The null curvature condition (NCC) is the requirement that the Ricci curvature of a Lorentzian manifold be nonnegative along null directions, which ensures the focusing of null geodesic congruences. In this note, we show that the NCC together with the causal structure significantly constrain the metric. In particular, we prove that any conformal rescaling of a vacuum spacetime introduces either geodesic incompleteness or negative null curvature, provided the conformal factor is non-constant on at least one complete null geodesic. In the context of bulk reconstruction in AdS/CFT, our results combined with the technique of light-cone cuts can be used in vacuum spacetimes to reconstruct the full metric in regions probed by complete null geodesics reaching the boundary. For non-vacuum spacetimes, our results constrain the conformal factor, giving an approximate reconstruction of the metric.

We study spherically symmetric spacetimes in Einstein-aether theory in three different coordinate systems, the isotropic, Painlev\`e-Gullstrand, and Schwarzschild coordinates, and present both time-dependent and time-independent exact vacuum solutions. In particular, in the isotropic coordinates we find a class of exact static solutions characterized by a single parameter $c_{14}$ in closed forms, which satisfies all the current observational constraints of the theory, and reduces to the Schwarzschild vacuum black hole solution in the decoupling limit ($c_{14} = 0$). However, as long as $c_{14} \not= 0$, a marginally trapped throat with a finite non-zero radius always exists, and in one side of it the spacetime is asymptotically flat, while in the other side the spacetime becomes singular within a finite proper distance from the throat, although the geometric area is infinitely large at the singularity. Moreover, the singularity is a strong and spacetime curvature singularity, at which both of the Ricci and Kretschmann scalars become infinitely large.

We report three manifestly Lorentz-invariant Hamiltonian formulations of minimally and nonminimally coupled fermion fields to the Holst action. These formulations are achieved by making a suitable parametrization of both the tetrad and the Lorentz connection, which allows us to integrate out some auxiliary fields without spoiling the local Lorentz symmetry. They have the peculiarity that their noncanonical symplectic structures as well as the phase-space variables for the gravitational sector are real. Moreover, two of these Hamiltonian formulations involve half-densitized fermion fields. We also impose the time gauge on these formulations, which leads to real connections for the gravitational configuration variables. Finally, we perform a symplectomorphism in one of the manifestly Lorentz-invariant Hamiltonian formulations and analyze the resulting formulation, which becomes the Hamiltonian formulation of fermion fields minimally coupled to the Palatini action for particular values of the coupling parameters.

Using sophisticated string theory calculations, Maldacena and Susskind have intriguingly shown that near-extremal black holes are characterized by a {\it finite} mass gap above the corresponding zero-temperature (extremal) black-hole configuration. In the present compact paper we explicitly prove that the minimum energy gap ${\cal E}_{\text{gap}}=\hbar^2/M^3$, which characterizes the mass spectra of near-extremal charged Reissner-Nordstr\"om black holes, can be inferred from a simple semi-classical analysis.

Starting with an entropy that includes volumetric, area and length terms as well as logarithmic contributions, we derive the corresponding modified Newtonian gravity and derive the expression for planetary orbits. We calculate the shift of the perihelion of Mercury to find bounds to the parameters associated to the modified Newtonian gravity. We compare the parameter associated to the volumetric contribution in the entropy-area relationship with the value derived for galactic rotation curves and the value obtained from the cosmological constant.

Gravitational waves from compact binary coalescences provide a unique laboratory to test properties of compact objects. As alternatives to the ordinary black holes in general relativity, various exotic compact objects have been proposed. Some of them have largely different values of the tidal deformability and spin-induced quadrupole moment from those of black holes, and their binaries could be distinguished from binary black hole by using gravitational waves emitted during their inspiral regime, excluding the highly model-dependent merger and ring-down regimes. We reanalyze gravitational waves from low-mass merger events in the GWTC-2, detected by the Advanced LIGO and Advanced Virgo. Focusing on the influence of tidal deformability and spin-induced quadrupole moment in the inspiral waveform, we provide model-independent constraints on deviations from the standard binary black hole case. We find that all events that we have analyzed are consistent with the waveform of binary black hole in general relativity. Bayesian model selection shows that the hypothesis that the binary is composed of exotic compact objects is disfavored by all events.

