Self-interacting Scalar Field Research Articles

Non-Gaussian entanglement renormalization for quantum fields

In this work, a non-Gaussian cMERA tensor network for interacting quantum field theories (icMERA) is presented. This consists of a continuous tensor network circuit in which the generator of the entanglement renormalization of the wavefunction is nonperturbatively extended with nonquadratic variational terms. The icMERA circuit nonperturbatively implements a set of scale dependent nonlinear transformations on the fields of the theory, which suppose a generalization of the scale dependent linear transformations induced by the Gaussian cMERA circuit. Here we present these transformations for the case of self-interacting scalar and fermionic field theories. Finally, the icMERA tensor network is fully optimized for the λϕ4 theory in (1 + 1) dimensions. This allows us to evaluate, nonperturbatively, the connected parts of the two- and four-point correlation functions. Our results show that icMERA wavefunctionals encode proper non-Gaussian correlations of the theory, thus providing a new variational tool to study phenomena related with strongly interacting field theories.

Gauge-invariant spherical linear perturbations of wormholes in Einstein gravity minimally coupled to a self-interacting phantom scalar field

Recently, there has been quite a lot of interest in static, spherical wormhole spacetimes and the question of their stability with respect to time-dependent perturbations. The consideration of linearized perturbations usually leads to a master wave equation with effective potential which can then be analyzed using standard tools from quantum mechanics. However, in the wormhole case, particular care must be taken with the gauge conditions when formulating the master equation. A poor coordinate choice, based for example on fixing the areal radial coordinate, may lead to singularities at the throat which complicate the stability analysis or might even lead to erroneous conclusions regarding the stability of the underlying wormhole configuration. In this work, we present a general method for deriving a gauge-invariant wave system of linearized perturbation equations in the spherically symmetric case, assuming that the matter supporting the wormhole is a phantom scalar field, that is, a self-interacting scalar field whose kinetic energy has the reversed sign. We show how this system can be decoupled and reduced to a single master wave equation with a regular potential, with no intermediate steps involving singularities at the throat. Two applications of our formalism are given. First, we rederive the master equation for the linearly perturbed Ellis-Bronnikov wormhole using our new, singularity-free method. Second, we derive the master equation describing the linear perturbations of a certain Anti de Sitter wormhole, provide a detailed analysis of the spectral properties of the underlying operator and prove that this wormhole is linearly unstable. In the final part of the paper, we consider a wormhole with de Sitter-type ends, whose spacetime presents horizons and admits a nonstatic extension beyond them; for this system we derive partial results of linear instability.

Large and ultracompact Gauss-Bonnet black holes with a self-interacting scalar field

We consider the Einstein-scalar-Gauss-Bonnet theory, and study the case where a negative cosmological constant is replaced by a more realistic, negative scalar-field potential. We study different forms of the coupling function between the scalar field and the Gauss-Bonnet term as well as of the scalar potential. In all cases, we obtain asymptotically-flat, regular black-hole solutions with a non-trivial scalar field which naturally dies out at large distances. For a quadratic negative potential, two distinct subgroups of solutions emerge: the first comprises light black holes with a large horizon radius, and the second includes massive, ultra-compact black holes. The most ultra-compact solutions, having approximately the 1/20 of the horizon radius of the Schwarzschild solution with the same mass, emerge for the exponential and linear coupling functions. For other polynomial forms of the scalar potential, the subgroup of ultra-compact solutions disappears, and the black holes obtained may have a horizon radius larger or smaller than the Schwarzschild solution depending on the particular value of their mass.

The global existence of small self-interacting scalar field propagating in the contracting universe

We present a condition on the self-interaction term that guaranties the existence of the global in time solution of the Cauchy problem for the semilinear Klein-Gordon equation in the Friedmann-Lama$\hat{i}$tre-Robertson-Walker model of the contracting universe. For the Klein-Gordon equation with the Higgs potential we give a lower estimate for the lifespan of solution.

