Auxiliary Scalar Field Research Articles

Black hole quasinormal modes and isospectrality in Deser-Woodard nonlocal gravity

We investigate the gravitational perturbations of the Schwarzschild black hole in the nonlocal gravity model recently proposed by Deser and Woodard. The analysis is performed in the localized version in which the nonlocal corrections are represented by some auxiliary scalar fields. We find that the nonlocal corrections do not affect the axial gravitational perturbations, and hence the axial modes are completely identical to those in general relativity (GR). However, the polar modes become different from their GR counterparts when the scalar fields are excited at the background level. In such a case the polar modes are sourced by an additional massless scalar mode and, as a result, the isospectrality between the axial and the polar modes breaks down. We also perform a similar analysis for the predecessor of this model and arrive at the same conclusion for it.

Toward a unified equation of state for multi-messenger astronomy

Aims. We aim to present a first step in developing a benchmark equation-of-state (EoS) model for multi-messenger astronomy that unifies the thermodynamics of quark and hadronic degrees of freedom. Methods. A Lagrangian approach to the thermodynamic potential of quark-meson-nucleon matter was used. In this approach, dynamical chiral-symmetry breaking is described by the scalar mean-field dynamics coupled to quarks and nucleons and their chiral partners, whereby its restoration occurs in the hadronic phase by parity doubling, as well as in the quark phase. Quark confinement was achieved by an auxiliary scalar field that parametrizes a dynamical infrared cut-off in the quark sector, serving as an ultraviolet cut-off for the nucleonic phase space. The gap equations were solved for the isospin-symmetric case, as well as for neutron star (NS) conditions. We also calculated the mass-radius (MR) relation of NSs and their tidal deformability (TD) parameter. Results. The obtained EoS is in accordance with nuclear matter properties at saturation density and with the flow constraint from heavy ion collision experiments. For isospin-asymmetric matter, a sequential occurrence of light quark flavors is obtained, allowing for a mixed phase of chirally-symmetric nucleonic matter with deconfined down quarks. The MR relations and TDs for compact stars fulfill the constraints from the latest astrophysical observations for PSR J0740+6620, PSR J0030+0451, and the NS merger GW170817, whereby the tension between the maximum mass and compactness constraints rather uniquely fixes the model parameters. The model predicts the existence of stars with a core of chirally restored but purely hadronic (confined) matter for masses beyond 1.8 M⊙. Stars with pure-quark matter cores are found to be unstable against the gravitational collapse. This instability is shifted to even higher densities if repulsive interactions between quarks are included.

Holographic RG and exact RG in O(N) model

In this paper an Exact Renormalization Group (ERG) equation is written for the critical O(N) model in D-dimensions (with D≈3) at the Wilson-Fisher fixed point perturbed by a scalar composite operator. The action is written in terms of an auxiliary scalar field and reproduces correlation functions of a scalar composite operator. The equation is derived starting from the Polchinski ERG equation for the fundamental scalar field. As described in Sathiapalan and Sonoda (2017) [1] an evolution operator for the Polchinski ERG equation can be written in the form of a functional integral, with a D+1 dimensional scalar field theory action. In the case of the fundamental scalar field this action only has a kinetic term and therefore looks quite different from Holographic RG where there are potential terms. But in the composite operator case discussed in this paper, the ERG equation and consequently the D+1 dimensional action contains higher order potential terms for the scalar field and is therefore very similar to the case of Holographic RG. Furthermore this action can be mapped to a scalar field action in AdSD+1 using the techniques of ([1]). The leading cubic term of the potential is computed in this paper for D≈3 and expectedly vanishes in D=3 in agreement with results in the AdS/CFT literature.

