Symmetric Scalar Field Research Articles

Self-resonance during preheating: The case of [formula omitted]-attractor models

In this paper, for the first time, we obtain a new class of solutions for the Hill-type differential equations, which emerge in the preheating self-resonance phase of the expanding Universe. We study, in particular, the class of symmetric and asymmetric scalar field potentials coming from the so-called α-attractor models of the early Universe cosmology. By making a series expansion of the potential and employing perturbative techniques we reformulate the Mukhanov–Sasaki equation, which captures the dynamics of the curvature perturbation in these models, into a Hill equation. This last includes higher-order terms that were never solved in the literature. Namely, those coming from the cubic and quartic contributions of the scalar field potential. Then, we derive the expressions for the Floquet exponents of the Mukhanov–Sasaki variable. Our analytical results are then compared with numerical computations, showing a good agreement and thus making this method valuable for obtaining theoretical predictions with new observational applications in the contexts of Primordial Black Holes and Scalar-Induced Gravitational Waves.

Critical collapse of massless scalar fields in asymptotically anti-de Sitter spacetime* *Supported by the National Natural Science Foundation of China (11925503) and the Guangdong Major project of Basic and Applied Basic Research (2019B030302001). The computation is completed on the HPC Platform of Huazhong University of Science and Technology

We conduct numerical investigations on the critical collapse of spherically symmetric massless scalar fields in asymptotically anti-de Sitter spacetime. Our primary focus is on the behavior of the critical amplitude under various initial configurations of the scalar field. Through our numerical results, we obtain a formula that determines critical amplitude in terms of cosmological constant Λ: , where σ denotes the initial width of the scalar field and is the initial position of the scalar field. Notably, we highlight that the slope of this linear relationship depends on the initial configuration of the scalar field.

Scalar field dark matter: impact of supernova-driven blowouts on the soliton structure of low-mass dark matter haloes

ABSTRACT We present the first study on the gravitational impact of supernova feedback in an isolated soliton and a spherically symmetric dwarf scalar field dark matter (SFDM) halo of virial mass $1\times 10^{10}\,\mathrm{M_\odot }$. We use a boson mass $m=10^{-22}\,\mathrm{eV\,c^{-2}}$ and a soliton core $r_\mathrm{ c} \approx 0.7$ kpc, comparable to typical half-light radii of Local Group dwarf galaxies. We simulate the rapid gas removal from the centre of the soliton by a concentric external time-dependent Hernquist potential. We explore two scenarios of feedback blowouts: (i) a massive single burst and (ii) multiple consecutive blowouts injecting the same total energy to the system, including various magnitudes for the blowouts in both scenarios. In all cases, we find one single blowout has a stronger effect on reducing the soliton central density. Feedback leads to central soliton densities that oscillate quasi-periodically for an isolated soliton and stochastically for an SFDM halo. The range in the density amplitude depends on the strength of the blowout; however, we observe typical variations of a factor of $\geqslant$2. One important consequence of the stochastic fluctuating densities is that, if we had no prior knowledge of the system evolution, we can only know the configuration profile at a specific time within some accuracy. By fitting soliton profiles at different times to our simulated structures, we found the (1$\sigma$) scatter of their time-dependent density profiles. For configurations within the 1$\sigma$ range, we find the inferred boson mass is typically less than 20 per cent different from the real value used in our simulations. Finally, we compare the observed dynamical masses of field dwarf galaxies in our Local Group with the implied range of viable solitons from our simulations and find good agreement.

Black hole no-hair theorem for self-gravitating time-dependent spherically symmetric multiple scalar fields

We prove under certain weak assumptions a black hole no-hair theorem in spherically symmetric spacetimes for self-gravitating time-dependent multiple scalar fields with an arbitrary target space admitting a Killing field with a non-empty axis and arbitrary non-negative potential invariant under the flow of the Killing field. It is shown that for such configurations the only spherically symmetric and asymptotically flat black hole solutions consist of the Schwarzschild metric and a constant multi-scalar map. In due course of the proof we also unveil the intrinsic connection of the time-dependence of the scalar fields with the symmetries of the target space.