On restricting to one-loop order the radiative effects in quantum gravity

The dimensionful nature of the coupling in the Einstein–Hilbert action in four dimensions implies that the theory is non-renormalizable; explicit calculation shows that beginning at two loop order, divergences arise that cannot be removed by renormalization without introducing new terms in the classical action. It has been shown that, by use of a Lagrange multiplier field to ensure that the classical equation of motion is satisfied in the path integral, radiative effects can be restricted to one-loop order. We show that by use of such Lagrange multiplier fields, the Einstein–Hilbert action can be quantized without the occurrence of non-renormalizable divergences. We then apply this mechanism to a model in which there is in addition to the Einstein–Hilbert action, a fully covariant action for a self-interacting scalar field coupled to the metric. It proves possible to restrict loop diagrams involving internal lines involving the metric to one-loop order; diagrams in which the scalar field propagates occur at arbitrary high order in the loop expansion. This model also can be shown to be renormalizable. Incorporating spinor and vector fields in the same way as scalar fields is feasible, and so a fully covariant Standard Model with a dynamical metric field can also be shown to be renormalizable.

Thin-shell wormhole satisfying energy conditions

The quartic self-interacting conformal scalar field is used to construct a thin-shell wormhole satisfying all energy conditions. Accompanying the scalar field in the theory is the extremal Reissner-Nordström black hole with a positive cosmological constant. New junction conditions apt for the higher-order terms are derived in the Gaussian normal coordinates.

Quantum loop effects to the power spectrum of primordial perturbations during ultra slow-roll inflation

We examine the quantum loop effects on the single-field inflationary models in a spatially flat Friedmann-Robertson-Walker (FRW) cosmological space-time with a general self-interacting scalar field potential, which is modeled in terms of the Hubble flow parameters in the effective field theory approach. In particular, we focus on the scenarios in both slow-roll to ultra-slow-roll (SR-USR) and SR-USR-SR inflation, in which it is shown that density perturbations originated from quantum vacuum fluctuations can be enhanced at small-scales, and then potentially collapse into primordial black holes (PBHs). Here our estimates indicate significant one-loop corrections around the peak of the density power spectrum in both scenarios. The induced large quantum loop effects should be confirmed by a more formal quantum field theory, and, if so, should be treated in a self-consistent manner that will be discussed.

Finite lifespan of solutions of the semilinear wave equation in the Einstein–de Sitter spacetime

We examine the solutions of the semilinear wave equation, and, in particular, of the [Formula: see text] model of quantum field theory in the curved spacetime. More exactly, for [Formula: see text] we prove that the solution of the massless self-interacting scalar field equation in the Einstein–de Sitter universe has finite lifespan.

Equilibrium States in Thermal Field Theory and in Algebraic Quantum Field Theory

In this paper we compare the construction of equilibrium states at finite temperature for self-interacting massive scalar quantum field theories on Minkowski spacetime proposed by Fredenhagen and Lindner with results obtained in ordinary thermal field theory, by means of real time and Matsubara formalisms. In the construction of this state, even if the adiabatic limit is considered, the interaction Lagrangian is multiplied by a smooth time cut-off. In this way the interaction starts adiabatically and the correlation functions are free from divergences. The corresponding interaction Hamiltonian is a local interacting field smeared over the interval of time where the chosen cut-off is not constant. In order to cope with this smearing, the Matsubara propagator needs to be modified. We obtain an expansion of the correlation functions of the interacting equilibrium state as a sum over certain type of graphs with mixed edges, some of them correspond to modified Matsubara propagators and others to propagators of the real time formalism. An integration over the adiabatic time cut-off is present in every vertex. However, at every order in perturbation theory, the final result does not depend on the particular form of the cut-off function. The obtained graphical expansion contains in it both the real time formalism and the Matsubara formalism as particular cases. Finally, we show that a particular factorisation which is used to derive the ordinary real time formalism holds only in special cases and we present a counterexample. We conclude with the analysis of certain correlation functions and we notice that corrections to the self-energy in a $\lambda\phi^4$ at finite temperature theory are expected.

Stochastic quantization of a self-interacting nonminimal scalar field in semiclassical gravity

We employ stochastic quantization for a self-interacting nonminimal massive scalar field in curved spacetime. The covariant background field method and local momentum space representation are used to obtain the Euclidean correlation function and evaluate multi-loop quantum corrections through simultaneous expansions in the curvature tensor and its covariant derivatives and in the noise fields. The stochastic correlation function for a quartic self-interaction reproduces the well-known one-loop result by Bunch and Parker and is used to construct the effective potential in curved spacetime in an arbitrary dimension D up to the first order in curvature. Furthermore, we present a sample of numerical simulations for D=3 in the first order in curvature. We consider the model with spontaneous symmetry breaking and obtain fully nonperturbative solutions for the vacuum expectation value of the scalar field and compare them with one- and two-loop solutions.

