Gravitational Degrees Of Freedom Research Articles

A new gravitational theory and dark matter problem

We propose a new gravitational theory with torsion based on Riemann–Cartan geometry, in which all physical quantities are dynamical. In addition to the spacetime metric, the gravitational degrees of freedom in this theory also include the torsion and two scalar fields. The energy-momentum tensor of the matter fields in this theory is also proposed. A spherically symmetric static vacuum solution of the theory is obtained. It turns out that this solution can fit the observational data of the rotation curve outside the stellar disk in the Milky Way. Therefore, the galactic dark matter may just be the gravitational effect of the theory with torsion.

Carrollian hydrodynamics and symplectic structure on stretched horizons

The membrane paradigm displays underlying connections between a timelike stretched horizon and a null boundary (such as a black hole horizon) and bridges the gravitational dynamics of the horizon with fluid dynamics. In this work, we revisit the membrane viewpoint of a finite-distance null boundary and present a unified geometrical treatment of the stretched horizon and the null boundary based on the rigging technique of hypersurfaces. This allows us to provide a unified geometrical description of null and timelike hypersurfaces, which resolves the singularity of the null limit appearing in the conventional stretched horizon description. We also extend the Carrollian fluid picture and the geometrical Carrollian description of the null horizon, which have been recently argued to be the correct fluid picture of the null boundary, to the stretched horizon. To this end, we draw a dictionary between gravitational degrees of freedom on the stretched horizon and the Carrollian fluid quantities and show that Einstein’s equations projected onto the horizon are the Carrollian hydrodynamic conservation laws. Lastly, we report that the gravitational pre-symplectic potential of the stretched horizon can be expressed in terms of conjugate variables of Carrollian fluids and also derive the Carrollian conservation laws and the corresponding Noether charges from symmetries.

Hybrid geometrodynamics: a Hamiltonian description of classical gravity coupled to quantum matter

We generalize the Hamiltonian picture of general relativity coupled to classical matter, known as geometrodynamics, to the case where such matter is described by a quantum field theory in curved spacetime, but gravity is still described by a classical metric tensor field over a spatial hypersurface and its associated momentum. Thus, in our approach there is no non-dynamic background structure, apart from the manifold of events, and the gravitational and quantum degrees of freedom have their dynamics inextricably coupled. Given the Hamiltonian nature of the framework, we work with the generators of hypersurface deformations over the manifold of quantum states. The construction relies heavily on the differential geometry of a fibration of the set of quantum states over the set of gravitational variables. An important mathematical feature of this work is the use of Minlos’s theorem to characterize Gaussian measures over the space of matter fields and of Hida distributions to define a common superspace to all possible Hilbert spaces with different measures, to properly characterize the Schrödinger wave functional picture of QFT in curved spacetime. This allows us to relate states within different Hilbert spaces in the case of vacuum states or measures that depend on the gravitational degrees of freedom, as the ones associated to Ashtekar’s complex structure. This is achieved through the inclusion of a quantum Hermitian connection for the fibration, which will have profound physical implications. The most remarkable physical features of the construction are norm conservation of the quantum state (even if the total dynamics are non-unitary), the clear identification of the hybrid conserved quantities and the description of a dynamical backreaction of quantum matter on geometry and vice versa, which shall modify the physical properties the gravitational field would have in the absence of backreaction.

Pathological Character of Modifications to Coincident General Relativity: Cosmological Strong Coupling and Ghosts in f(Q) Theories.

The intrinsic presence of ghosts in the symmetric teleparallel framework is elucidated. We illustrate our general arguments in f(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(Q) cosmologies and clarify the number of propagating degrees of freedom in these theories.

Null Raychaudhuri: canonical structure and the dressing time

We initiate a study of gravity focusing on generic null hypersurfaces, non-perturbatively in the Newton coupling. We present an off-shell account of the extended phase space of the theory, which includes the expected spin-2 data as well as spin-0, spin-1 and arbitrary matter degrees of freedom. We construct the charges and the corresponding kinematic Poisson brackets, employing a Beltrami parameterization of the spin-2 modes. We explicitly show that the constraint algebra closes, the details of which depend on the non-perturbative mixing between spin-0 and spin-2 modes. Finally we show that the spin zero sector encodes a notion of a clock, called dressing time, which is dynamical and conjugate to the constraint.It is well-known that the null Raychaudhuri equation describes how the geometric data of a null hypersurface evolve in null time in response to gravitational radiation and external matter. Our analysis leads to three complementary viewpoints on this equation. First, it can be understood as a Carrollian stress tensor conservation equation. Second, we construct spin-0, spin-2 and matter stress tensors that act as generators of null time reparametrizations for each sector. This leads to the perspective that the null Raychaudhuri equation can be understood as imposing that the sum of CFT-like stress tensors vanishes. Third, we solve the Raychaudhuri constraint non-perturbatively. The solution relates the dressing time to the spin-2 and matter boost charge operators.Finally we establish that the corner charge corresponding to the boost operator in the dressing time frame is monotonic. These results show that the notion of an observer can be thought of as emerging from the gravitational degrees of freedom themselves. We briefly mention that the construction offers new insights into focusing conjectures.

