Additional Scalar Field Research Articles

Conformal Yang-Mills field in (A)dS space

Ordinary-derivative (second-derivative) Lagrangian formulation of classical conformal Yang-Mills field in the (A)dS space of six, eight, and ten dimensions is developed. For such conformal field, we develop two gauge invariant Lagrangian formulations which we refer to as generic formulation and decoupled formulation. In both formulations, the usual Yang-Mills field is accompanied by additional vector and scalar fields where the scalar fields are realized as Stueckelberg fields. In the generic formulation, the usual Yang-Mills field is realized as a primary field, while the additional vector fields are realized as auxiliary fields. In the decoupled formulation, the usual Yang-Mills field is realized as massless field, while the additional vector fields together with the Stueckelberg are realized as massive fields. Some massless/massive fields appear with the wrong sign of kinetic terms, hence demonstrating explicitly that the considered models are not unitary. The use of embedding space method allows us to treat the isometry symmetries of (A)dS space manifestly and obtain conformal transformations of fields in a relatively straightforward way. By accompanying each vector field by the respective gauge parameter, we introduce an extended gauge algebra. Levy-Maltsev decomposition of such algebra is noted. Use of the extended gauge algebra setup allows us to present concise form for the Lagrangian and gauge transformations of the conformal Yang-Mills field. Higher-derivative representation of the Lagrangian is also obtained.

Gravitational scattering and beyond from extreme mass ratio effective field theory

We explore a recently proposed effective field theory describing electromagnetically or gravitationally interacting massive particles in an expansion about their mass ratio, also known as the self-force (SF) expansion. By integrating out the deviation of the heavy particle about its inertial trajectory, we obtain an effective action whose only degrees of freedom are the lighter particle together with the photon or graviton, all propagating in a Coulomb or Schwarzschild background. The 0SF dynamics are described by the usual background field method, which at 1SF is supplemented by a “recoil operator” that encodes the wobble of the heavy particle, and similarly computable corrections appearing at 2SF and higher. Our formalism exploits the fact that the analytic expressions for classical backgrounds and particle trajectories encode dynamical information to all orders in the couplings, and from them we extract multiloop integrands for perturbative scattering. As a check, we study the two-loop classical scattering of scalar particles in electromagnetism and gravity, verifying known results. We then present new calculations for the two-loop classical scattering of dyons, and of particles interacting with an additional scalar or vector field coupling directly to the lighter particle but only gravitationally to the heavier particle.

Prediction of the dark fermion mass using multicritical-point principle

This paper proposes a method to determine the effective potential using the multicritical-point principle (MPP) under the additional scalar field. The MPP is applied to the model in which a singlet dark fermion and a singlet real scalar field are added to the Standard Model (SM) to predict the dark fermion mass. As a result, the dark fermion mass is predicted to be about 901–972 GeV.

Cosmological correlators through the looking glass: reality, parity, and factorisation

We consider the evolution of quantum fields during inflation, and show that the total-energy singularities appearing in the perturbative expansion of the late-time Wavefunction of the Universe are purely real when the external states are massless scalars and massless gravitons. Our proof relies on the tree-level approximation, Bunch-Davies initial conditions, and exact scale invariance (IR-convergence), but without any assumptions on invariance under de Sitter boosts. We consider all n-point functions and allow for the exchange of additional states of any mass and integer spin. Our proof makes use of a decomposition of the inflationary bulk-bulk propagator of massive spinning fields which preserves UV-convergence and ensures that the time-ordered contributions are purely real after we rotate to Euclidean time. We use this reality property to show that the maximally-connected parts of wavefunction coefficients, from which total-energy singularities originate, are purely real. In a theory where all states are in the complementary series, this reality extends to the full wavefunction coefficient. We then use our reality theorem to show that parity-odd correlators (correlators that are mirror asymmetric) are factorised and do not diverge when the total-energy is conserved. We pay special attention to the parity-odd four-point function (trispectrum) of inflationary curvature perturbations and use our reality/factorisation theorems to show that this observable is factorised into a product of cubic diagrams thereby enabling us to derive exact shapes. We present examples of couplings between the inflaton and massive spin-1 and spin-2 fields, with the parity-violation in the trispectrum driven by Chern-Simons corrections to the spinning field two-point function, or from parity-violating cubic interactions which we build within the Effective Field Theory of Inflation. In addition, we present a first-of-its-kind example of a parity-violating trispectrum, generated at tree-level, that arises in a purely scalar theory where the inflaton mixes linearly with an additional massive scalar field.