Numerical studies on core collapse supernova in self-interacting massive scalar-tensor gravity

We investigate stellar core collapse in scalar-tensor theory with a massive self-interacting scalar field. In these theories, strong long-lived inverse chirp signals could be induced during the stellar core collapse, which provides us with several potential smoking-gun signatures that could be found using current ground-based detectors. We show that the existence of self-interaction in the potential of the scalar field can significantly suppress spontaneous scalarization and the amplitude of the monopole gravitational-wave radiation. Moreover, this suppression due to self-interaction is frequency dependent and may be discernible in LIGO/Virgo's sensitive band. Therefore, self-interaction should be considered when constraining scalar-tensor coupling parameters with gravitational-wave detections. Alternatively, if such monopole gravitational-wave signals are detected, then one may be able to infer the presence of self-interaction.

Axial quasinormal modes of scalarized neutron stars with massive self-interacting scalar field

We study the axial quasi-normal modes of neutron stars in scalar-tensor theories with massive scalar field including a self-interacting term in the potential. Various realistic equations of state including nuclear, hyperonic and hybrid matter are employed. Although the effect of spontaneous scalarization of neutron stars can be very large, binary pulsar observations and gravitational wave detections significantly constrain the massless scalar-tensor theories. If we consider a properly chosen nonzero mass for the scalar field, though, the scalar-tensor parameters cannot be restricted by the observations, resulting in large deviation from pure general relativity. With this motivation in mind, we extend the universal relations for axial quasi-normal modes known in general relativity to neutron stars in massive scalar-tensor theories with self-interaction using a wide range of realistic EOS. We confirm the universality of the scaled frequency and damping time in terms of the compactness and scaled moment of inertia for neutron stars with and without massive scalarization.

Axionic charged black branes with arbitrary scalar nonminimal coupling

In this paper, we construct four-dimensional charged black branes of a nonminimally coupled and self-interacting scalar field. In addition to the scalar and Maxwell fields, the model involves two axionic fields homogeneously distributed along the two-dimensional planar base manifold providing in turn a simple mechanism of momentum dissipation. Interestingly enough, the horizon of the solution can be located at two different positions depending on the sign of the parameter associated to the axionic field, and in both cases there exists a wide range of values of the nonminimal coupling parameter yielding to physical acceptable solutions. For a negative parameter that sustains the axionic fields, the allowed nonminimal coupling parameters take discrete values and the solution turns out to be extremal since its has zero temperature. A complete analysis of the thermodynamic features of the solutions is also carried out. Finally, thanks to the mechanism of momentum dissipation, the holographic DC conductivities of the solutions are computed in terms of the black hole horizon data, and we analyze the effects of the nonminimal coupling parameter on these conductivities. For example, in the purely electric case, we notice that as long as the nonminimal coupling parameter takes the discrete values associated to the extremal solution, the DC conductivity vanishes identically reproducing in turn an insulator behavior. In the non extremal case, we point out the existence of a particular value of the nonminimal coupling parameter (which is greater than the conformal one in four dimensions) yielding an infinite conductivity; this is due to the fact that the translation invariance is restored at this point. Finally, in the dyonic case, we show that the conductivity matrix for the extremal solution has a Hall effect-like behavior.

Cosmic acceleration in the Randall-Sundrum II brane world

In this paper, we implement the dynamical system tools to study the dynamics of a self-interacting scalar field for suitable interactions of dark energy and dark matter in the Randall-Sundrum II brane scenario. Here we investigate three distinct forms of interaction strength namely, $I_{\phi}=\alpha\dot{\rho_{\phi}}$ , $I_{m1}=\delta \dot{\phi} \rho_{m}$ and $I_{m2}=\frac{\sigma\dot{\phi}^{2} \rho_{m}}{H}$ . We consider a homogeneous and isotropic Friedmann-Robertson-Walker brane model. The transformation equations are simplified to an autonomous system of ordinary differential equations by a suitable change of variables and hence a dynamical system analysis is performed for the respective interacting models in RS II brane cosmology. During the dynamical system analysis, we use the linear stability theory to study the stability of hyperbolic points, but these linearization techniques fail for non-hyperbolic points. So we apply the center manifold theory to determine the stability of non-hyperbolic points. For these specific interaction strengths, the 3D and 4D dynamical system analysis infers the existence of late-time attractors. These attractors are found for constant potential and inverse power law potential. The presence of these attractors results in late-time cosmic acceleration.