Scalar-tensor theory with EGB term from Einstein Chern-Simons gravity

It is shown that the compactification á la Randall-Sundrum of the so-called, five-dimensional Einstein-Chern-Simons action gravity leads to an action for a four-dimensional scalar-tensor gravity that includes a Gauss-Bonnet term, which belongs to a particular case of the action of the Horndeski theory. The five-dimensional action includes new gravitational degrees of freedom that were introduced requiring that the action be invariant under symmetries greater than the usual Poincaré or (A)dS symmetries, namely the so-called generalized Poincare algebras B5.

Direct Tests of General Relativity under Screening Effect with Galaxy-scale Strong Lensing Systems

Observations of galaxy-scale strong gravitational lensing (SGL) systems have enabled unique tests of nonlinear departures from general relativity (GR) on the galactic and supergalactic scales. One of the most important cases of such tests are constraints on the gravitational slip between two scalar gravitational potentials. In this paper, we use a newly compiled sample of strong gravitational lenses to test the validity of GR, focusing on the screening effects on the apparent positions of lensed sources relative to the GR predictions. This is the first simultaneous measurement of the post-Newtonian parameter (γ PN) and the screening radius (Λ) without any assumptions about the contents of the universe. Our results suggest that the measured parameterized post-Newtonian is marginally consistent with GR (γ PN = 1) with increasing screening radius (Λ = 10–300 kpc), although the choice of lens models may have a significant influence on the final measurements. Based on a well-defined sample of 5000 simulated strong lenses from the forthcoming LSST, our methodology will provide a strong extragalactic test of GR with an accuracy of 0.5%, assessed up to scales of Λ ∼ 300 kpc. For the current and future observations of available SGL systems, there is no noticeable evidence indicating some specific cutoff scale on kiloparsec-megaparsec scales, beyond which new gravitational degrees of freedom are expressed.

Broader view of bimetric MOND

All existing treatments of bimetric MOND (BIMOND) -- a class of relativistic versions of MOND -- have dealt with a rather restricted sub-class: The Lagrangian of the interaction between the gravitational degrees of freedom -- the two metrics -- is a function of a certain {\it single} scalar argument built from the difference in connections of the two metrics. I show that the scope of BIMOND is much richer: The two metrics can couple through several scalars to give theories that all have a "good" nonrelativistic (NR) limit -- one that accounts correctly, a-la MOND, for the dynamics of galactic systems, {\it including gravitational lensing}. This extended-BIMOND framework exhibits a qualitative departure from the way we think of MOND at present, as encapsulated, in all its aspects, by one "interpolating function" of one acceleration variable. After deriving the general field equations, I pinpoint the subclass of theories that satisfy the pivotal requirement of a good NR limit. These involve three independent, quadratic scalar variables. In the NR limit these scalars all reduce to the same acceleration scalar, and the NR theory then does hinge on one function of a {\it a single} acceleration variable -- representing the NR MOND "interpolating function", whose form is largely dictated by the observed NR galactic dynamics. However, these scalars behave differently, in different relativistic contexts. So, the full richness of the multi-variable Lagrangian, as it enters cosmology, for example, is hardly informed by what we learn from observations of galactic dynamics. In this paper, I present the formalism, with some generic examples. I also consider some cosmological solutions where the two metrics are small departures from one Friedman-Lemaitre-Robertson-Walker metric. This may offer a framework for describing cosmology within the extended BIMOND.

Coherent state superpositions, entanglement, and gauge/gravity correspondence

We focus on two types of coherent states, the coherent states of multi-graviton states and the coherent states of giant graviton states, in the context of gauge/gravity correspondence. We conveniently use a phase shift operator and its actions on the superpositions of these coherent states. We find N-state Schrödinger cat states, which approach the one-row Young tableau states, with fidelity between them asymptotically reaching 1 at large N. The quantum Fisher information of these states is proportional to the variance of the excitation energy of the underlying states and characterizes the localizability of the states in the angular direction in the phase space. We analyze the correlation and entanglement between gravitational degrees of freedom using different regions of the phase space plane in bubbling AdS. The correlation between two entangled rings in the phase space plane is related to the area of the annulus between the two rings. We also analyze two types of noisy coherent states, which can be viewed as interpolated states that interpolate between a pure coherent state in the noiseless limit and a maximally mixed state in the large noise limit.