This article provides a self-contained pedagogical introduction to the relativistic kinetic theory of a dilute gas propagating on a curved spacetime manifold (M,g) of arbitrary dimension. Special emphasis is made on geometric aspects of the theory in order to achieve a formulation which is manifestly covariant on the relativistic phase space. Whereas most previous work has focussed on the tangent bundle formulation, here we work on the cotangent bundle associated with (M,g) which is more naturally adapted to the Hamiltonian framework of the theory. In the first part of this work we discuss the relevant geometric structures of the cotangent bundle T*M, starting with the natural symplectic form on T*M, the one-particle Hamiltonian and the Liouville vector field, defined as the corresponding Hamiltonian vector field. Next, we discuss the Sasaki metric on T*M and its most important properties, including the role it plays for the physical interpretation of the one-particle distribution function. In the second part of this work we describe the general relativistic theory of a collisionless gas, starting with the derivation of the collisionless Boltzmann equation for a neutral simple gas. Subsequently, the description is generalized to a charged gas consisting of several species of particles and the general relativistic Vlasov-Maxwell equations are derived for this system. The last part of this work is devoted to a transparent derivation of the collision term, leading to the general relativistic Boltzmann equation on (M,g). The meaning of global and local equilibrium and the strident restrictions for the existence of the former on a curved spacetime are discussed. We close this article with an application of our formalism to the expansion of a homogeneous and isotropic universe filled with a collisional simple gas and its behavior in the early and late epochs. [abbreviated version]

It is commonly known that Killing vectors and tensors are in one-to-one correspondence with polynomial first integrals of the geodesic equation. In this work, metrics admitting nonpolynomial first integrals of the geodesic equation are constructed, each of which revealing a chain of generalised Killing vectors.

I discuss possible consequences of A. D. Sakharov's hypothesis of cosmological transitions with changes in the signature of the metric, based on the path integral approach. This hypothesis raises a number of mathematical and philosophical questions. Mathematical questions concern the definition of the path integral to include integration over spacetime regions with different signatures of the metric. One possible way to describe the changes in the signature is to admit time and space coordinates to be purely imaginary. It may look like a generalization of what we have in the case of pseudo-Riemannian manifolds with a non-trivial topology. The signature in these regions can be fixed by special gauge conditions on components of the metric tensor. The problem is what boundary conditions should be imposed on the boundaries of these regions and how they should be taken into account in the definition of the path integral. The philosophical question is what distinguishes the time coordinate among other coordinates but the sign of the corresponding principal value of the metric tensor. In particular, I try to speculate how the existence of the regions with different signature can affect the evolution of the Universe.

We study how higher-order gravity affects Higgs inflation in the Palatini formulation. We first review the metric and Palatini formulations in comparative manner and discuss their differences. Next cosmic inflation driven by a scalar field and inflationary observables are discussed. After this we review the Higgs inflation and compute the inflationary observables both in the metric and Palatini formulations. We then consider adding higher-order terms of the curvature to the action. We derive the equations of motion for the most general action quadratic in the curvature that does not violate parity in both the metric and Palatini formulations. Finally we present a new result. We analyse Higgs inflation in the Palatini formulation with higher-order curvature terms. We consider a simplified scenario where only terms constructed from the symmetric part of the Ricci tensor are added to the action. This implies that there are no new gravitational degrees of freedom, which makes the analysis easier. As a new result we found out that the scalar perturbation spectrum is unchanged, but the tensor perturbation spectrum is suppressed by the higher-order curvature couplings.

Dark energy stars research is an issue of great interest since recent astronomical observations with respect to measurements in distant supernovas, cosmic microwave background and weak gravitational lensing confirm that the universe is undergoing a phase of accelerated expansion and this cosmological behavior is caused by the presence of a cosmic fluid which has a strong negative pressure that allows to explain the expanding universe. In this paper, we obtained new relativistic stellar configurations within the framework of Einstein-Gauss-Bonnet (EGB) gravity considering negative anisotropic pressures and the equation of state pr={\omega}\r{ho} where pr is the radial pressure, {\omega} is the dark energy parameter, and \r{ho} is the dark energy density. We have chosen a modified version of metric potential proposed by Korkina-Orlyanskii (1991). For the new solutions we checked that the radial pressure, metric coefficients, energy density and anisotropy are well defined and are regular in the interior of the star and are dependent of the values of the Gauss-Bonnet coupling constant. The solutions found can be used in the development of dark energy stars models satisfying all physical acceptability conditions, but the causality condition and strong energy condition cannot be satisfied.

