Self-interacting Scalar Field Research Articles

Æther coupling effects on casimir energy for self-interacting scalar field within extra dimension

This paper presents comprehensive calculations for thermal and first-order radiative corrections to the Casimir energy in systems involving self-interacting massive and massless scalar fields coupled with æther in a fifth compact dimension. The method used to compute the radiative correction to the Casimir energy differs from conventional approaches by applying a unique renormalization scheme that is consistent with specific boundary conditions or backgrounds. Despite this divergence from conventional methodologies, our results demonstrate consistency within established physical limits. Furthermore, employing a toy model, we calculated the total Casimir energy density in the bulk, taking into account both thermal and radiative corrections. We also provide a thorough characterization of the total Casimir energy density in the compact dimension, detailing its magnitude and sign using graphical representations and quantitative data.

Quantum Big-Bounce as a phenomenology of RQM in the Mini-superspace

We investigate the emergence of a quantum Big-Bounce in the context of an isotropic Universe, filled by a self-interacting scalar field, which plays the role of a physical clock. The bouncing cosmology is the result of a scattering process, driven by the scalar field potential, which presence breaks down the frequency separation of the Wheeler-DeWitt equation, treated in strict analogy to a relativistic quantum system. Differently from previous analyses, we consider a really perturbative self-interaction potential, affecting the dynamics in a finite range of the time labeled by the scalar clock (and in particular we remove the divergent character previously allowed). The main result of the present analysis is that, when the Relativistic Quantum Mechanics formalism is properly implemented in the Mini-superspace analogy, the probability amplitude for the bounce is, both in the standard and polymerized case, characterized by a maximum in correspondence of the quasi-classical condition of a Universe minimum volume.

Infinite Order Hydrodynamics: An Analytical Example.

We construct a kinetic model for matter-radiation interactions whose hydrodynamic gradient expansion can be computed analytically up to infinite order in derivatives, in the fully nonlinear regime, and for arbitrary flows. The frequency dependence of the opacity of matter is chosen to mimic the relaxation time of a self-interacting scalar field. In this way, the transient sector simulates that of a realistic quantum field theory. The gradient series is found to diverge for most flows, in agreement with previous findings. We identify, for the model at hand, the mechanism at the origin of the divergence, and we provide a successful regularization scheme. Additionally, we propose a universal qualitative framework for predicting the breakdown of the gradient expansion of an arbitrary microscopic system undergoing a given flow. This framework correctly recovers all previously known instances of gradient expansion divergence. As a new prediction, we show that the gradient expansion diverges when the energy-dependent mean free path is unbounded above.

Self-interacting scalar field in (2+1) dimensions Einstein gravity with torsion

We study a massless real self-interacting scalar field φ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varphi $$\\end{document} non-minimally coupled to Einstein gravity with torsion in (2+1) space-time dimensions in the presence of a cosmological constant. The field equations with a self-interaction potential V(φ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V(\\varphi )$$\\end{document} including φn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varphi ^{n}$$\\end{document} terms are derived by a variational principle. By numerically solving these field equations with the 4th Runge–Kutta method, the circularly symmetric rotating solutions for (2+1) dimensions Einstein gravity with torsion are obtained. Exact analytical solutions to the field equations are derived for the proposed metric in the absence of both torsion and angular momentum. We find that the self-interacting potential only exists for n=6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=6$$\\end{document}, as requested by conformal symmetry. We also study the motion of massive and massless particles in (2+1) Einstein gravity with torsion coupled to a self-interacting scalar field. The effect of torsion on the behavior of the effective potentials of the particles is analyzed numerically.