Non-uniqueness of massless transverse-traceless graviton

We study a theory of minimally modified gravity called cuscuton/VCDM that propagates only two gravitational degrees of freedom. Despite being apparently different from general relativity (GR), it is in principle possible that this theory might be obtained via a field redefinition starting from the GR action. This would make the vacuum theory equivalent to GR and the theory would differ from GR only in the presence of matter. In this paper, studying the dispersion relation of gravitational waves and the dynamics of the Bianchi-I universe, we prove that such a field redefinition does not exist and that the theory differs from GR already in vacuum.

Possible Explanation of the Dynamics of the Universe Expansion without Dark Energy and without New Gravitational Degrees of Freedom

The commonly accepted view is that the Universe is currently in the dark energy dominance era (estimated to start about 5 billion years ago)—the era where yet unknown dark energy dominates over the gravitation and is responsible for the observed acceleration of the Universe expansion. In the present paper, we consider a “gas” of a large number of gravitating neutral nonrelativistic particles having a practically infinite lifetime and zero or very little interaction with the rest of the matter (neutrinos could be an example). One of the central points is the application of Dirac’s Generalized Hamiltonian Dynamics to pairs of these particles. Another central point is the application of the virial theorem to pairs of zero total energy. We demonstrate that as a result, the gravitational interaction within the entire system effectively decreases. Together with the observational fact of the Universe rotation (according to Shamir’s study of 2020), this model provides a possible explanation of the entire history of the Universe expansion: both the era of the decelerating expansion and the current era of the accelerated expansion.

Generalized SU(2) Proca theory reconstructed and beyond

As a modified gravity theory that introduces new gravitational degrees of freedom, the generalized SU(2) Proca theory (GSU2P for short) is the non-Abelian version of the well-known generalized Proca theory where the action is invariant under global transformations of the SU(2) group. This theory was formulated for the first time in Phys. Rev. D 94 (2016) 084041, having implemented the required primary constraint-enforcing relation to make the Lagrangian degenerate and remove one degree of freedom from the vector field in accordance with the irreducible representations of the Poincar\'e group. It was later shown in Phys. Rev. D 101 (2020) 045008, ibid 045009, that a secondary constraint-enforcing relation, which trivializes for the generalized Proca theory but not for the SU(2) version, was needed to close the constraint algebra. It is the purpose of this paper to implement this secondary constraint-enforcing relation in GSU2P and to make the construction of the theory more transparent. Since several terms in the Lagrangian were dismissed in Phys. Rev. D 94 (2016) 084041 via their equivalence to other terms through total derivatives, not all of the latter satisfying the secondary constraint-enforcing relation, the work was not so simple as directly applying this relation to the resultant Lagrangian pieces of the old theory. Thus, we were motivated to reconstruct the theory from scratch. In the process, we found the beyond GSU2P.

AdS instability: resonant system for gravitational perturbations of AdS5 in the cohomogeneity-two biaxial Bianchi IX ansatz

We consider five-dimensional, vacuum Einstein equations with negative cosmological constant within cohomogenity-two biaxial Bianchi IX ansatz. This model allows to investigate the stability of AdS without adding any matter to the energy-momentum tensor, thus analyzing instability of genuine gravitational degrees of freedom. We derive the resonant system and identify vanishing secular terms. The results resemble those obtained for Einstein equations coupled to a spherically-symmetric, massless scalar field, backing the evidence that the scalar field model captures well the relevant features of AdS instability problem. We also list recurrence relations for the interaction coefficients of the resonant system, which might be useful in both numerical simulations and further analytical studies.

Cosmological perturbations in the Regge-Wheeler formalism

We study linear perturbations of the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological model in the Regge-Wheeler formalism which is a standard framework to study perturbations of spherically-symmetric black holes. In particular, we show that the general solution of linear perturbation equations can be given in terms of two copies of a master scalar satisfying scalar wave equation on the FLRW background (with a Regge-Wheeler/Zerilli type potential) thus representing two gravitational degrees of freedom, and one scalar satisfying a transport type equation representing (conformal) matter perturbation. We expect the Regge-Wheeler formalism to be easily extended to include nonlinear perturbations, akin to to the recent work [Phys. Rev. D 96, 124026 (2017)].