With the increasing sensitivities of the gravitational wave detectors and more detectors joining the international network, the chances of detection of a stochastic GW background (SGWB) is progressively increasing. Different astrophysical and cosmological processes are likely to give rise to backgrounds with distinct spectral signatures and distributions on the sky. The observed background will therefore be a superposition of these components. Hence, one of the first questions that will come up after the first detection of a SGWB will likely be about identifying the dominant components and their distributions on the sky. Both these questions were addressed separately in the literature, namely, how to separate components of isotropic backgrounds and how to probe the anisotropy of a single component. Here, we address the question of how to separate distinct anisotropic backgrounds with (sufficiently) different spectral shapes. We first obtain the combined Fisher information matrix from folded data using an efficient analysis pipeline PyStoch, which incorporates covariances between pixels and spectral indices. This is necessary for estimating the detection statistic and setting upper limits. However, based on a recent study, we ignore the pixel-to-pixel noise covariance that does not have a significant effect on the results at the present sensitivity levels of the detectors. We establish the validity of our formalism using injection studies. We show that the joint analysis accurately separates and estimates backgrounds with different spectral shapes and different sky distributions with no major bias. This does come at the cost of increased variance. Thus making the joint upper limits safer, though less strict than the individual analysis. We finally set joint upper limits on the multi-component anisotropic background using aLIGO data taken up to the first half of the third observing run.

The diffraction patterns of lensed gravitational waves encode information about their propagation speeds. If gravitons have mass, the dispersion relation and speed of gravitational waves will be affected in a frequency-dependent manner, which would leave potentially detectable traces in the diffraction pattern if the waves are lensed. In this paper, we study how the alternative dispersion relation induced by massive gravitons affects gravitational waves lensed by point-mass lenses, such as intermediate-mass black holes. By detecting a single lensed gravitational-wave signal, we can measure the graviton mass with an accuracy better than the combined measurement across $\mathcal{O}(10^2)$ unlensed signals. Our method can be generalised to other lens types, gravitational-wave sources, and detector networks, opening up new ways to measure the graviton mass through gravitational-wave detection.

In this paper, a complexity factor is devised for a non-static cylindrical system in the framework of massive Brans-Dicke theory. The definition of complexity is developed by taking into account the essential physical characteristics (such as anisotropy, inhomogeneity, etc.) of the system. In order to determine the complexity factor of the self-gravitating object, we acquire structure scalars from the orthogonal splitting of the Riemann tensor. Moreover, we discuss two patterns of evolution and choose the homologous mode as the simplest pattern under the influence of massive scalar field. We derive solutions in the absence as well as presence of heat dissipation for a specific form of the scalar field. The factors that induce complexity in an initially complexity-free system are also examined. It is concluded that the massive scalar field as well as heat dissipation contribute to the complexity of the celestial system. Thus, a dynamical cylinder is more complex as compared to its static counterpart.

In a recent series of papers we have shown how the eikonal/geometrical optics approximation can be used to calculate analytically the fundamental quasinormal mode frequencies associated with coupled systems of wave equations, which arise, for instance, in the study of perturbations of black holes in gravity theories beyond General Relativity. As a continuation to this series, we here focus on the quasinormal modes of nonrotating black holes in scalar Gauss-Bonnet gravity assuming a small-coupling expansion. We show that the axial perturbations are purely tensorial and are described by a modified Regge-Wheeler equation, while the polar perturbations are of mixed scalar-tensor character and are described by a system of two coupled wave equations. When applied to these equations, the eikonal machinery leads to axial modes that deviate from the general relativistic results at quadratic order in the Gauss-Bonnet coupling constant. We show that this result is in agreement with an analysis of unstable circular null orbits around blackholes in this theory, allowing us to establish the geometrical optics-null geodesic correspondence for the axial modes. For the polar modes the small-coupling approximation forces us to consider the ordering between eikonal and small-coupling perturbative parameters; one of which we show, by explicit comparison against numerical data, yields the correct identification of the quasinormal modes of the scalar-tensor coupled system of wave equations. These corrections lift the general relativistic degeneracy between scalar and tensorial eikonal quasinormal modes at quadratic order in Gauss-Bonnet coupling in a way reminiscent of the Zeeman effect. In general, our analytic, eikonal quasinormal mode frequencies (normalized to the General Relativity ones) agree with numerical results with an error of $\sim 10\%$ in the regime of small coupling constant. (abridged)

We study the plane-symmetric collision of two gravitational waves and describe the global spacetime geometry generated by this collision. To this end, we formulate the characteristic initial value problem for the Einstein equations, when Goursat data describing the incoming waves are prescribed on two null hypersurfaces. We then construct a global solution representing a cyclic spacetime based on junction conditions associated with a prescribed singularity scattering map (a notion recently introduced by the authors). From a mathematical analysis standpoint, this amounts to a detailed analysis of the Goursat and Fuchsian initial value problems associated with singular hyperbolic equations, when junction conditions at interfaces are prescribed. In our construction, we introduce a partition into monotonicity diamonds (that is, suitable spacetime domains) and we construct the solution by concatenating domains across interfaces of timelike, null, or spacelike type.