Production of gravitational waves during preheating in the Starobinsky inflationary model

The production of GWs during preheating in the Starobinsky model with a nonminimally coupled auxiliary scalar field is studied through the lattice simulation in this paper. We find that the GW spectrum Omega _{mathrm{gw}} grows fast with the increase of the absolute value of coupling parameter xi . This is because the resonant bands become broad with the increase of |xi |. When xi <0, Omega _{mathrm{gw}} begins to grow once the inflation ends and grows faster than the case of xi >0. Omega _{mathrm{gw}} reaches the maximum at xi =-20 (xi =42 for the case xi >0) and then decreases with slight oscillation. Furthermore we find that the GWs produced in the era of preheating satisfy the limits from the Planck and next-generation CMB experiments.

Families of Rational and Semirational Solutions of the Partial Reverse Space-Time Nonlocal Mel′nikov Equation

Exact periodic and localized solutions of a nonlocal Mel′nikov equation are derived by the Hirota bilinear method. Many conventional nonlocal operators involve integration over a spatial or temporal domain. However, the present class of nonlocal equations depends on properties at selected far field points which result in a potential satisfying parity time symmetry. The present system of nonlocal partial differential equations consists of two dependent variables in two spatial dimensions and time, where the dependent variables physically represent a wave packet and an auxiliary scalar field. The periodic solutions may take the forms of breathers (pulsating modes) and line solitons. The localized solutions can include propagating lumps and rogue waves. These nonsingular solutions are obtained by appropriate choice of parameters in the Hirota expansion. Doubly periodic solutions are also computed with elliptic and theta functions. In sharp contrast with the local Mel′nikov equation, the auxiliary scalar field in the present set of solutions can attain complex values. Through a coordinate transformation, the governing equation can reduce to the Schrödinger–Boussinesq system.

A note on unimodular N=1, d=4 AdS supergravity

We put forward a unimodular N=1, d=4 anti-de Sitter supergravity theory off shell. This theory, where the Cosmological Constant does not couple to gravity, has a unique maximally supersymmetric classical vacuum which is Anti-de Sitter spacetime with radius given by the equation of motion of the auxiliary scalar field, i.e., S=3/κ L. However, we see that the non-supersymmetric classical vacua of the unimodular theory are Minkowski and de Sitter spacetimes as well as anti-de Sitter spacetime with radius l≠ L.

Ghost-free modification of the Polyakov action and Hawking radiation

In this paper we discuss possible effects of non-locality in black hole spacetimes. We consider a two-dimensional theory in which the action describing matter is a ghost-free modification of the Polyakov action. For this purpose we write the Polyakov action in a local form by using an auxiliary scalar field and modify its kinetic term by including into it a non-local ghost-free form factor. We demonstrate that the effective stress-energy tensor is modified and we study its properties in a background of a two-dimensional black hole. We obtain the expression for the contribution of the ghost-free auxiliary field to the entropy of the black hole. We also demonstrate that if the back-reaction effects are not taken into account, such a ghost-free modification of the theory does not change the energy flux of the Hawking radiation measured at infinity. We illustrate the discussed properties for black hole solution of a 2D dilaton gravity model which admits a rather complete analytical study.

Parity singlets and doublets of massive spin-3 particles in D = 2 + 1 via Noether gauge embedding

Here we demonstrate that the sixth-order (in derivatives) spin-3 self-dual model can be obtained from the fifth-order self-dual model via a Noether Gauge Embedding (NGE) of longitudinal Weyl transformations $ \eta_{(\mu\nu} \partial_{\alpha)} \Phi$ . In the case of doublet models we can show that the massive spin-3 Singh-Hagen theory is dual to a fourth- and to a sixth-order theory, via a double round of the NGE procedure by imposing traceless longitudinal (reparametrization-like) symmetries $ \partial_{(\mu} \tilde{\xi}_{\nu\alpha)}$ in the first round and transverse Weyl transformations $ \eta_{(\mu\nu}\psi^T_{\alpha)}$ in the second one. Our procedure automatically furnishes the dual maps between the corresponding fields. Contrary to the spin-2 case where an extra (Weyl) symmetry shows up in the highest-order term, in the spin-3 case only the required symmetries by the NGE procedure appear in the sixth-order doublet model. Consequently, the absence of ghosts still demands an auxiliary scalar field.

