Non-geodesic Motion Research Articles

Multi-field inflation with large scalar fluctuations: non-Gaussianity and perturbativity

Recently multi-field inflation models that can produce large scalar fluctuations on small scales have drawn a lot of attention, primarily because they could lead to primordial black hole production and generation of large second-order gravitational waves. In this work, we focus on models where the scalar fields responsible for inflation live on a hyperbolic field space. In this case, geometrical destabilisation and non-geodesic motion are responsible for the peak in the scalar power spectrum. We present new results for scalar non-Gaussianity and discuss its dependence on the model's parameters. On scales around the peak, we typically find that the non-Gaussianity is large and close to local in form. We validate our results by employing two different numerical techniques, utilising the transport approach, based on full cosmological perturbation theory, and the δN formalism, based on the separate universe approximation. We discuss implications of our results for the perturbativity of the underlying theory, focusing in particular on versions of these models with potentially relevant phenomenology at interferometer scales.

Third post-Newtonian effective-one-body Hamiltonian in scalar-tensor and Einstein-scalar-Gauss-Bonnet gravity

We build an effective-one-body (EOB) Hamiltonian at third post-Newtonian (3PN) order in scalar-tensor (ST) and Einstein-scalar-Gauss-Bonnet (ESGB) theories of gravity. The latter is an extension of general relativity that predicts scalar hair for black holes. We start from the known two-body Lagrangian at 3PN order, and use order-reduction methods to construct its ordinary Hamiltonian counterpart. We then reduce the conservative two-body dynamics to the (nongeodesic) motion of a test particle in an effective metric by means of canonical transformations. The resulting EOB Hamiltonian is a modification of the general relativistic Hamiltonian, and already at 3PN order, it must account for nonlocal-in-time tail contributions. We include the latter beyond circular orbits and up to sixth order in the binary's orbital eccentricity. We finally calculate the orbital frequency at the innermost stable circular orbit (ISCO) of binary black holes in the shift-symmetric ESGB model. Our work extends F.L. Juli\'e and N. Deruelle [Phys. Rev. D 95, 124054 (2017)], and it is an essential step toward the accurate modeling of gravitational waveforms beyond general relativity.

Revisiting small-scale fluctuations in α-attractor models of inflation

Cosmological α-attractors stand out as particularly compelling models to describe inflation in the very early universe, naturally meeting tight observational bounds from cosmic microwave background (CMB) experiments. We investigate α-attractor potentials in the presence of an inflection point, leading to enhanced curvature perturbations on small scales. We study both single- and multi-field models, driven by scalar fields living on a hyperbolic field space.In the single-field case, ultra-slow-roll dynamics at the inflection point is responsible for the growth of the power spectrum, while in the multi-field set-up we study the effect of geometrical destabilisation and non-geodesic motion in field space. The two mechanisms can in principle be distinguished through the spectral shape of the resulting scalar power spectrum on small scales. These enhanced scalar perturbations can lead to primordial black hole (PBH) production and second-order gravitational wave (GW) generation.Due to the existence of universal predictions in α-attractors, consistency with current CMB constraints on the large-scale spectral tilt implies that PBHs can only be produced with masses smaller than 108 g and are accompanied by ultra-high frequency GWs, with a peak expected to be at frequencies of order 10 kHz or above.

Curvature–matter couplings in modified gravity: From linear models to conformally invariant theories

In this paper, we review modified theories of gravity with a curvature–matter coupling between an arbitrary function of the scalar curvature and the Lagrangian density of matter. This explicit nonminimal coupling induces a nonvanishing covariant derivative of the energy–momentum tensor, that implies nongeodesic motion and consequently leads to the appearance of an extra force. Here, we explore the physical and cosmological implications of the nonconservation of the energy–momentum tensor by using the formalism of irreversible thermodynamics of open systems in the presence of matter creation/annihilation. The particle creation rates, pressure, and the expression of the comoving entropy are obtained in a covariant formulation and discussed in detail. Applied together with the gravitational field equations, the thermodynamics of open systems lead to a generalization of the standard [Formula: see text]CDM cosmological paradigm, in which the particle creation rates and pressures are effectively considered as components of the cosmological fluid energy–momentum tensor. Furthermore, we also briefly present the coupling of curvature to geometry in conformal quadratic Weyl gravity, by assuming a coupling term of the form [Formula: see text], where [Formula: see text] is the ordinary matter Lagrangian, and [Formula: see text] is the Weyl scalar. The coupling explicitly satisfies the requirement of the conformal invariance of the theory. Expressing [Formula: see text] with the use of an auxiliary scalar field and of the Weyl scalar, the gravitational action can be linearized in the Ricci scalar, leading in the Riemann space to a conformally invariant [Formula: see text]-type theory, with the matter Lagrangian nonminimally coupled to geometry.