Constraining self-interacting scalar field dark matter from the black hole shadow of the Event Horizon Telescope

Constraining self-interacting scalar field dark matter from the black hole shadow of the Event Horizon Telescope

Correlation functions and stochastic Feynman rules for self-interacting scalar fields

It is well known that perturbative solutions of the Langevin equation can be used to calculate correlation functions in stochastic quantization. However, this work is challenging due to the absence of generalized rules. In this paper, we address this difficulty by studying correlation functions up to certain orders for self-interacting scalar fields. Through the perturbative approach, we establish stochastic Feynman rules applicable to both finite and large fictitious times. Within this process, we introduce a fictitious-time ordering diagram, which serves as a keystone for finding all possible fictitious-time orderings and directly writing down an exact contribution for a given stochastic diagram with its fixed fictitious-time ordering.

Unfolded dynamics approach and quantum field theory

We study quantization of a self-interacting scalar field within the unfolded dynamics approach. To this end we find and analyze a classical unfolded system describing 4d off-shell scalar field with a general self-interaction potential. Then we systematically construct three different but related unfolded formulations of the corresponding quantum field theory, supporting them with illustrative calculations: an unfolded functional Schwinger-Dyson system, an unfolded system for correlation functions and an unfolded effective system for vertex functions. The most curious feature we reveal is that an unfolded quantum commutator gets naturally regularized: a standard delta-function is replaced with a heat kernel, parameterized by the unfolded proper time. We also identify an auxiliary 5d system, having this proper time as a physical time, which generates 4d scalar action as its on-shell action.

Accretion of self-interacting scalar field dark matter onto a Reissner-Nordström black hole

Accretion of self-interacting scalar field dark matter onto a Reissner-Nordström black hole

The cosmological model in [formula omitted] gravity with Scalar Field conformity

The homogeneous and isotropic cosmological model in generalized f(R,Tϕ) theories associated with the scalar field is discussed, which is motivated by the f(R,T) theory of gravity studied by Harko et al. (2011), Harko (2014) [1,2]. The f(R,Tϕ) gravity can be explained as f(R,T) gravity with a self-interacting scalar field ϕ, where Tϕ is the trace of the energy–momentum tensor. The parametrization of Hubble parameter H(t) is taken as α−βe−γt, where α, β, and γ are arbitrary constants such that α,γ>0, and β<0. The model shows no space–time singularity, and the expansion of the universe will continue forever, i.e., the future scenario of the universe attains Big Freeze. The model predicts the moderate inflationary scenario at the time of the evolution of the universe, and it is consistent with ΛCDM in the late times. The consistency of the model has also been examined using the recent observational Hubble dataset and supernovae dataset. Finally, the physical features of the model have been discussed in some detail.

Quantum Big Bounce of the Isotropic Universe Using Relational Time

We analyze the canonical quantum dynamics of the isotropic Universe with a metric approach by adopting a self-interacting scalar field as relational time. When the potential term is absent, we are able to associate the expanding and collapsing dynamics of the Universe with the positive- and negative-frequency modes that emerge in the Wheeler–DeWitt equation. On the other side, when the potential term is present, a non-zero transition amplitude from positive- to negative-frequency states arises, as in standard relativistic scattering theory below the particle creation threshold. In particular, we are able to compute the transition probability for an expanding Universe that emerges from a collapsing regime both in the standard quantization procedure and in the polymer formulation. The probability distribution results similar in the two cases, and its maximum takes place when the mean values of the momentum essentially coincide in the in-going and out-going wave packets, as it would take place in a semiclassical Big Bounce dynamics.

Borel resummation of secular divergences in stochastic inflation

We make use of Borel resummation to extract the exact time dependence from the divergent series found in the context of stochastic inflation. Correlation functions of self-interacting scalar fields in de Sitter spacetime are known to develop secular IR divergences via loops, and the first terms of the divergent series have been consistently computed both with standard techniques for curved spacetime quantum field theory and within the framework of stochastic inflation. We show that Borel resummation can be used to interpret the divergent series and to correctly infer the time evolution of the correlation functions. In practice, we adopt a method called Borel-Padé resummation where we approximate the Borel transformation by a Padé approximant. We also discuss the singularity structures of Borel transformations and mention possible applications to cosmology.