ELECTROCHEMICAL ANALYSIS ON OUTPUT CURRENTS OF NEUTRINO ANTINEUTRINO-SENSITIVE APPARATUS

We analyze the interaction of antineutrinos with water particle in electrochemical detectors. We postulate that some biological products generate a scalar auxiliary field B0 which breaks low-energy antineutrinos into boson vb and fermion v f particles. Low-energy anti neutrinos are suggested to interact with water molecules and produce output currents. We examine the output current of neutrino interactions in the electrochemical apparatus with chemical-reaction equations and half-cell model under postulated influence of weak interaction. The environmental neutrino is analysed. The output currents are treated to be generated by hydrogen ion and oxygen with the half-cell model with inclusion of weak interaction effect on hydrooxide ion recombination.

Cross-correlations between scalar perturbations and magnetic fields in bouncing universes

Bouncing scenarios offer an alternative to the inflationary paradigm for the generation of perturbations in the early universe. Recently, there has been a surge in interest in examining the issue of primordial magnetogenesis in the context of bouncing universes. As in the case of inflation, the conformal invariance of the electromagnetic action needs to be broken in bouncing scenarios in order to generate primordial magnetic fields which correspond to observed strengths today. The non-minimal coupling, which typically depends on a scalar field that possibly drives the homogeneous background, leads to a cross-correlation at the level of the three-point function between the perturbation in the scalar field and the magnetic fields. This has been studied in some detail in the context of inflation and, specifically, it has been established that the three-point function satisfies the so-called consistency relation in the squeezed limit. In this work, we study the cross-correlation between the magnetic fields and the perturbation in an auxiliary scalar field in a certain class of bouncing scenarios. We consider couplings that lead to scale invariant spectra of the magnetic field and evaluate the corresponding cross-correlation between the magnetic field and the perturbation in the scalar field. We find that, when compared to de Sitter inflation, the dimensionless non-Gaussianity parameter that characterizes the amplitude of the cross-correlations proves to be considerably larger in bouncing scenarios. We also show that the aforementioned consistency condition governing the cross-correlation is violated in the bouncing models. We discuss the implications of our results.

Inflationary magnetogenesis with added helicity: constraints from non-Gaussianities

In previous work (Caprini and Sorbo 2014 J. Cosmol. Astropart. Phys. JCAP10(2014)056), two of us have proposed a model of inflationary magnetogenesis based on a rolling auxiliary field able both to account for the magnetic fields inferred by the (non) observation of gamma-rays from blazars, and to start the galactic dynamo, without incurring in any strong coupling or strong backreaction regime. Here we evaluate the correction to the scalar spectrum and bispectrum with respect to single-field slow-roll inflation generated in that scenario. The strongest constraints on the model originate from the non-observation of a scalar bispectrum. Nevertheless, even when those constraints are taken into consideration, the scenario can successfully account for the observed magnetic fields as long as the energy scale of inflation is smaller than GeV, under some conditions on the slow roll of the auxiliary scalar field.

Hamiltonian formalism forf(T)gravity

We present the Hamiltonian formalism for $f(T)$ gravity, and prove that the theory has $\frac{n(n-3)}{2}+1$ degrees of freedom (d.o.f.) in $n$ dimensions. We start from a scalar-tensor action for the theory, which represents a scalar field minimally coupled with the torsion scalar $T$ that defines the teleparallel equivalent of general relativity (TEGR) Lagrangian. $T$ is written as a quadratic form of the coefficients of anholonomy of the vierbein. We obtain the primary constraints through the analysis of the structure of the eigenvalues of the multi-index matrix involved in the definition of the canonical momenta. The auxiliary scalar field generates one extra primary constraint when compared with the TEGR case. The secondary constraints are the super-Hamiltonian and supermomenta constraints, that are preserved from the Arnowitt-Deser-Misner formulation of GR. There is a set of $\frac{n(n-1)}{2}$ primary constraints that represent the local Lorentz transformations of the theory, which can be combined to form a set of $\frac{n(n-1)}{2}-1$ first-class constraints, while one of them becomes second-class. This result is irrespective of the dimension, due to the structure of the matrix of the brackets between the constraints. The first-class canonical Hamiltonian is modified due to this local Lorentz violation, and the only one local Lorentz transformation that becomes second-class pairs up with the second-class constraint $\pi \approx 0$ to remove one d.o.f. from the $n^2+1$ pairs of canonical variables. The remaining $\frac{n(n-1)}{2}+2n-1$ primary constraints remove the same number of d.o.f., leaving the theory with $\frac{n(n-3)}{2}+1$ d.o.f. This means that $f(T)$ gravity has only one extra d.o.f., which could be interpreted as a scalar d.o.f.