Beyond Einstein’s General Relativity: Hybrid metric-Palatini gravity and curvature-matter couplings

Einstein’s General Relativity (GR) is possibly one of the greatest intellectual achievements ever conceived by the human mind. In fact, over the last century, GR has proven to be an extremely successful theory, with a well established experimental footing, at least for weak gravitational fields. Its predictions range from the existence of black holes and gravitational radiation (now confirmed) to the cosmological models. Indeed, a central theme in modern Cosmology is the perplexing fact that the Universe is undergoing an accelerating expansion, which represents a new imbalance in the governing gravitational equations. The cause of the late-time cosmic acceleration remains an open and tantalizing question, and has forced theorists and experimentalists to question whether GR is the correct relativistic theory of gravitation. This has spurred much research in modified theories of gravity, where extensions of the Hilbert–Einstein action describe the gravitational field, in particular, [Formula: see text] gravity, where [Formula: see text] is the curvature scalar. In this review, we perform a detailed theoretical and phenomenological analysis of specific modified theories of gravity and investigate their astrophysical and cosmological applications. We present essentially two largely explored extensions of [Formula: see text] gravity, namely: (i) the hybrid metric-Palatini theory; (ii) and modified gravity with curvature-matter couplings. Relative to the former, it has been established that both metric and Palatini versions of [Formula: see text] gravity possess interesting features but also manifest severe drawbacks. A hybrid combination, containing elements from both of these formalisms, turns out to be very successful in accounting for the observed phenomenology and avoids some drawbacks of the original approaches. Relative to the curvature-matter coupling theories, these offer interesting extensions of [Formula: see text] gravity, where the explicit nonminimal couplings between an arbitrary function of the scalar curvature [Formula: see text] and the Lagrangian density of matter, induces a nonvanishing covariant derivative of the energy-momentum tensor, which implies nongeodesic motion and consequently leads to the appearance of an extra force. We extensively explore both theories in a plethora of applications, namely, the weak-field limit, galactic and extragalactic dynamics, cosmology, stellar-type compact objects, irreversible matter creation processes and the quantum cosmology of a specific curvature-matter coupling theory.

Scaling attractors in multi-field inflation

Multi-field inflation with a curved scalar geometry has been found to support background trajectories that violate the slow-roll, slow-turn conditions and thus have the potential to evade the swampland constraints. In order to understand how generic this novel behaviour is and what conditions lead to it, we perform a classification of dynamical attractors of two-field inflation that are of the scaling type. Scaling solutions form a one-parameter generalization of De Sitter solutions with a constant value of the first Hubble flow parameter ϵ and, as we argue and demonstrate, form a natural starting point for the study of non-slow-roll slow-turn behaviour. All scaling solutions can be classified as critical points of a specific dynamical system. We recover known multi-field inflationary attractors as approximate scaling solutions and classify their stability using dynamical system techniques. In particular, we discover that dynamical bifurcations play an integral role in the transition between geodesic and non-geodesic motion and discuss the ability of scaling solutions to describe realistic multi-field models. We revisit the criteria for background stability and show cases where the usual criteria found in the literature do not capture the background evolution of the system.

Hyper-Non-Gaussianities in Inflation with Strongly Nongeodesic Motion.

Several recent proposals to embed inflation into high-energy physics rely on inflationary dynamics characterized by a strongly nongeodesic motion in negatively curved field space. This naturally leads to a transient instability of perturbations on sub-Hubble scales, and to their exponential amplification. Supported by first-principles numerical computations, and by the analytical insight provided by the effective field theory of inflation, we show that the bispectrum is enhanced in flattened configurations, and we argue that an analogous result holds for all higher-order correlation functions. These "hyper-non-Gaussianities" thus provide powerful model-independent constraints on nonstandard inflationary attractors motivated by the search for ultraviolet completions of inflation.