The dynamics of three-forms in thick branes

In this work, we investigate thick brane models with a single three-form field. We find novel solutions for thick braneworlds where only three-forms exist and interact gravitationally in the bulk, both with and without matter fields. We use an additional scalar field as proxy for the matter fields. As an initial study, we consider the results here in contrast to the single scalar field thick braneworld case. The properties of the specific three-form parameterisation limits the freedom we have to choose the form of the warp factor, leading to a closed system of equations with nontrivial yet unstable solutions. The stability of the gravitational sector for thick brane three-forms is investigated and the models are shown to be unstable against small perturbations of the metric, further indicating that three-forms cannot exist stably in thick braneworld settings.

A New 2D Formulation of Modified General Relativity

AbstractIt is well known that the Einstein–Hilbert action in two dimensions is topological and yields an identically vanishing Einstein tensor. Consequently one is faced with difficulties when formulating a non‐trivial gravity model. The authors present a new, intrinsically two‐dimensional, approach to this problem based on the Einstein action. This yields a well defined variational approach which results in new field equations that break diffeomorphism invariance. This proposed approach does not require the introduction of additional scalar fields, nor the use of conformal transformations. However, how including conformal counter terms leads to equivalent results is shown. In doing so, an explanation for why previous approaches worked can be provided. Solutions to the field equations are briefly discussed.

Cosmological teleparallel perturbations

There has been growing interest in f(ℚ) gravity, which has led to significant advancements in the field. However, it is important to note that most studies in this area were based on the coincident gauge, thus overlooking the impact of the connection degrees of freedom. In this work, we pay special attention to the connection when studying perturbations in general teleparallel, metric teleparallel, and symmetric teleparallel theories of gravity. We do not just examine perturbations in the metric, but also in the affine connection. To illustrate this, we investigate cosmological perturbations in f(G), f(𝕋), and f(ℚ) gravity with and without matter in form of an additional scalar field for spatially flat and curved FLRW geometries. Our perturbative analysis reveals that for general f(ℚ) backgrounds, there are up to seven degrees of freedom, depending on the background connection. This is in perfect agreement with the upper bound on degrees of freedom established for the first time in https://doi.org/10.1002/prop.202300185 Fortschr. Phys. 71 (2023) 2300185. In f(G) and f(𝕋) gravity theories, only two tensor modes propagate in the gravity sector on generic curved cosmological backgrounds, indicating strong coupling problems. In the context of f(ℚ) cosmology, we find that for a particular background connection, where all seven modes propagate, there is at least one ghost degree of freedom. For all other choices of the connection the ghost can be avoided at the cost of strong coupling problem, where only four degrees of freedom propagate. Hence, all of the cosmologies within the teleparallel families of theories in form of f(G), f(ℚ), and f(𝕋) suffer either from strong coupling or from ghost instabilities. A direct coupling of the matter field to the connection or non-minimal couplings might alter these results.

Effective Field Theory for Extreme Mass Ratio Binaries.

We derive an effective field theory describing a pair of gravitationally interacting point particles in an expansion in their mass ratio, also known as the self-force (SF) expansion. The 0SF dynamics are trivially obtained to all orders in Newton's constant by the geodesic motion of the light body in a Schwarzschild background encoding the gravitational field of the heavy body. The corrections at 1SF and higher are generated by perturbations about this configuration-that is, the geodesic deviation of the light body and the fluctuation graviton-but crucially supplemented by an operator describing the recoil of the heavy body as it interacts with the smaller companion. Using this formalism we compute new results at third post-Minkowskian order for the conservative dynamics of a system of gravitationally interacting massive particles coupled to a set of additional scalar and vector fields.

On the direct quantization of Proca gauge invariant field

In this study, we use the generalized integration constants method “GCI” [1,2] to quantize two fields with constraints. Indeed, Proca field, that describes a massive boson is studied first, based on a Lagrangian without gauge symmetry, in order to determine the necessary brackets for its canonical quantization. Then, another gauge invariant version of this field, obtained by adding an additional scalar field in the mass term, is quantized after fixing this gauge.”

Sustaining Quasi De-Sitter Inflation with Bulk Viscosity

The de-Sitter spacetime is a maximally symmetric Lorentzian manifold with constant positive scalar curvature that plays a fundamental role in modern cosmology. Here, we investigate bulk-viscosity-assisted quasi de-Sitter inflation, that is the period of accelerated expansion in the early universe during which −H˙≪H2, with H(t) being the Hubble expansion rate. We do so in the framework of a causal theory of relativistic hydrodynamics, which takes into account non-equilibrium effects associated with bulk viscosity, which may have been present as the early universe underwent an accelerated expansion. In this framework, the existence of a quasi de-Sitter universe emerges as a natural consequence of the presence of bulk viscosity, without requiring introducing additional scalar fields. As a result, the equation of state, determined by numerically solving the generalized momentum-conservation equation involving bulk viscosity pressure turns out to be time dependent. The transition timescale characterising its departure from an exact de-Sitter phase is intricately related to the magnitude of the bulk viscosity. We examine the properties of the new equation of state, as well as the transition timescale in the presence of bulk viscosity pressure. In addition, we construct a fluid description of inflation and demonstrate that, in the context of the causal formalism, it is equivalent to the scalar field theory of inflation. Our analysis also shows that the slow-roll conditions are realised in the bulk-viscosity-supported model of inflation. Finally, we examine the viability of our model by computing the inflationary observables, namely the spectral index and the tensor-to-scalar ratio of the curvature perturbations, and compare them with a number of different observations, finding good agreement in most cases.