Lefschetz thimbles in fermionic effective models with repulsive vector-field

We discuss two problems in complexified auxiliary fields in fermionic effective models, the auxiliary sign problem associated with the repulsive vector-field and the choice of the cut for the scalar field appearing from the logarithmic function. In the fermionic effective models with attractive scalar and repulsive vector-type interaction, the auxiliary scalar and vector fields appear in the path integral after the bosonization of fermion bilinears. When we make the path integral well-defined by the Wick rotation of the vector field, the oscillating Boltzmann weight appears in the partition function. This “auxiliary” sign problem can be solved by using the Lefschetz-thimble path-integral method, where the integration path is constructed in the complex plane. Another serious obstacle in the numerical construction of Lefschetz thimbles is caused by singular points and cuts induced by multivalued functions of the complexified scalar field in the momentum integration. We propose a new prescription which fixes gradient flow trajectories on the same Riemann sheet in the flow evolution by performing the momentum integration in the complex domain.

Dual formulation of covariant nonlinear duality-symmetric action of kappa-symmetric D3-brane

We study the construction of covariant nonlinear duality-symmetric actions in dual formulation. Essentially, the construction is the PST-covariantisation and nonlinearisation of Zwanziger action. The covariantisation made use of three auxiliary scalar fields. Apart from these, the construction proceed in a similar way to that of the standard formulation. For example, the theories can be extended to include interactions with external fields, and that the theories possess two local PST symmetries. We then explicitly demonstrate the construction of covariant nonlinear duality-symmetric actions in dual formulation of DBI theory, and D3-brane. For each of these theories, the twisted selfduality condition obtained from duality-symmetric actions are explicitly shown to match with the duality relation between field strength and its dual from the one-potential actions. Their on-shell actions between the duality-symmetric and the one-potential versions are also shown to match. We also explicitly prove kappa-symmetry of the covariant nonlinear duality-symmetric D3-brane action in dual formulation.

A covariantisation of M5-brane action in dual formulation

We construct a manifestly diffeomorphic M5-brane action in dual formulation coupled to an eleven-dimensional supergravity target space. The covariantisation is carried out by using (generalised) PST technique with 5 auxiliary scalar fields, which are obtained by using a geometrical consideration as a reduction of an auxiliary 4−form of Maznytsia-Preitschopf-Sorokin. As is typical in PST-covariantised theory, our construction possesses as usual the two local PST symmetries. By using one of the local PST symmetries, the action can be reduced to the non-manifestly covariant M5-brane action in dual formulation constructed earlier by the authors. The discussion on double dimensional reduction to D4-brane, and on the comparison of on-shell action then easily follows.

Reconstruction from scalar\u2013tensor theory and the inhomogeneous equation of state in f(T) gravity

General relativity (GR) characterizes gravity as a geometric properly exhibited as curvature on spacetime. Teleparallelism describes gravity through torsional properties, and can reproduce GR at the level of equations. Similar to f(R) gravity, on taking a generalization, f(T) gravity can produce various modifications its gravitational mechanism. The resulting field equations are inherently distinct to f(R) gravity in that they are second order. In the present work, f(T) gravity is examined in the cosmological context with a number of solutions reconstructed by means of an auxiliary scalar field. To do this, various forms of the Hubble parameter are considered with an f(T) Lagrangian emerging for each instance. In addition, the inhomogeneous equation of state (EoS) is investigated with a particular Hubble parameter model used to show how this can be used to reconstruct the f(T) Lagrangian. Observationally, the auxiliary scalar field and the exotic terms in the FRW field equations give the same results, meaning that the variation in the Hubble parameter may be interpreted as the need to reformulate gravity in some way, as in f(T) gravity.