Cosmic evolution in the background of R (1 + αQ) gravity

In this paper, we discuss the cosmic evolution in a modified theory involving non-minimal interaction of geometry and matter, labeled as [Formula: see text] gravity, where [Formula: see text] is the non-minimal interaction term. First, we develop the dynamical [Formula: see text] field equations for Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime and then by using divergence of these equations, we explore its interesting outcome of non-conserved energy–momentum tensor (EMT). The presence of geometry matter coupling in such theories results in non-geodesic test particles motion and hence causes an additional force orthogonal to four-velocity of these particles. By taking these interesting features into account along with a particular choice of Lagrangian [Formula: see text], we explore the resulting expression of energy density. Further, the free model parameters are constrained using energy condition bounds where it is concluded that these values of free parameters are compatible with the recent data.

Entanglement-induced deviation from the geodesic motion in quantum gravity

We study the derivation of the effective equation of motion for a pointlike particle in the framework of quantum gravity. Just like the geodesic motion of a classical particle is a consequence of classical field theory coupled to general relativity, we introduce the similar notion of an effective equation of motion, but starting from an abstract quantum gravity description. In the presence of entanglement between gravity and matter, quantum effects give rise to modifications of the geodesic trajectory, primarily as a consequence of the interference between various coherent states of the gravity-matter system. Finally, we discuss the status of the weak equivalence principle in quantum gravity and its possible violation due to the nongeodesic motion.

Non-geodesic circular motion of massive spinning test bodies around a Schwarzschild field in the Lagrangian theory

Recent interest on studying possible violations of the Equivalence Principle has led to the development of space satellite missions testing it for bodies moving on circular orbits around Earth. This experiment establishes that the validity of the equivalence principle is independent of the composition of bodies. However, the internal degrees of freedom of the bodies (such as spin) were not taken into account. In this work, it is shown exactly that the circular orbit motion of test bodies does present a departure from geodesic motion when spin effects are not negligible. Using a Lagrangian theory for spinning massive bodies, an exact solution for their circular motion is found showing that the non-geodesic behavior manifests through different tangential velocities of the test bodies, depending on the orientation of its spin with respect to the total angular momentum of the satellite. Besides, for circular orbits, spinning test bodies present no tangential acceleration. We estimate the difference of the two possible tangential velocities for the case of circular motion of spinning test bodies orbiting Earth.

Quantification of GR effects in muon g-2, EDM and other spin precession experiments

Recently, Morishima, Futamase and Shimizu published a series of manuscripts, putting forward arguments, based on a post-Newtonian approximative calculation, that there can be a sizable general relativistic (GR) correction in the experimental determination of the muon magnetic moment based on spin precession, i.e. in muon g-2 experiments. In response, other authors argued that the effect must be much smaller than claimed. Further authors argued that the effect exactly cancels. Also, the known formulae for the de Sitter and Lense–Thirring effect do not apply due to the non-geodesic motion. All this indicates that it is difficult to estimate from first principles the influence of GR corrections in the problem of spin propagation. Therefore, in this paper we present a full general relativistic calculation in order to quantify this effect. The main methodology is the purely differential geometrical tool of Fermi–Walker transport over a Schwarzschild background. The Larmor precession due to the propagation in the electromagnetic field of the experimental apparatus is also included. For the muon g-2 experiments the GR correction turns out to be very small, well below the present sensitivity. However, in other similar storage ring experimental settings, such as electric dipole moment search experiments, where the so-called frozen spin method is used, GR gives a well detectable effect, and should be corrected for. All frozen spin scenarios are affected which intend to reach a sensitivity of 0.1 μrad s−1 for the spin precession in the vertical plane.