New results on the dynamics of critical collapse* *JQG is Supported by the Natural Science Foundation of Shandong Province, China (ZR2019MA068). YH, PPW and CGS are Supported by the National Natural Science Foundation of China (11925503)

We study the dynamics of the critical collapse of a spherically symmetric scalar field. Approximate analytic expressions for the metric functions and matter field in the large-radius region are obtained. In the central region, owing to the boundary conditions, the equation of motion for the scalar field is reduced to the flat-spacetime form.

Quantum Scalar Fields Interacting with Quantum Black Hole Asymptotic Regions

We continue our work on the study of spherically symmetric loop quantum gravity coupled to two spherically symmetric scalar fields, with one that acts as a clock. As a consequence of the presence of the latter, we can define a true Hamiltonian for the theory. In previous papers, we studied the theory for large values of the radial coordinate, i.e., far away from any black hole or star that may be present. This makes the calculations considerably more tractable. We have shown that in the asymptotic region, the theory admits a large family of quantum vacua for quantum matter fields coupled to quantum gravity, as is expected from the well-known results of quantum field theory on classical curved space-time. Here, we study perturbative corrections involving terms that we neglected in our previous work. Using the time-dependent perturbation theory, we show that the states that represent different possible vacua are essentially stable. This ensures that one recovers from a totally quantized gravitational theory coupled to matter the standard behavior of a matter quantum field theory plus low probability transitions due to gravity between particles that differ at most by a small amount of energy.

Quantization of spherically symmetric loop quantum gravity coupled to a scalar field and a clock: the asymptotic limit

We continue our work on the study of spherically symmetric loop quantum gravity coupled to two spherically symmetric scalar fields, one which acts as a clock. As a consequence of the presence of the latter, we can define a true Hamiltonian for the theory. The spherically symmetric context allows to carry out precise detailed calculations. Here we study the theory for regions of large values of the radial coordinate. This allows us to define in detail the vacuum of the theory and study its quantum states, yielding a quantum field theory on a quantum space time that makes contact with the usual treatment on classical space times.

The connection between nonzero density and spontaneous symmetry breaking for interacting scalars

We consider U(1)-symmetric scalar quantum field theories at zero temperature. At nonzero charge densities, the ground state of these systems is usually assumed to be a superfluid phase, in which the global symmetry is spontaneously broken along with Lorentz boosts and time translations. We show that, in d > 2 spacetime dimensions, this expectation is always realized at one loop for arbitrary non-derivative interactions, confirming that the physically distinct phenomena of nonzero charge density and spontaneous symmetry breaking occur simultaneously in these systems. We quantify this result by deriving universal scaling relations for the symmetry breaking scale as a function of the charge density, at low and high density. Moreover, we show that the critical value of μ above which a nonzero density develops coincides with the pole mass in the unbroken, Poincaré invariant vacuum of the theory. The same conclusions hold non-perturbatively for an O(N) theory with quartic interactions in d = 3 and 4, at leading order in the 1/N expansion. We derive these results by computing analytically the zero-temperature, finite-μ one-loop effective potential, paying special attention to subtle points related to the iε terms. We check our results against the one-loop low-energy effective action for the superfluid phonons in λϕ4 theory in d = 4 previously derived by Joyce and ourselves, which we further generalize to arbitrary potential interactions and arbitrary dimensions. As a byproduct, we find analytically the one-loop scaling dimension of the lightest charge-n operator for the λϕ6 conformal superfluid in d = 3, at leading order in 1/n, reproducing a numerical result of Badel et al. For a λϕ4 superfluid in d = 4, we also reproduce the Lee-Huang-Yang relation and compute relativistic corrections to it. Finally, we discuss possible extensions of our results beyond perturbation theory.