It is well known in the literature that vacuum fluctuations can induce a random motion of particles which is sometimes called quantum Brownian motion or quantum stochastic motion. In this paper, we consider Lorentz Invariance Violation (LIV) in an acoustic spatially flat Friedman-Robertson-Walker (FRW) geometry. In particular, we are looking for the LIV effects in the stochastic motion of scalar and massive test particles. This motion is induced by a massless quantized scalar field on this geometry, which in turn is derived from an Abelian Higgs model with LIV. Deviations in the velocity dispersion of the particles proportional to the LIV parameter are found.

In a previous work (arXiv:1609.05654v2), an experimental setup aiming at the measurement of deviations from the Newtonian $1/r^2$ distance dependence of gravitational interactions was proposed. The theoretical idea behind this setup was to study the trajectories of a "Satellite" with a mass $m_{\rm S} \sim {\cal O}(10^{-9})$ $\mathrm{g}$ around a "Planet" with mass $m_{\rm P} \in [10^{-7},10^{-5} ]$ $\mathrm{g}$, looking for precession of the orbit. The observation of such feature induced by gravitational interactions would be an unambiguous indication of a gravitational potential with terms different from $1/r$ and, thus, a powerful tool to detect deviations from Newton's $1/r^2$ law. In this paper we optimize the proposed setup in order to achieve maximal sensitivity to look for {\em Beyond-Newtonian} corrections. We study in detail possible background sources that could induce precession and quantify their impact on the achievable sensitivity. We conclude that a dynamical measurement of deviations from newtonianity can test Yukawa-like corrections to the $1/r$ potential with strength as low as $\alpha \sim 10^{-2}$ for distances as small as $\lambda \sim 10 \, \mu\mathrm{m}$.

In relativistic Quantum Field Theory (QFT) ideal measurements of certain observables are physically impossible without violating causality. This prompts two questions: i) can a given observable be ideally measured in QFT, and ii) if not, in what sense can it be measured? Here we formulate a necessary and sufficient condition that any measurement, and more generally any state update (quantum operation), must satisfy to respect causality. Our focus is scalar QFT, although our results should be applicable to observables in fermionic QFT. We argue that for unitary `kicks' and operations involving 1-parameter families of Kraus operators, e.g. Gaussian measurements, the only causal observables are smeared fields and the identity - the basic observables in QFT. We provide examples with more complicated operators such as products of smeared fields, and show that the associated state updates are acausal, and hence impossible. Despite this, one can still recover expectation values of such operators, and we show how to do this using only causal measurements of smeared fields.

Bimetric gravity is a ghost-free and observationally viable extension of general relativity, exhibiting both a massless and a massive graviton. The observed abundances of light elements can be used to constrain the expansion history of the Universe at the period of Big Bang nucleosynthesis. Applied to bimetric gravity, we readily obtain constraints on the theory parameters which are complementary to other observational probes. For example, the mixing angle between the two gravitons must satisfy $\theta \lesssim 18^\circ$ in the graviton mass range $m_\mathrm{FP} \gtrsim 10^{-16} \, \mathrm{eV}/c^2$, representing a factor of two improvement compared with other cosmological probes.

Orbital eccentricity is one of the most robust discriminators for distinguishing between dynamical and isolated formation scenarios of binary black holes mergers using gravitational-wave observatories such as LIGO and Virgo. Using state-of-the-art cluster models, we show how selection effects impact the detectable distribution of eccentric mergers from clusters. We show that the observation (or lack thereof) of eccentric binary black hole mergers can significantly constrain the fraction of detectable systems that originate from dynamical environments such as dense star clusters. After roughly 150 observations, observing no eccentric binary signals would indicate that clusters cannot make up the majority of the merging binary black hole population in the local Universe (95% credibility). However, if dense star clusters dominate the rate of eccentric mergers and a single system is confirmed to be measurably eccentric in the first and second gravitational-wave transient catalogues, clusters must account for at least 14% of detectable binary black hole mergers. The constraints on the fraction of detectable systems from dense star clusters become significantly tighter as the number of eccentric observations grows, and will be constrained to within 0.5 dex once 10 eccentric binary black holes are observed.