Metric-affine f(R,T) theories of gravity and their applications

We study f(R,T) theories of gravity, where T is the trace of the energy-momentum tensor T_{\mu\nu}, with independent metric and affine connection (metric-affine theories). We find that the resulting field equations share a close resemblance with their metric-affine f(R) relatives once an effective energy-momentum tensor is introduced. As a result, the metric field equations are second-order and no new propagating degrees of freedom arise as compared to GR, which contrasts with the metric formulation of these theories, where a dynamical scalar degree of freedom is present. Analogously to its metric counterpart, the field equations impose the non-conservation of the energy-momentum tensor, which implies non-geodesic motion and consequently leads to the appearance of an extra force. The weak field limit leads to a modified Poisson equation formally identical to that found in Eddington-inspired Born-Infeld gravity. Furthermore, the coupling of these gravity theories to perfect fluids, electromagnetic, and scalar fields, and their potential applications are discussed.

Underlining some mathematical and physical aspects about the concept of motion in general relativity

The Einstein initial foundations of general relativity have to do with his great intuition and they are not clear as it is for special relativity. As has been widely emphasized, for example, in the book of Ohanian and Ruffini, the very name of the theory indicates a misconception. Despite this, the high school textbooks (at least the Italian ones) and books of scientific divulgation introduce the Einstein gravitational theory still following the initial approach leading, in our opinion, to misinterpretations. A careful student, for example, immediately asks: it is not true that the Earth rotates because I can consider it at rest thanks to general relativity theory. The relativity of motion is trivial in mathematics while it has deep meaning in physics and it is not sufficiently analyzed. Similarly, the arbitrary choice of the origin and the perfect equivalence between all coordinate systems are mathematical properties satisfied by general relativity and students can confuse it with physical equivalence between reference systems that have a deeper meaning and the Einstein theory does not verify it. Gravitational force does not exist and this is the real core of Einsteinian revolution. As happens in Newtonian physics and Special Relativity, also in general relativity the relative motions are the geodesic motions with the difference that spacetime can be curved and geodesics may not be a straight line. Similarly, in general relativity forces cause non-geodesic motion. Geodesic and non-geodesic are tensorial properties and for this reason they are absolute.

On the possibility of non-geodesic motion of massless spinning tops

The motion of spinning massless particles in gravitationally curved backgrounds is revisited by considering new types of constraints. Those constraints guarantee zero mass () and they allow for the possibility of trajectories which are not simply null geodesics. To exemplify this previously unknown possibility, the equations of motion are solved for radial motion in Schwarzschild background. It is found that the particle experiences a spin-induced energy shift, which is proportional to the Hawking temperature of the black hole background.

A machian request for the equivalence principle in extended gravity and nongeodesic motion

Starting from the origin of Einstein general relativity (GR) the request of Mach on the theory's structure has been the core of the foundational debate. That problem is strictly connected with the nature of the mass-energy equivalence. It is well known that this is exactly the key point that Einstein used to realize a metric theory of gravitation having an unequalled beauty and elegance. On the other hand, the current requirements of particle physics and the open questions within extended gravity theories request a better understanding of Equivalence Principle (EP). The MOND theory by Milgrom proposes a modification of Newtonian dynamics and we consider a direct coupling between the Ricci curvature scalar and the matter Lagrangian showing that a non geodesic ratio m_{i}/m_{g} can be fixed and that Milgrom acceleration is retrieved at low energies.

The emission of Gamma Ray Bursts as a test-bed for modified gravity

The extreme physical conditions of Gamma Ray Bursts can constitute a useful observational laboratory to test theories of gravity where very high curvature regimes are involved. Here we propose a sort of curvature engine capable, in principle, of explaining the huge energy emission of Gamma Ray Bursts. Specifically, we investigate the emission of radiation by charged particles non-minimally coupled to the gravitational background where higher order curvature invariants are present. The coupling gives rise to an additional force inducing a non-geodesic motion of particles. This fact allows a strong emission of radiation by gravitationally accelerated particles. As we will show with some specific model, the energy emission is of the same order of magnitude of that characterizing the Gamma Ray Burst physics. Alternatively, strong curvature regimes can be considered as a natural mechanism for the generation of highly energetic astrophysical events. Possible applications to cosmology are discussed.