Integration of trace anomaly in 6D

The trace anomaly in six-dimensional space is given by the local terms which have six derivatives of the metric. We find the effective action which is responsible for the anomaly. The result is presented in non-local covariant form and also in the local covariant form with two auxiliary scalar fields.

Wavelet-based adaptation methodology combined with finite difference WENO to solve ideal magnetohydrodynamics

In this paper, we present an accurate and efficient wavelet-based adaptive weighted essentially non-oscillatory (WENO) scheme for hydrodynamics and ideal magnetohydrodynamics (MHD) equations arising from the hyperbolic conservation systems. The proposed method works with the finite difference weighted essentially non-oscillatory (FD-WENO) method in space and the third order total variation diminishing (TVD) Runge–Kutta (RK) method in time. The philosophy of this work is to use the lifted interpolating wavelets as not only detector for singularities but also interpolator. Especially, flexible interpolations can be performed by an inverse wavelet transformation. When the divergence cleaning method introducing auxiliary scalar field ψ is applied to the base numerical schemes for imposing divergence-free condition to the magnetic field in a MHD equation, the approximations to derivatives of ψ require the neighboring points. Moreover, the fifth order WENO interpolation requires large stencil to reconstruct high order polynomial. In such cases, an efficient interpolation method is necessary. The adaptive spatial differentiation method is considered as well as the adaptation of grid resolutions. In order to avoid the heavy computation of FD-WENO, in the smooth regions fixed stencil approximation without computing the non-linear WENO weights is used, and the characteristic decomposition method is replaced by a component-wise approach. Numerical results demonstrate that with the adaptive method we are able to resolve the solutions that agree well with the solution of the corresponding fine grid.

On multifield Born and Born-Infeld theories and their non-Abelian generalizations

Starting from a recently proposed linear formulation in terms of auxiliary fields, we study $n$-field generalizations of Born and Born-Infeld theories. In this description the Lagrangian is quadratic in the vector field strengths and the symmetry properties (including the characteristic self-duality) of the corresponding non-linear theory are manifest as on-shell duality symmetries and depend on the choice of the (homogeneous) manifold spanned by the auxiliary scalar fields and the symplectic frame. By suitably choosing these defining properties of the quadratic Lagrangian, we are able to reproduce some known multi-field Born-Infeld theories and to derive new non-linear models, such as the $n$-field Born theory. We also discuss non-Abelian generalizations of these theories obtained by choosing the vector fields in the adjoint representation of an off-shell compact global symmetry group $K$ and replacing them by non-Abelian, $K$-covariant field strengths, thus promoting $K$ to a gauge group.

Cosmological evolution of generalized non-local gravity

We construct a class of generalized non-local gravity (GNLG) model which is the modified theory of general relativity (GR) obtained by adding a term m2n−2 R□−nR to the Einstein-Hilbert action. Concretely, we not only study the gravitational equation for the GNLG model by introducing auxiliary scalar fields, but also analyse the classical stability and examine the cosmological consequences of the model for different exponent n. We find that the half of the scalar fields are always ghost-like and the exponent n must be taken even number for a stable GNLG model. Meanwhile, the model spontaneously generates three dominant phases of the evolution of the universe, and the equation of state parameters turn out to be phantom-like. Furthermore, we clarify in another way that exponent n should be even numbers by the spherically symmetric static solutions in Newtonian gauge. It is worth stressing that the results given by us can include ones in refs. [28, 34] as the special case of n=2.