A large class of two dimensional quantum gravity theories of Jackiw-Teitelboim form have a description in terms of random matrix models. Such models, treated fully non-perturbatively, can give an explicit and tractable description of the underlying ``microstate'' degrees of freedom. They play a prominent role in regimes where the smooth geometrical picture of the physics is inadequate. This is shown using a natural tool for extracting the detailed microstate physics, a Fredholm determinant ${\rm det}(\mathbf{1}{-}\mathbf{ K})$. Its associated kernel $K(E,E^\prime)$ can be defined explicitly for a wide variety of JT gravity theories. To illustrate the methods, the statistics of the first several energy levels of a non-perturbative definition of JT gravity are constructed explicitly using numerical methods, and the full quenched free energy $F_Q(T)$ of the system is computed for the first time. These results are also of relevance to quantum properties of black holes in higher dimensions.

We perform force-free simulations for a neutron star orbiting a black hole, aiming at clarifying the main magnetosphere properties of such binaries towards their innermost stable circular orbits. Several configurations are explored, varying the orbital separation, the individual spins and misalignment angle among the magnetic and orbital axes. We find significant electromagnetic luminosities, $L\sim 10^{42-46} \, [B_{\rm pole}/ 10^{12}{\rm G}]^2 \, {\rm erg/s}$ (depending on the specific setting), primarily powered by the orbital kinetic energy, being about one order of magnitude higher than those expected from unipolar induction. The systems typically develop current sheets that extend to long distances following a spiral arm structure. The intense curvature of the black hole produces extreme bending on a particular set of magnetic field lines as it moves along the orbit, leading to magnetic reconnections in the vicinity of the horizon. For the most symmetric scenario (aligned cases), these reconnection events can release large-scale plasmoids that carry the majority of the Poynting fluxes. On the other hand, for misaligned cases, a larger fraction of the luminosity is instead carried outwards by large-amplitude Alfv{\'e}n waves disturbances. We estimate possible precursor electromagnetic emissions based on our numerical solutions, finding radio signals as the most promising candidates to be detectable within distances of $\lesssim 200$\,Mpc by forthcoming facilities like the Square Kilometer Array.

The Event Horizon Telescope (EHT) collaboration, an Earth-size sub-millimetre radio interferometer, recently captured the first images of the central supermassive black hole in M87. These images were interpreted as gravitationally-lensed synchrotron emission from hot plasma orbiting around the black hole. In the accretion flows around low-luminosity active galactic nuclei such as M87, electrons and ions are not in thermal equilibrium. Therefore, the electron temperature, which is important for the thermal synchrotron radiation at EHT frequencies of 230 GHz, is not independently determined. In this work, we investigate the commonly used parameterised ion-to-electron temperature ratio prescription, the so-called R-$\beta$ model, considering images at 230 GHz by comparing with electron-heating prescriptions obtained from general-relativistic magnetohydrodynamical (GRMHD) simulations of magnetised accretion flows in a Magnetically Arrested Disc (MAD) regime with different recipes for the electron thermodynamics. When comparing images at 230 GHz, we find a very good match between images produced with the R-$\beta$ prescription and those produced with the turbulent- and magnetic reconnection- heating prescriptions. Indeed, this match is on average even better than that obtained when comparing the set of images built with the R-$\beta$ prescription with either a randomly chosen image or with a time-averaged one. From this comparative study of different physical aspects, which include the image, visibilities, broadband spectra, and light curves, we conclude that, within the context of images at 230 GHz relative to MAD accretion flows around supermassive black holes, the commonly-used and simple R-$\beta$ model is able to reproduce well the various and more complex electron-heating prescriptions considered here.

We develop a nonperturbative method through the Hartree factorization to examine the quantum fluctuation effects on the single-field inflationary models in a spatially flat FRW cosmological space-time. Apart from the background field equation as well as the Friedmann equation with the corrections of quantum field fluctuations, the modified Mukhanov-Sasaki equations for the mode functions of the quantum scalar field are also derived by introducing the nonzero $\Delta_B$ term. We consider the Universe undergoing the slow roll (SR)-ultra slow roll (USR) -slow roll (SR) inflation where in particular the presence of the USR inflation triggers the huge growth of $\Delta_B$ that in turn gives the boost effects to the curvature perturbations for the modes that leave horizon in the early times of the inflation. However, the cosmic friction term in the mode equation given by the Hubble parameter presumably prohibits the boost effects. Here we propose two representative models to illustrate these two competing terms.