Gravitational waves from phase transitions in scale invariant models

We investigate the properties of the gravitational waves (GW) generated during a strongly first order electroweak phase transition (EWPT) in models with the classical scale invariance (CSI). Here, we distinguish two parameter space regions that correspond to the cases of (1) light dilaton and (2) purely radiative Higgs mass (PRHM). In the CSI models, the dilaton mass, or the Higgs mass in the PRHM case, in addition to some triple scalar couplings are fully triggered by the radiative corrections (RCs). In order to probe the RC effects on the EWPT strength and on the GW spectrum, we extend the standard model by a real singlet to assist the electroweak symmetry breaking and an additional scalar field Q with multiplicity NQ and mass mQ. After imposing all theoretical and experimental constraints, we show that a strongly first order EWPT with detectable GW spectra can be realized for the two cases of light dilaton and PRHM. We also show the corresponding values of the relative enhancement of the cross section for the di-Higgs production process, which is related to the triple Higgs boson coupling. We obtain the region in which the GW spectrum can be observed by different future experiments such as LISA and DECIGO. We also show that the scenarios (1) and (2) can be discriminated by future GW observations and measurements of the di-Higgs productions at future colliders.

Quantum-enhanced screened dark energy detection

We propose an experiment based on a Bose–Einstein condensate interferometer for strongly constraining fifth-force models. Additional scalar fields from modified gravity or higher dimensional theories may account for dark energy and the accelerating expansion of the Universe. These theories have led to proposed screening mechanisms to fit within the tight experimental bounds on fifth-force searches. We show that our proposed experiment would greatly improve the existing constraints on these screening models by many orders of magnitude.

Interactions between several types of cosmic strings

We study the interaction of several types of static straight cosmic strings, including local strings, global strings, and bosonic superconducting strings with and without magnetic currents. First, we evaluate the interaction energy of two widely separated cosmic strings using the point source formalism and show that the most dominant contribution to the interaction energy comes from the excitation of the lightest mediator particles in a underlying theory. The interaction energy at arbitrary separation distances is then analyzed numerically by the gradient flow method. It turns out that an additional scalar field introduced in the bosonic superconducting string becomes an additional source of attraction. For such a bosonic superconducting string, we find that a string with two winding numbers is energetically favorable compared to two strings with a single winding number in a certain parameter region. Our analysis reveals that a phase structure of bosonic superconducting strings is richer than that of local and global strings and that the formation of bound states at intersections of bosonic superconducting strings is favored.

Testing theories of gravitation with the Interstellar Probe Radio Experiment

General Relativity (GR) will soon celebrate its 110th birthday, holding up against all experimental enquiry. Nonetheless, unification theories attempting to quantize gravity, such as string theory, are gaining footing. These hypothesize additional scalar, vector, and tensor long-range fields that couple to matter (Will, 2014), introducing violations to GR. Although such violations have never been detected, it is likely that GR will not be the ultimate theory of gravity. What is certain is that gravity tests are alive and well, pushing the validity of GR to new scales and accuracies, or -potentially- suggesting alternative routes for new physics.Building upon the legacy of Voyager and Pioneer missions, which demonstrated the capability to survive in the outer reaches of the solar system, the Interstellar Probe mission concept (McNutt et al., 2022) aims to characterise our heliosphere through state-of-the-art instrumentation, opening new frontiers also for GR testing. In this work, we investigate the possibility of constraining the Nordtvedt parameter η and the mass of the graviton via the Compton wavelength λC, by simulating the processing of 10 years of radiometric data from the Interstellar Probe. Station calibration and clock synchronisation, as well as limiting spacecraft precession manoeuvres are highlighted as key strategies for obtaining high-quality estimates. In the most favourable scenario, η can be constrained to less than 1.5·10-5, reducing the uncertainty obtained via Lunar Laser Ranging (Hofmann and Müller, 2018), and a lower bound of 1.4·1014 km is set for λC, improving the estimates obtained from planetary ephemerides (Bernus et al., 2020) and gravitational wave detection (Abbott et al., Jun 2021). Extending ranging measurement acquisition to 20 years improves the results tenfold. This experiment interrogates fundamental physics from a unique dynamical setting, investigating possible violations of the Equivalence Principle (EP) underlying GR.

