Nonlinear generalizations of teleparallel gravity entail the modification of a Lagrangian that is pseudoinvariant under local Lorentz transformations of the tetrad field. This procedure consequently leads to the loss of the local pseudoinvariance and the appearance of additional degrees of freedom (d.o.f.). The constraint structure of f(T) gravity suggests the existence of one extra d.o.f. when compared with GR, which should describe some aspect of the orientation of the tetrad. The purpose of this article is to better understand the nature of this extra d.o.f. by means of a toy model that mimics essential features of f(T) gravity. We find that the nonlinear modification of a Lagrangian L possessing a local rotational pseudoinvariance produces two types of solutions. In one case the original gauge-invariant variables -- the analogue of the metric in teleparallelism -- evolve like when governed by the (nondeformed) Lagrangian L; these solutions are characterized by a (selectable) constant value of its Lagrangian, which is the manifestation of the extra d.o.f. In the other case, the solutions do contain new dynamics for the original gauge-invariant variables, but the extra d.o.f. does not materialize because the Lagrangian remains invariant on-shell. Coming back to f(T) gravity, the first case includes solutions where the torsion scalar T is a constant, to be chosen at the initial conditions (extra d.o.f.), and no new dynamics for the metric is expected. The latter case covers those solutions displaying a genuine modified gravity; T is not a constant, but it is (on-shell) invariant under Lorentz transformations depending only on time. Both kinds of f(T) solutions are exemplified in a flat FLRW universe. Finally, we present a toy model for a higher-order Lagrangian with rotational invariance [analogous to f(R) gravity] and derive its constraint structure and number of d.o.f.
The existence of an extra degree of freedom (d.o.f.) in $f(T)$ gravity has been recently proved by means of the Dirac formalism for constrained Hamiltonian systems. We will show a toy model displaying the essential feature of $f(T)$ gravity, which is the pseudoinvariance of T under a local symmetry, to understand the nature of the extra d.o.f.
It has recently been shown that $f(T)$ gravity has $\frac{n(n-3)}{2}+1$ physical degrees of freedom (d.o.f.) in $n$ dimensions, contrary to previous claims. The simplest physical interpretation of this fact is that the theory possesses a scalar d.o.f. This is the case of $f(R)$ gravity, a theory that can be understood in the Einstein frame as general relativity plus a scalaron. The scalar field that represents the extra d.o.f. in $f(T)$ gravity encodes information about the parallelization of the spacetime, which is detected through a reinterpretation of the equations of motion in both the tel…
In this paper, we investigate a scenario in which late time cosmic acceleration might arise due to coupling between dark matter and baryonic matter without resorting to dark energy or large scale modification of gravity associated with extra degrees of freedom. The scenario can give rise to late time acceleration in Jordan frame and no acceleration in Einstein frame - \textit{generic modification of gravity} caused by disformal coupling. Using a simple parametrization of the coupling function, in maximally disformal case, we constrain the model parameters by using the age constraints due to gl…
We consider a recently proposed generalization of unimodular gravity, where the lapse function is constrained to be equal to a function of the determinant of the spatial metric $f(h)$, as a potential origin of a dark fluid with a generally $h$-dependent equation of state parameter. We establish the Hamiltonian analysis and the canonical path integral for the theory. All the special cases that do not match unimodular gravity involve violation of general covariance, and consequently the physical content of the theory is changed significantly. Particularly, the case of a constant function $f$ is …
We provide a cosmological test of modified gravity with two tensorial degrees of freedom and no extra propagating scalar mode. The theory of gravity we consider admits a cosmological model that is indistinguishable from the $Λ$CDM model at the level of the background evolution. The model has a single modified-gravity parameter $β$, the effect of which can be seen in linear perturbations, though no extra scalar mode is propagating. Using the Boltzmann code modified to incorporate the present model, we derive the constraints $-0.047 < β< -0.028$ at 68$\%$ confidence from Planck CMB data. Since o…
The ultraviolet completion of gauge theories by higher derivative terms can dramatically change their behavior at high energies. The requirement of asymptotic freedom imposes very stringent constraints that are only satisfied by a small family of higher derivative theories. If the number of derivatives is large enough ($n > 4$) the theory is strongly interacting both at extreme infrared and ultraviolet regimes whereas it remains asymptotically free for a low number of extra derivatives ($n \leqslant 4$). In all cases the theory improves its ultraviolet behavior leading in some cases to ultravi…