Generalized Curvature-Matter Couplings in Modified Gravity

In this work, we review a plethora of modified theories of gravity with generalized curvature-matter couplings. The explicit nonminimal couplings, for instance, between an arbitrary function of the scalar curvature R and the Lagrangian density of matter, induces a non-vanishing covariant derivative of the energy-momentum tensor, implying non-geodesic motion and, consequently, leads to the appearance of an extra force. Applied to the cosmological context, these curvature-matter couplings lead to interesting phenomenology, where one can obtain a unified description of the cosmological epochs. We also consider the possibility that the behavior of the galactic flat rotation curves can be explained in the framework of the curvature-matter coupling models, where the extra terms in the gravitational field equations modify the equations of motion of test particles and induce a supplementary gravitational interaction. In addition to this, these models are extremely useful for describing dark energy-dark matter interactions and for explaining the late-time cosmic acceleration.

Lessons fromf(R,Rc2,Rm2,Lm)gravity: Smooth Gauss-Bonnet limit, energy-momentum conservation, and nonminimal coupling

This paper studies a generic fourth-order theory of gravity with Lagrangian density $f(R,R_c^2,R_m^2, \mathscr{L}_m)$. By considering explicit $R^2$ dependence and imposing the "coherence condition" $f_{R^2}\!=\!f_{R_m^2}\!=\! -f_{R_c^2}/4$, the field equations of $f(R,R^2,R_c^2,R_m^2, \mathscr{L}_m)$ gravity can be smoothly reduced to that of $f(R,\mathcal{G},\mathscr{L}_m)$ generalized Gauss-Bonnet gravity. We use Noether's conservation law to study the $f(\mathcal{R}_1,\mathcal{R}_2\ldots,\mathcal{R}_n,\mathscr{L}_m)$ model with nonminimal coupling between $\mathscr{L}_m$ and Riemannian invariants $ \mathcal{R}_i$, and conjecture that the gradient of nonminimal gravitational coupling strength $\nabla^\mu f_{\!\mathscr{L}_m}$ is the only source for energy-momentum non-conservation. This conjecture is applied to the $f(R,R_c^2,R_m^2, \mathscr{L}_m)$ model, and the equations of continuity and non-geodesic motion of different matter contents are investigated. Finally, the field equation for Lagrangians including the traceless-Ricci square and traceless-Riemann (Weyl) square invariants is derived, the $f(R,R_c^2,R_m^2, \mathscr{L}_m)$ model is compared with the $f(R,R_c^2,R_m^2,T)+2\kappa \mathscr{L}_m$ model, and consequences of nonminimal coupling for black hole and wormhole physics are considered.

Electro-gravitational Technology via Chronon Field

Aim: To develop a model of matter that will account for electro-gravity. Matter is characterized by force fields and in non-inertial and non-geodesic motion as a result of interactions. The measurement of how non geodesic a test particle is can be done by non-geodesic acceleration which in 4 dimensional space-time is perpendicular to the 4-velocity. In order to give a new meaning to matter by using such acceleration there is a need to reach a formalism free of specific trajectories, namely by a scalar curvature field. This can be done by an introduction of a new meaning of time that can't be realized as a coordinate. From every event, we define the limit of the maximal possible measurable proper time back to the big bang singularity or manifold of events from which we can say cosmic expansion had began. Yet such time is not a physical observable in the sense that it can't be locally calculated and it may exist as a limit only. The gradient of such time, however, is local and thus physical. If more than one curve measuring such time cross the same event then the gradient which is a vector field can't be parallel to all such intersecting trajectories. That implies that the gradient as a vector field will not be parallel to itself or in other words, will manifest a curvature field. This idea leads to a new formalism of matter that replaces the conventional stress-energymomentum-tensor. The formalism will be mainly developed for classical but also for quantum physics and will result in a theory of electro-gravity.

Effects of friction forces on the motion of objects in smoothly matched interior/exterior spacetimes

We investigate the non-geodesic motion of a test particle inside a fluid in equilibrium, as described by the interior Schwarzschild solution, in the presence of a Poynting–Robertson-like dissipative force. The accelerated motion in the interior spacetime is (regularly) connected to the geodesic one in the corresponding external Schwarzschild background, mimicking physical conditions often occurring in spacetime regions close to stellar or compact objects. A similar analysis is repeated for the case in which the interior Schwarzschild solution is given by a Pant–Sah perfect-fluid solution. This latter case, supporting a polytropic equation of state for the interior fluid source, appears to be more appropriate for modeling situations of either stellar or cosmological interest.