Aretakis hair for extreme Kerr black holes with axisymmetric scalar perturbations

We study the evolution of axially symmetric scalar field perturbations on an extreme Kerr spacetime for initial data with multipole moments ${\ensuremath{\ell}}^{\ensuremath{'}}$ higher than the least radiative mode, and we measure modes $\ensuremath{\ell}$---and, for the first time, also horizon charges---that are excited by mode-coupling interactions. We then find the Ori-Sela prefactors, a certain quantity that can be evaluated at finite distances, and the Aretakis constant along the event horizon of the extreme Kerr black hole for a sequence of initial data preparations that differ only by their distance from the event horizon. We find that for initial data in the near field there is a linear relationship of the Aretakis constant and the Ori-Sela prefactor. For initial data farther than these, the linear relationship is not universal, and we propose that stronger numerical simulations would be needed to regain linearity. The linear relationship suggests that the Aretakis charge along the event horizon can be measured at a finite distance, thereby extending this type of violation of the no-hair theorems from the least radiative axisymmetric mode also to situations that involve mode coupling.

Loop quantum gravity of a spherically symmetric scalar field coupled to gravity with a clock

The inclusion of matter fields in spherically symmetric loop quantum gravity has proved problematic at the level of implementing the constraint algebra including the Hamiltonian constraint. Here we consider the system with the introduction of a clock. Using the abelianizaton technique we introduced in previous papers in the case of gravity coupled to matter, the system can be gauge fixed and rewritten in terms of a restricted set of dynamical variables that satisfy simple Poisson bracket relations. This creates a true Hamiltonian and therefore one bypasses the issue of the constraint algebra. We show how loop quantum gravity techniques may be applied for the vacuum case and show that the Hamiltonian system reproduces previous results for the physical space of states and the observables of a Schwarzchild black hole.

Wilsonian approach to the interactionϕ2(iϕ)ϵ

We study the renormalisation of the non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric scalar field theory with the interaction $\phi^2(i\phi)^\varepsilon$ using the Wilsonian approach and without any expansion in $\varepsilon$. Specifically, we solve the Wetterich equation in the local potential approximation, both in the ultraviolet regime and with the loop expansion. We calculate the scale-dependent effective potential and its infrared limit. The theory is found to be renormalisable at the one-loop level only for integer values of $\varepsilon$, a result which is not yet established within the $\varepsilon$-expansion. Particular attention is therefore paid to the two interesting cases $\varepsilon=1,2$, and the one-loop beta functions for the coupling associated with the interaction $i\phi^3$ and $-\phi^4$ are computed. It is found that the $-\phi^4$ theory has asymptotic freedom in four-dimensional spacetime. Some general properties for the Euclidean partition function and $n$-point functions are also derived.

Multiscalar Gauss-Bonnet gravity: Scalarized black holes beyond spontaneous scalarization

Recently, a new nonlinear mechanism for black hole scalarization, different from the standard spontaneous scalarization, was demonstrated to exist for scalar Gauss-Bonnet theories in which no tachyonic instabilities can occur. Thus the Schwarzschild black hole is linearly stable but instead nonlinear instability can kick in. In the present paper we expand on this idea in the case of multiscalar Gauss-Bonnet gravity with exponential coupling functions of third and fourth leading order in the scalar field. The main motivation comes from the fact that these theories admit hairy compact objects with zero scalar charge, thus zero scalar-dipole radiation, which automatically evades the binary pulsar constraints on the theory parameters. We demonstrate numerically the existence of scalarized black holes for both coupling functions and for all possible maximally symmetric scalar field target spaces. The thermodynamics and the stability of the obtained solution branches is also discussed.