General Relativity can be reformulated as a diffeomorphism invariant gauge theory of the Lorentz group, with Lagrangian of the type $f(F\wedge F)$, where $F$ is the curvature 2-form of the spin connection. A theory from this class with a generic $f$ is known to propagate eight degrees of freedom: a massless graviton, a massive graviton and a scalar. General Relativity in this formalism avoids extra degrees of freedom because the function $f$ is special and leads to the appearance of six extra primary constraints on the phase space variables. Our main new result is that there are other theories…
f(T) gravity is a generalization of the teleparallel equivalent of general relativity (TEGR), where T is the torsion scalar made up of the Weitzenböck connection. This connection describes a spacetime with zero curvature but with nonvanishing torsion, which fully encodes the gravitational phenomena. We will present recent results in f(T) gravity related with the issue of the degrees of freedom of the theory. In particular, we discuss the recent finding that f(T) gravity has one extra degree of freedom compared with TEGR, which was concluded through a detailed Hamiltonian analysis of the constr…
Constraining neutrino mass and extra relativistic degrees of freedom in dynamical dark energy models using Planck 2015 data in combination with low-redshift cosmological probes: basic extensions to $Λ$CDM cosmology
We consider massive higher-spin multiplets coupled to quantum gravity and compute their contributions to the gravitational beta functions at one loop. Such theories, if quantized with the Feynman prescription, would contain ghosts. Instead, those degrees of freedom are turned into purely virtual particles by means of the fakeon prescription and the resulting theories are both renormalizable and unitary. We extract the necessary number of fields to obtain asymptotic freedom by solving the relevant renormalization-group equations in the ultraviolet limit. We show that in the case of irreducible …
Scuola Superiore Meridionale（南方高等学院）；INFN, Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）；Theoretical Particle Physics and Cosmology Group, Physics Department, King’s College London, University of London（伦敦大学国王学院理论粒子物理与宇宙学组）；Department of Physics and EHU Quantum Center, University of the Basque Country UPV/EHU（巴斯克大学物理学系和EHU量子中心）
Gravitational-wave detectors are exquisitely sensitive instruments and routinely enable ground-breaking observations of novel astronomical phenomena. However, they also witness non-stationary, non-Gaussian noise that can be mistaken for astrophysical sources, lower detection confidence, or simply complicate the extraction of signal parameters from noisy data. To address this, we present iDQ, a supervised learning framework to autonomously detect noise artifacts in gravitational-wave detectors based only on auxiliary degrees of freedom insensitive to gravitational waves. iDQ has operated in low…
Degenerate scalar-tensor theories of gravity extend general relativity by a single degree of freedom, despite their equations of motion being higher than second order. In some cases, this is a mere consequence of a disformal field redefinition carried out in a non-degenerate theory. More generally, this is made possible by the existence of an additional constraint that removes the would-be ghost. It has been noted that this constraint can be thwarted when the coupling to matter involves time derivatives of the metric, which results in a modification of the canonical momenta of the gravitationa…
We investigate the linear regime of f(R) = R + alpha R^2 gravity for static, spherically symmetric and asymptotically flat configurations of matter. We show that, in vacuum and deep inside the range of the extra scalar degree of freedom, the post-Newtonian parameter gamma is not equal to 1/2, as established in the literature, but it assumes larger values depending on the pressure of the star. We provide an explicit expression for gamma in terms of the mass, of the integrated pressure of the star and of the ratio between the star's radius and the range of the extra degree of freedom. We corrobo…
We prove the equivalence between non-local gravity with an arbitrary form factor and a non-local gravitational system with an extra rank-2 symmetric tensor. Thanks to this reformulation, we use the diffusion-equation method to transform the dynamics of renormalizable non-local gravity with exponential operators into a higher-dimensional system local in spacetime coordinates. This method, first illustrated with a scalar field theory and then applied to gravity, allows one to solve the Cauchy problem and count the number of initial conditions and of non-perturbative degrees of freedom, which is …
We compute non-perturbative flow equations for the couplings of quantum gravity in fourth order of a derivative expansion. The gauge invariant functional flow equation for arbitrary metrics allows us to extract $β$-functions for all couplings. In our truncation we find two fixed points. One corresponds to asymptotically free higher derivative gravity, the other is an extension of the asymptotically safe fixed point in the Einstein-Hilbert truncation or extensions thereof. The infrared limit of the flow equations entails only unobservably small modifications of Einstein gravity coupled to a sca…