Effective potential and mass behavior of a self-interacting scalar field theory due to thermal and external electric and magnetic fields effects

Effective potential and mass behavior of a self-interacting scalar field theory due to thermal and external electric and magnetic fields effects

Legendre scalarization in gravity and cosmology

We propose a new formulation of f(R) gravity, dubbed scalarized f(R) gravity, in which the Legendre transform is included as a dynamical term. This leads to a theory with second-order field equations that describes general relativity with a self-interacting scalar field, without requiring the introduction of conformal frames. We demonstrate that the quadratic version of scalarized f(R) gravity reduces to general relativity with a massive scalar field, and we explore its implications for Friedmann cosmology. Our findings suggest that scalarized f(R) gravity may lead to simplified descriptions of cosmological applications, while the proposed formulation could offer a new perspective on the relationship between f(R) gravity and scalar–tensor theories.

Exact Bianchi type-I inflationary model with non-minimally coupled scalar field

In the present work, we try to build up an inflationary model within the framework of Bianchi type-I spacetime using a non-minimally coupled, homogeneous, self-interacting canonical scalar field. Specifically, using the Lie symmetry method, we are able to find some novel exact solutions to the Einstein field equations by assuming a power-law relationship between the scalar field and average scale factor. These symmetry-based solutions have been used to derive the values of some important parameters of the anisotropic universe. In this anisotropic model, we find that the volume of space expands with time in an inflationary scenario, depicting the Universe’s accelerating phases. An important characteristic of this model is that it initially represents anisotropic spacetime and then isotropizes the spacetime as time goes on, which favors recent cosmological observations.

On the equivalence between Sáez–Ballester theory and Einstein-scalar field system

Here, we discuss a topic that comes up more often than expected: A same theory or theoretical model arises in two different presentations which are assumed to be actually different theories so that these are independently developed. Sometimes this leads to an unwanted doubling of the results. In this paper, we illustrate this issue with the example of two apparently different gravitational theories: (i) the (minimally coupled) Einstein-massless-scalar (EMS) system and (ii) the Sáez–Ballester theory (SBT). We demonstrate that the latter is not a scalar–tensor theory of gravity, as widely acknowledged. Moreover, SBT is identified with the EMS theory. As illustrations of this identification we show that several known solutions of SBT are also solutions of the EMS system and vice versa. Cosmological arguments are also considered. In particular, a dynamical systems-based demonstration of the dynamical equivalence between these theories is given. The study of the asymptotic dynamics of the Sáez–Ballester-based cosmological model shows that there are no equilibrium points which could be associated with accelerated expansion, unless one includes a cosmological constant term or a self-interacting scalar field. This is a well-known result for cosmological models which are based on the Einstein-self-interacting-scalar theory, also known as quintessence.

Self-interacting gravitational atoms in the strong-gravity regime

We numerically investigate free and self-interacting ultralight scalar fields around black holes in General Relativity. We focus on complex scalar fields Φ whose self-interactions are described by the quartic potential V ∝ λ |Φ|4, and ignore the black hole spin in order to disentangle the effects of self interactions on the boson cloud. Using the spectral solver Kadath, we compute quasi-equilibrium configurations of the dominant eigenstates, including their backreaction on the spacetime metric. For scenarios with -10-2 ≲ λ ≲ 10-2 we find the mass of the self-interacting scalar cloud to be up to ∼ 70% larger than that of a free scalar cloud, though the additional backreaction effect on the spacetime metric is only up to ∼ 1% due to the low-density nature of the bosonic configurations. In this region of parameter space we observe approximate quadratic scalings between the mass of the cloud with λ, the scalar field amplitude, and the couplings between these two parameters. For systems with λ beyond this range, the eigenfrequencies differ sufficiently from the known free-test-field values used as inputs in our numerical setupto make the results, though convergent, physically unreliable.This bounds the range of λ in which the free scalar field solution remains a good approximation to self-interacting scalar field configurations. Our work is among the first nonperturbative explorations of self-interacting bosonic clouds around black holes, yielding detailed new insights into such systems in the nonlinear regime, while also overcoming technical challenges and quantifying limitations. Additionally, our results provide useful inputsfor fully dynamical numerical relativity simulations and for future explorations of spinning black holes and real scalar fields.