Causal effective field theories

Physical principles such as unitarity, causality, and locality can constrain the space of consistent effective field theories (EFTs) by imposing two-sided bounds on the allowed values of Wilson coefficients. In this paper, we consider the bounds that arise from the requirement of low energy causality alone, without appealing to any assumptions about UV physics. We focus on shift-symmetric theories, and consider bounds that arise from the propagation around both a homogeneous and a spherically symmetric scalar field background. We find that low energy causality, namely the requirement that there are no resolvable time advances within the regime of validity of the EFT, produces two-sided bounds in agreement with compact positivity constraints previously obtained from $2\ensuremath{\rightarrow}2$ scattering amplitude dispersion relations using full crossing symmetry.

Slowly rotating spacetimes with scalar hair

We consider asymptotically flat, rotating configurations of a selfgravitating real scalar field minimally coupled to Einstein gravity. For the sake of completeness and to introduce convenient notation, we formulate the EinsteinKlein-Gordon equations in the orthonormal tetrad uniquely associated with the metric of a nonstationary axisymmetric spacetime. First, in the stationary case, we study Bianchi identities to find appropriate variants for reducing the EinsteinKlein-Gordon system to a complete subsystem of independent equations. It turns out that this procedure can be performed in three ways. Second, assuming that the rotation is slow, the full system of these equations is linearized about a spherically symmetric scalar field configuration, which may be thought of as some exact solution. In doing so, we do not assume that the scalar field is small, and do not specify the type of the basic spherically symmetric configuration, which can be a black hole, a naked singularity, or a wormhole.

Semiclassical gravitational collapse of a radially symmetric massless scalar quantum field

We present a method to study the semiclassical gravitational collapse of a radially symmetric scalar quantum field in a coherent initial state. The formalism utilizes a Fock space basis in the initial metric, is unitary and time reversal invariant up to numerical precision. It maintains exact compatibility of the metric with the expectation values of the energy momentum tensor in the scalar field coherent state throughout the entire time evolution. We find a simple criterion for the smallness of discretization effects, which is violated when a horizon forms. As a first example, we study the collapse of a specific state in the angular momentum $l=0$ approximation. Outside the simulated volume it produces a Schwarzschild metric with $r_s \sim 3.5 \ell_p$. We see behaviour that is compatible with the onset of horizon formation both in the semiclassical and corresponding classical cases in a regime where we see no evidence for large discretization artefacts. In our example setting, we see that quantum effects accelerate the possible horizon formation and move it radially outward. We find that this effect is robust against variations of the radial resolution, the time step, the volume, the initial position and shape of the inmoving state, the vacuum subtraction, the discretization of the time evolution operator and the integration scheme of the metric. We briefly discuss potential improvements of the method and the possibility of applying it to black hole evaporation. We also briefly touch on the extension of our formalism to higher angular momenta, but leave the details and numerics for a forthcoming publication.

Nonlinear effects in the black hole ringdown: Absorption-induced mode excitation

Gravitational-wave observations of black hole ringdowns are commonly used to characterize binary merger remnants and to test general relativity. These analyses assume linear black hole perturbation theory, in particular that the ringdown can be described in terms of quasinormal modes even for times approaching the merger. Here we investigate a nonlinear effect during the ringdown, namely how a mode excited at early times can excite additional modes as it is absorbed by the black hole. This is a third-order secular effect: the change in the black hole mass causes a shift in the mode spectrum, so that the original mode is projected onto the new ones. Using nonlinear simulations, we study the ringdown of a spherically symmetric scalar field around an asymptotically anti--de Sitter black hole, and we find that this ``absorption-induced mode excitation'' is the dominant nonlinear effect. We show that this effect takes place well within the nonadiabatic regime, so we can analytically estimate it using a sudden mass-change approximation. Adapting our estimation technique to asymptotically flat Schwarzschild black holes, we expect absorption-induced mode excitation to play a role in the analysis and interpretation of current and future gravitational wave observations.