Horizonless ultracompact objects and dark matter in quadratic gravity

We show that in quadratic gravity sufficiently light objects must be horizonless and construct explicit analytic examples of horizonless ultracompact objects (UCOs), which are more compact than Schwarzschild black holes. Due to the quadratic terms, gravity becomes soft and eventually vanishes in the high-energy limit leading to a “linearization mechanism”: light objects can be described by the linearized theory when their Schwarzschild radius is smaller than the Compton wavelength of the new gravitational degrees of freedom. As a result, we can analytically describe UCOs with a mass-to-radius ratio higher than for a Schwarzschild black hole. The corresponding spacetime is regular everywhere. We show that the Ostrogradsky instabilities can be avoided and discuss the relation with the Higgs vacuum metastability. Due to the lack of a horizon, light UCOs do not evaporate. Therefore, they may play the role of dark matter. We briefly discuss their phenomenology.

Quantum Mechanics, Formalization and the Cosmological Constant Problem

Based on formal arguments from Zermelo–Fraenkel set theory we develop the environment for explaining and resolving certain fundamental problems in physics. By these formal tools we show that any quantum system defined by an infinite dimensional Hilbert space of states interferes with the spacetime structure M. M and the quantum system both gain additional degrees of freedom, given by models of Zermelo–Fraenkel set theory. In particular, M develops the ground state where classical gravity vanishes. Quantum mechanics distinguishes set-theoretic random forcing such that M and gravitational degrees of freedom are parameterized by extended real line. The large scale smooth geometry compatible with the forcing extensions is one of exotic smoothness structures of $${\mathbb {R}}^4$$ . The amoeba forcing makes the old real line to have Lebesgue measure zero in the extended one. We apply the entire procedure to the cosmological constant problem, especially to discard the zero-modes contributions to the gravitational vacuum density. Moreover, there exists certain exotic smooth $${\mathbb {R}}^4$$ from which one determines the realistic, agreeing with observation, small value of the vacuum energy density.

The gravitational rainbow beyond Einstein gravity

The recent direct detection of gravitational waves have been successfully used to examine the basic properties of the gravitational degrees of freedom. They set an upper bound on their mass and constrain their speed of propagation with unprecedented accuracy. Within the current realm of observational and theoretical constraints, we explore the possibility for gravity to depart from general relativity (GR) in the infrared and derive the implications on our observable Universe. We also investigate whether these types of models could ever enjoy a standard analytic UV completion.

Inflationary perturbations with Lifshitz scaling

Instead of Lorentz invariance, gravitational degrees of freedom may obey Lifshitz scaling at high energies, as it happens in Hořava's proposal for quantum gravity. We study consequences of this proposal for the spectra of primordial perturbations generated at inflation. Breaking of 4D diffeomorphism (Diff) invariance down to the foliation-preserving Diff in Hořava-Lifshitz (HL) gravity leads to appearance of a scalar degree of freedom in the gravity sector, khronon, which describes dynamics of the time foliation. One can naively expect that mixing between inflaton and khronon will jeopardize conservation of adiabatic perturbations at super Hubble scales. This indeed happens in the projectable version of the theory. By contrast, we find that in the non-projectable version of HL gravity, khronon acquires an effective mass which is much larger than the Hubble scale well before the Hubble crossing time and decouples from the adiabatic curvature perturbation ζ sourced by the inflaton fluctuations. As a result, at super Hubble scales the adiabatic perturbation ζ behaves as in an effectively single field system and its spectrum is conserved in time. Lifshitz scaling is imprinted in the power spectrum of ζ through the modified dispersion relation of the inflaton. We point out violation of the consistency relation between the tensor-to-scalar ratio and the spectral tilt of primordial gravitational waves and suggest that it can provide a signal of Lorentz violation in inflationary era.

Yang-Mills theory from the worldsheet

We give a new description of classical Yang-Mills theory by coupling a two-dimensional chiral CFT (which gives the tree-level S-matrix of Yang-Mills theory at genus zero) to a background non-abelian gauge field. The resulting model is solvable, and when the gravitational degrees of freedom are decoupled the non-linear Yang-Mills equations are imposed as an exact worldsheet anomaly cancellation condition. When gravitational modes are reinstated, we find gauge anomalies analogous to those appearing in heterotic string theory.

Noncommutative gravity with self-dual variables

We build a noncommutative extension of Palatini–Holst theory on a twist-deformed spacetime, generalizing a model that has been previously proposed by Aschieri and Castellani. The twist deformation entails an enlargement of the gauge group, and leads to the introduction of new gravitational degrees of freedom. In particular, the tetrad degrees of freedom must be doubled, thus leading to a bitetrad theory of gravity. The model is shown to exhibit new duality symmetries. The introduction of the Holst term leads to a dramatic simplification of the dynamics, which is achieved when the Barbero–Immirzi parameter takes the value , corresponding to a self-dual action. We study in detail the commutative limit of the model, focusing in particular on the role of torsion and non-metricity. The effects of spacetime noncommutativity are taken into account perturbatively, and are computed explicitly in a simple example. Connections with bimetric theories and the role of local conformal invariance in the commutative limit are also explored.