Dimension-8 SMEFT analysis of minimal scalar field extensions of the Standard Model

We analyze the constraints obtainable from present data using the Standard Model Effective Field Theory (SMEFT) on extensions of the Standard Model with additional electroweak singlet or triplet scalar fields. We compare results obtained using only contributions that are linear in dimension-6 operator coefficients with those obtained including terms quadratic in these coefficients as well as contributions that are linear in dimension-8 operator coefficients. We also implement theoretical constraints arising from the stability of the electroweak vacuum and perturbative unitarity. Analyzing the models at the dimension-8 level constrains scalar couplings that are not bounded at the dimension-6 level. The strongest experimental constraints on the singlet model are provided by Higgs coupling measurements, whereas electroweak precision observables provide the strongest constraints on the triplet model. In the singlet model the present di-Higgs constraints already play a significant role. We find that the current constraints on model parameters are already competitive with those anticipated from future di- and tri-Higgs measurements. We compare our results with calculations in the full model, exhibiting the improvements when higher-order SMEFT terms are included. We also identify regions in parameter space where the SMEFT approximation appears to break down. We find that the combination of current constraints with the theoretical bounds still admits regions where the SMEFT approach is not valid, particularly for lower scalar boson masses.

Introduction of a recurrent neural network constitutive description within an implicit gradient enhanced damage framework

The contribution at hand presents a method for the application of Recurrent neural network based constitutive models within a coupled field Finite Element Analysis. Thereby, an additional scalar field is coupled to the displacement field and evolved by a scalar variable at the integration points. By employing implicit gradient enhancement as regularization framework, the representation of softening material behavior is possible without the generation of localization phenomena. The feasibility of this approach is shown for an anisotropic constitutive description based on the microplane model, by employing a self-adversarial training scheme for enhanced robustness which was proposed to work for arbitrary inelastic materials. Its capabilities and limitations during application in Finite Element Analysis are evaluated and discussed for two numerical simulations.

Cosmological simulations of a momentum coupling between dark matter and quintessence

ABSTRACT Dark energy is frequently modelled as an additional dynamical scalar field component in the Universe, referred to as ‘quintessence’, which drives the late-time acceleration. Furthermore, the quintessence field may be coupled to dark matter and/or baryons, leading to a fifth force. In this paper, we explore the consequences for non-linear cosmological structure formation arising from a momentum coupling between the quintessence field and dark matter only. The coupling leads to a modified Euler equation, which we implement in an N-body cosmological simulation. We then analyse the effects of the coupling on the non-linear power spectrum and the properties of the dark matter haloes. We find that, for certain quintessence potentials, a positive coupling can lead to significantly reduced structure on small scales and somewhat enhanced structure on large scales, as well as reduced halo density profiles and increased velocity dispersions.

Path integral quantization of generalized Stueckelberg electrodynamics: A Faddeev-Jackiw approach

We build a setup for path integral quantization through the Faddeev-Jackiw approach, extending it to include Grassmannian degrees of freedom, to be later implemented in a model of generalized electrodynamics that involves fourth-order derivatives in the components of a massive vector field being endowed with gauge freedom, due to an additional scalar field. Namely, the generalized Stueckelberg electrodynamics. In the first instance, we work on the free case to gain some familiarity with the program and, subsequently, we add the interaction with fermionic matter fields to complete our aim. In addition to deriving the correct classical brackets for such a model, we get the full expression for the associated generating functional and its associated integration measure.

Cosmological application of the Maxwell gravity

In this study, we consider a cosmological model for the Maxwell gravity which is constructed by gauging the semi-simple extended Poincaré algebra. Inspired by the Einstein–Yang–Mills theory, we describe the Maxwell gauge field in terms of two additional time-dependent scalar fields. Within the context of a homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker universe, we derive the Friedmann equations together with new contributions. Additionally, we examine the modified Friedmann equation to demonstrate how diverse cosmological scenarios can be achieved within this framework. Moreover, we investigate the gauge theory of gravity based on the Maxwell algebra and show that this model leads to the (anti)-de Sitter universe as well as a non-accelerated universe model.

Critical collapse for the Starobinsky R2 model

We study gravitational collapse for the Starobinsky R2 model, a particular example of an f(r) theory, in a spherically symmetric spacetime. We add a massless scalar field as matter content to the spacetime. We work in the Einstein frame, where an additional scalar field arises due to the conformal transformation. As in general relativity, depending on the initial data, we found that the gravity scalar field and the physical scalar field can collapse, forming a black hole, in which the final solution is the Schwarzschild metric. We found the threshold of black hole formation through a fine-tuning method and studied critical collapse near this regime.