Global Non-linearly Stable Large Data Solutions to the Einstein Scalar Field System

I study a class of global, causal geodesically complete solutions to the spherically symmetric Einstein scalar field (SSESF) system . Extending results of Luk-Oh (Quantitative Decay Rates for Dispersive Solutions to the Einstein-Scalar Field System in Spherical Symmetry, arXiv:1402.2984), Luk-Oh-Yang (Solutions to the Einstein-Scalar-Field System in Spherical Symmetry with Large Bounded Variation Norms, arXiv:1605.03893), I provide new bounds controlling higher derivatives of both the metric components of the solution and the scalar field itself for large data solutions to SSESF. Moreover, by constructing a particular set of generalized wave-coordinates, I show that, assuming sufficient regularity of the data, these solutions are globally non-linearly stable to non-spherically symmetric perturbations by recent results of Luk and Oh. In particular, I demonstrate the existence of a large collection of non-trivial examples of large data, globally nonlinearly stable, dispersive solutions to the Einstein scalar field system.

Monodromy defects from hyperbolic space

We study monodromy defects in O(N) symmetric scalar field theories in d dimensions. After a Weyl transformation, a monodromy defect may be described by placing the theory on S1 × Hd−1, where Hd−1 is the hyperbolic space, and imposing on the fundamental fields a twisted periodicity condition along S1. In this description, the codimension two defect lies at the boundary of Hd−1. We first study the general monodromy defect in the free field theory, and then develop the large N expansion of the defect in the interacting theory, focusing for simplicity on the case of N complex fields with a one-parameter monodromy condition. We also use the ϵ-expansion in d = 4 − ϵ, providing a check on the large N approach. When the defect has spherical geometry, its expectation value is a meaningful quantity, and it may be obtained by computing the free energy of the twisted theory on S1 × Hd−1. It was conjectured that the logarithm of the defect expectation value, suitably multiplied by a dimension dependent sine factor, should decrease under a defect RG flow. We check this conjecture in our examples, both in the free and interacting case, by considering a defect RG flow that corresponds to imposing alternate boundary conditions on one of the low-lying Kaluza-Klein modes on Hd−1. We also show that, adapting standard techniques from the AdS/CFT literature, the S1 × Hd−1 setup is well suited to the calculation of the defect CFT data, and we discuss various examples, including one-point functions of bulk operators, scaling dimensions of defect operators, and four-point functions of operator insertions on the defect.

Gravitational collapse of quantum fields and Choptuik scaling

Gravitational collapse into a black hole has been extensively studied with classical sources. We develop a new formalism to simulate quantum fields forming a black hole. By choosing a convenient coherent state, this formalism taps into well-established techniques used for classical collapse and adds on the evolution of the mode functions of the quantum field operator. Divergences are regularized with the cosmological constant and Pauli-Villars fields. Using a massless spherically symmetric scalar field as an example, we demonstrate the effectiveness of the formalism by reproducing some classical results in gravitational collapse, and identifying the difference due to the quantum effects. We also find that Choptuik scaling in critical collapse survives in the semiclassical simulation, and furthermore the quantum deviation from the classical Choptuik scaling decreases when the system approaches the critical point.

NRPyCritCol & SFcollapse1D: an open-source, user-friendly toolkit to study critical phenomena

We present a new open-source, user-friendly toolkit of two codes—SFcollapse1D and NRPyCritCol—to study critical phenomena in the context of gravitational collapse. SFcollapse1D is a C/C++ tool designed to solve the problem of gravitational collapse of massless, spherically symmetric scalar fields with the ADM formalism in spherical-like coordinates. NRPyCritCol is a collection of Python modules that leverage the NRPy+ infrastructure to generate a highly optimized C-code for evolving massless scalar fields within a covariant BSSN formalism. The toolkit was developed with user-friendliness and code efficiency in mind, enabling the exploration of critical phenomena with consumer-grade computers. We present a study of critical phenomena from the collapse of massless scalar fields in spherical symmetry, using only these two codes and a laptop computer.