Global existence of the self-interacting scalar field in the de Sitter universe

We present some sufficient conditions for the global in time existence of solutions of the semilinear Klein-Gordon equation of the self-interacting scalar field with complex mass. The coefficients of the equation depend on spatial variables as well, which makes results applicable, in particular, to the spacetime with the time slices being Riemannian manifolds. The least lifespan estimate is given for the class of equations including the Higgs boson equation, which according to physics has a finite lifetime.

On iϵ prescription in cosmology

This is a technical note on the iϵ prescription in cosmology where we consider a self-interacting scalar field in the Poincare patch of the de Sitter space whose Hamiltonian has explicit time dependence. We use both path integral and operator formalisms to work out the evolution of states from asymptotic past infinity with iϵ prescription, which becomes nontrivial even in the free theory, and explicitly show how arbitrary states are projected onto the vacuum. We establish that in perturbation theory the ie prescription can be implemented in Weinberg's commutator formula by just inserting ϵ dependent convergence factors that make the oscillating time integrals at infinity meaningful.

One-dimensional soliton system of gaugedQ-ball and anti-Q-ball

The (1+1)-dimensional gauge model of two complex self-interacting scalar fields that interact with each other through an Abelian gauge field and a quartic scalar interaction is considered. It is shown that the model has nontopological soliton solutions describing soliton systems consisting of two Q-ball components possessing opposite electric charges. The two Q-ball components interact with each other through the Abelian gauge field and the quartic scalar interaction. The interplay between the attractive electromagnetic interaction and the repulsive quartic interaction leads to the existence of symmetric and nonsymmetric soliton systems. Properties of these systems are investigated by analytical and numerical methods. The symmetric soliton system exists in the whole allowable interval of the phase frequency, whereas the nonsymmetric soliton system exists only in some interior subinterval. Despite the fact that these soliton systems are electrically neutral, they nevertheless possess nonzero electric fields in their interiors. It is found that the nonsymmetric soliton system is more preferable from the viewpoint of energy than the symmetric one. Both symmetric and nonsymmetric soliton systems are stable to the decay into massive scalar bosons.

Exact inflationary solutions in exponential gravity

We consider a modified gravity model of the form $ f(R,\phi)=R e^{h(\phi)R} $, where the strong gravity corrections are taken to all orders and $\phi$ is a self-interacting massless scalar field. We show that the conformal transformation of this model to Einstein frame leads to non-canonical kinetic term and negates the advantage of the Einstein frame. We obtain exact solutions for the background in the Jordan frame without performing conformal transformations and show that the model leads to inflation with exit. We obtain scalar and tensor power-spectrum in Jordan frame and show that the model leads to red-tilt. We discuss the implications of the same in the light of cosmological observations.

Moment of inertia\u2013mass universal relations for neutron stars in scalar-tensor theory with self-interacting massive scalar field

We are investigating universal relations between different normalisations of the moment of inertia and the compactness of neutron stars in slow rotation approximation. We study the relations in particular class of massive scalar-sensor theories with self-interaction, for which significant deviations from General Relativity are allowed for values of the parameters that are in agreement with the observations. Moment of inertia-compactness relations are examined for different normalisation of the moment of inertia. It is shown that for all studied cases the deviations from EOS universality are small for the examined equations of state. On the other hand the scalarization can lead to large deviations from the general relativistic universal relations for values of the parameters that are in agreement with the current observations that can be potentially used to set further test the scalar-tensor theories.

Recovering P(X) from a canonical complex field

We study the correspondence between models of a self-interacting canonical complex scalar field and P(X)-theories/shift-symmetric k-essence. Both describe the same background cosmological dynamics, provided that the amplitude of the complex scalar is frozen modulo the Hubble drag. We compare perturbations in these two theories on top of a fixed cosmological background. The dispersion relation for the complex scalar has two branches. In the small momentum limit, one of these branches coincides with the dispersion relation of the P(X)-theory. Hence, the low momentum phase velocity agrees with the sound speed in the corresponding P(X)-theory. The behavior of high frequency modes associated with the second branch of the dispersion relation depends on the value of the sound speed. In the subluminal case, the second branch has a mass gap. On the contrary, in the superluminal case, this branch is vulnerable to a tachyonic instability. We also discuss the special case of the P(X)-theories with an imaginary sound speed leading to the catastrophic gradient instability. The complex field models provide with a cutoff on the momenta involved in the instability.