Symmetry restoration in the vicinity of neutron stars with a nonminimal coupling

We propose a new model of scalarized neutron stars (NSs) realized by a self-interacting scalar field ϕ nonminimally coupled to the Ricci scalar R of the form F(ϕ)R. The scalar field has a self-interacting potential and sits at its vacuum expectation value ϕv far away from the source. Inside the NS, the dominance of a positive nonminimal coupling over a negative mass squared of the potential leads to a symmetry restoration with the central field value ϕc close to 0. This allows the existence of scalarized NS solutions connecting ϕv with ϕc whose difference is significant, whereas the field is located in the vicinity of ϕ=ϕv for weak gravitational stars. The Arnowitt-Deser-Misner mass and radius of NSs as well as the gravitational force around the NS surface can receive sizable corrections from the scalar hair, while satisfying local gravity constraints in the Solar system. Unlike the original scenario of spontaneous scalarization induced by a negative nonminimal coupling, the catastrophic instability of cosmological solutions can be avoided. We also study the cosmological dynamics from the inflationary epoch to today and show that the scalar field ϕ finally approaches the asymptotic value ϕv without spoiling a successful cosmological evolution. After ϕ starts to oscillate about the potential minimum, the same field can also be the source for cold dark matter.

Self-interacting scalar field distributions around Schwarzschild black holes

Long-lived configurations of massive scalar fields around black holes may form if the coupling between the mass of the scalar field and the mass of the black hole is very small. In this work we analyze the effect of self-interaction in the distribution of the long-lived cloud surrounding a static black hole. We consider both attractive and repulsive self-interactions. By solving numerically the Klein Gordon equation on a fixed background in the frequency domain, we find that the spatial distribution of quasi stationary states may be larger as compared to the non interacting case. We performed a time evolution to determine the effect of the self-interaction on the life time of the configurations our findings indicate that the contribution of the self-interaction is subdominant.

Loop corrections in Minkowski spacetime away from equilibrium. Part I. Late-time resummations

Loop corrections to unequal-time correlation functions in Minkowski spacetime exhibit secular growth due to a breakdown of time-dependent perturbation theory. This is analogous to secular growth in equal-time correlators on time-dependent backgrounds, except that in Minkowski the divergences must not signal a real IR issue. In this paper, we calculate the late-time limit of the two-point correlator for different massless self-interacting scalar quantum field theories on a Minkowski background. We first use a late-time version of the in-in path integral starting in the vacuum of the free theory; in this limit, the calculation, including UV renormalization, reduces to that in in-out. We find linear or logarithmic growth in time, depending on whether the interaction strength is dimension-one or dimensionless, respectively. We next develop the Weisskopf-Wigner resummation method, that proceeds by demanding unitarity within a truncated Hilbert space, to calculate the resummed correlator and find that it gives an exact exponentiation of the late-time perturbative result. The resummed (unequal-time) correlator thus decays with an exponential or polynomial time-dependence, which is suggestive of ‘universal’ behavior that depends on the dimensions of the interaction strength.

Loop corrections in Minkowski spacetime away from equilibrium. Part II. Finite-time results

Loop corrections to finite-time correlation functions in quantum field theories away from equilibrium can be calculated using the in-in path integral approach. In this paper, we calculate the unequal-time two-point correlator for different massless self-interacting scalar quantum field theories on a Minkowski background, starting the field evolution at an arbitrary initial time. We find the counterterms that need to be added to UV-renormalize the result, including usual in-out counterterms in the dynamics and additional initial state counterterms that are required to cancel all UV divergences. We find that the late-time limit of the renormalized correlation function exhibits a linear or logarithmic growth in time, depending on whether the interaction strength is dimension-one or dimensionless, respectively. The late-time correlations match those obtained in our companion paper and, as shown there, the divergences do not indicate a real IR issue, consistent with what one would expect in Minkowski.