated. We illustrate our general arguments in $f(\mathbb{Q})$ theories by studying perturbations in the three inequivalent spatially flat cosmologies. Two of these branches exhibit reduced linear spectra, signalling they are infinitely strongly coupled. For the remaining branch we unveil the presence of seven gravitational degrees of freedom and show that at least one of them is a ghost. Our results rule out $f(\mathbb{Q})$ cosmologies and clarify the number of propagating degrees of freedom in these theories.
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.
General (tele)parallel Relativity, G$_\parallel$R, is the relativistic completion of Einstein's theories of gravity. The focus of this article is the derivation of the homogeneous and isotropic solution in G$_\parallel$R. The first-principles derivation, based on a non-trivial realisation of the symmetry, supersedes and unifies previous constructions of Riemannian and teleparallel cosmologies, and establishes the uniqueness of the physical solution. The constitutive law and the form of the material and inertial source currents is presented in the tensor (Palatini) formalism and adapted to the cosmological background, which exhibits novel features absent in the previously studied, static solutions to the theory. The results are contrasted with those in some incomplete theories, such as sitting at the three corners of the geometrical trinity and corresponding to particular reference frames in G$_\parallel$R.
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.
General Relativity and the $Λ$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''.
Symmetric teleparallel gravity is shown to be integrable in the presence of boundaries, given the consistent implementation of constraints in the covariant phase space formalism.
In this essay, we immerse into the framework of normed division algebras as a suitable arena to accommodate the standard model of elementary particles, and we explore some applications to cosmology. Remarkably, they permit interesting non-trivial realisations of the cosmological principle with an interplay between the symmetry groups of the quaternions and octonions. We also argue how these realisations give rise to potentially observational signatures in gravitational waves astronomy.
All energy is gravitational energy. That is the consequence of the equivalence principle, according to which gravity is the universal interaction. The physical charges of this interaction have remained undisclosed, but the Adventof the Geometrical Trinity opened a new approach to this foundational problem. Here it is shown to provide a background-independent unification of the previous, non-covariant approaches of Bergmann-Thomson, Cooperstock, Einstein, von Freud, Landau-Lifshitz, Papapetrou and Weinberg. First, the Noether currents are derived for a generic Palatini theory of gravity coupled with generic matter fields, and then the canonical i.e. the unique charges are robustly derived and analysed, particularly in the metric teleparallel and the symmetric teleparallel versions of General Relativity. These results, and their application to black holes and gravitational waves, are new.
The simplest i.e. the Abelian i.e. the commutative i.e. the integrable i.e. the flat and torsion-free i.e. the symmetric teleparallel affine connection has been considered in many recent works in the literature. Such an affine connection is characterised by the property that it can be vanished by a general coordinate transformation, by fixing the so called coincident gauge. This article focuses on the subtleties involved in the applications of the coincident gauge.
The Noether currents are derived in a generic metric-affine theory of gravity, and the holographic nature of the gravitational entropy and energy-momentum is clarified. The main result is the verification of the canonical resolution to the energy-momentum problem in the Noether formalism.