We study the inflationary consequences of Degenerate Higher Order Scalar Tensor (DHOST) theories in a de Sitter background. We perturb the de Sitter background by operators breaking either the degeneracy condition, i.e scordatura DHOST, or the shift symmetry in the scalar field. We first consider derivative scodurata and find that in all cases the power spectra of curvature perturbations are scale-invariant. We then investigate small perturbations by an axion-like potential, and show that in this scenario the power spectrum becomes scale-dependent. The modifications to the spectral index and its first two derivatives are compatible with the latest inflationary constraints. Moreover the tensor to scalar ratio and the non-Gaussianities of these models could be within reach of future experiments.

Using the ``complexity equals action''(CA) conjecture, for an ordinary charged system, it has been shown that the late-time complexity growth rate is given by a difference between the value of $\Phi_{H}Q+\Omega_H J$ on the inner and outer horizons. In this paper, we investigate the complexity of the boundary quantum system with conical deficits. From the perspective of holography, we consider a charged accelerating black holes which contain conical deficits on the north and south poles in the bulk gravitational theory and evaluate the complexity growth rate using the CA conjecture. As a result, the late-time growth rate of complexity is different from the ordinary charged black holes. It implies that complexity can carry the information of conical deficits on the boundary quantum system.

We study the ultraviolet behaviour of Higgs inflation models above the apparent unitarity violation scale arising from the large non minimal coupling to gravity, by computing on-shell 4-point scattering amplitudes in the presence of a large inflaton background, away from the electroweak vacuum. We find that all tree-level amplitudes are well behaved at high energies below the inflaton background that can thus take values up to the Planck scale. This result holds in both the metric and Palatini formulation, and is independent of the frame (Jordan or Einstein) as expected. The same result also holds if an $R^2$ term is added to the action.

In a recent paper, we argued that systematic uncertainties related to the choice of Cepheid color-luminosity calibration may have a large influence on the tension between the Hubble constant as inferred from distances to Type Ia supernovae and the cosmic microwave background as measured with the Planck satellite. Here, we investigate the impact of other sources of uncertainty in the supernova distance ladder, including Cepheid temperature and metallicity variations, supernova magnitudes and GAIA parallax distances. Excluding Milky Way Cepheids based on parallax calibration uncertainties, for the color excess calibration we obtain $H_0 = 70.8\pm 2.1$ km/s/Mpc, in $1.6\,\sigma$ tension with the Planck value.

Gravitational leptogenesis is an elegant way of explaining the matter-antimatter asymmetry in the universe. This paper is a review of the recently proposed mechanism of radiatively-induced gravitational leptogenesis (RIGL), in which loop effects in QFT in curved spacetime automatically generate an asymmetry between leptons and antileptons in thermal quasi-equilibrium in the early universe. The mechanism is illustrated in a simple see-saw BSM model of neutrinos, where the lepton-number violating interactions required by the Sakharov conditions are mediated by right-handed neutrinos with Majorana masses of O(10^10) GeV. The Boltzmann equations are extended to include new, loop-induced gravitational effects and solved to describe the evolution of the lepton number asymmetry in the early universe. With natural choices of neutrino parameters, the RIGL mechanism is able to generate the observed baryon-to-photon ratio in the universe today.

We study a deformation of a $2$-graded Poisson algebra where the functions of the phase space variables are complemented by linear functions of parity odd velocities. The deformation is carried by a $2$-form $B$-field and a bivector $\Pi$, that we consider as gauge fields of the geometric and non-geometric fluxes $H$, $f$, $Q$ and $R$ arising in the context of string theory compactification. The technique used to deform the Poisson brackets is widely known for the point particle interacting with a $U(1)$ gauge field, but not in the case of non-abelian or higher spin fields. The construction is closely related to Generalized Geometry: With an element of the algebra that squares to zero, the graded symplectic picture is equivalent to an exact Courant algebroid over the generalized tangent bundle $E \cong TM \oplus T^{*}M$, and to its higher gauge theory. A particular idempotent graded canonical transformation is equivalent to the generalized metric. Focusing on the generalized differential geometry side we construct an action functional with the Ricci tensor of a connection on covectors, encoding the dynamics of a gravitational theory for a contravariant metric tensor and $Q$ and $R$ fluxes. We also extract a connection on vector fields and determine a non-symmetric metric gravity theory involving a metric and $H$-flux.