Nonlinear Scalar Field Research Articles

Neutron limit on the strongly-coupled chameleon field.

The physical origin of the dark energy that causes the accelerated expansion rate of the Universe is one of the major open questions of cosmology. One set of theories postulates the existence of a self-interacting scalar field for dark energy coupling to matter. In the chameleon dark energy theory, this coupling induces a screening mechanism such that the field amplitude is nonzero in empty space but is greatly suppressed in regions of terrestrial matter density. However measurements performed under appropriate vacuum conditions can enable the chameleon field to appear in the apparatus, where it can be subjected to laboratory experiments. Here we report the most stringent upper bound on the free neutron-chameleon coupling in the strongly coupled limit of the chameleon theory using neutron interferometric techniques. Our experiment sought the chameleon field through the relative phase shift it would induce along one of the neutron paths inside a perfect crystal neutron interferometer. The amplitude of the chameleon field was actively modulated by varying the millibar pressures inside a dual-chamber aluminum cell. We report a 95% confidence level upper bound on the neutron-chameleon coupling β ranging from β < 4.7 × 106 for a Ratra-Peebles index of n = 1 in the nonlinear scalar field potential to β < 2.4 × 107 for n = 6, one order of magnitude more sensitive than the most recent free neutron limit for intermediate n. Similar experiments can explore the full parameter range for chameleon dark energy in the foreseeable future.

The big bang as a result of the first-order phase transition driven by a change of the scalar curvature in an expanding early Universe: The “hyperinflation” scenario

We suggest that the "Big Bang" may be a result of the first-order phase transition driven by changing scalar curvature of the 4D space-time in expanding cold Universe, filled with nonlinear scalar field $\phi $ and neutral matter with equation of state $p=\nu \varepsilon $ (where $p$ and $\varepsilon $ are pressure and energy density of matter). We consider a Lagrangian for scalar field in curved space-time with nonlinearity $\phi ^{4} $, which along with the quadratic term $-\xi R\left|\phi \right|^{2} $ (where $\xi $ is the interaction constant and $R$ is scalar curvature) contains a term $\sim \xi R\left(\phi +\phi ^{+} \right)$ linear in $\phi $. Due to this term the condition for the extrema of the potential energy of scalar field is given by a cubic equation. Provided $\nu > 1/3$ the scalar curvature $R=[\kappa (3\nu -1)\varepsilon -4\Lambda ]$ (where $\kappa $ and $\Lambda $ are Einstein's gravitational and cosmological constants) decreases along with decreasing $\varepsilon $ in the process of the Universe's expansion, and at some critical value $R_{c} < 0$ a first-order phase transition occurs, induced by an "external field" parameter proportional to $R$. Given certain conditions the critical radius of the early Universe at the point of the first-order phase transition may reach arbitrary large values, so this scenario of unrestricted "inflation" of the Universe may be called "hyperinflation". Beyond the point of phase transition the system is rolling down into the potential minimum with the release of the potential energy of scalar field, accompanied by oscillations of its amplitude $\phi $. The powerful heating of the Universe in the course of attenuation of these oscillations plays the role of "Big Bang".

Thermodynamics of rotating black branes in higher dimensional Einstein – nonlinear electrodynamics – dilaton gravity

In this paper, we propose a n-dimensional action in which gravity is coupled to exponential nonlinear electrodynamics and scalar dilaton field with Liouville-type potential. By varying the action, we obtain the field equations. Then, we construct a new class of charged, rotating black brane solutions, with k = [(n – 1)/2] rotation parameters, of this theory. Because of the presence of the Liouville-type dilaton potential, the asymptotic behavior of the obtained solutions is neither flat nor (anti)-de Sitter. We investigate the causal structure of the space–time in ample details. We find the suitable counter term that removes the divergences of the action in the presence of the dilaton field, and calculate the conserved and thermodynamic quantities of the space–time. Interestingly enough, we find that the conserved quantities crucially depend on the dilaton coupling constant, α, while they are independent of the nonlinear parameter, β. We also check the validity of the first law of thermodynamics on the black brane horizon. Finally, we study thermal stability of the solutions by computing the heat capacity in the canonical ensemble. We disclose the effects of rotation parameter, nonlinearity of electrodynamics, and dilaton field on the thermal stability conditions.

Lightlike solitons with spin

New exact solution class of Born - Infeld type nonlinear scalar field model is obtained. These solutions are three-dimensional solitons propagating with speed of light. The appropriate twisted solitons are considered. Energy and absolute value of momentum for such soliton are proportional to absolute value of its angular momentum or spin in some approximation. The model of ideal gas for the twisted lightlike solitons with lowest twist parameter is considered. Explicit conditions provide that the spin of each soliton equals Planck constant. It is shown that these solitons look like photons.

Future global nonlinear stability of surface symmetric solutions of the Einstein–Vlasov system with a cosmological constant

We show future global nonlinear stability of surface symmetric solutions of the Einstein–Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an inductive argument. In a recent research monograph Ringström shows future nonlinear stability of (not necessarily symmetric) solutions of the Einstein–Vlasov system with a nonlinear scalar field if certain local estimates on the geometry and the matter terms are fulfilled. We show that these assumptions are satisfied at late times for the case under consideration here which together with Cauchy stability leads to our main conclusion.

Infinitely many positive and sign-changing solutions for nonlinear fractional scalar field equations

We consider the following nonlinear fractional scalar field equation $$ (-\Delta)^s u + u = K(|x|)u^p, u > 0 \hbox{in} \mathbb{R}^N, $$ where $K(|x|)$ is a positive radial function, $N\ge 2$, $0 < s < 1$, and $1 < p < \frac{N+2s}{N-2s}$. Under various asymptotic assumptions on $K(x)$ at infinity, we show that this problem has infinitely many non-radial positive solutions and sign-changing solutions, whose energy can be made arbitrarily large.

Backreaction in growing neutrino quintessence

We investigate the cosmological effects of neutrino lumps in Growing Neutrino Quintessence. The strongly non-linear effects are resolved by means of numerical N-body simulations which include relativistic particles, non-linear scalar field equations and backreaction effects. For the investigated models with a constant coupling between the scalar field and the neutrinos the backreaction effects are so strong that a realistic cosmology is hard to realize. This points towards the necessity of a field dependent coupling in Growing Neutrino Quintessence. In this case realistic models of dynamical Dark Energy exist which are testable by the observation or non-observation of large neutrino lumps.

Critical behavior in a massless scalar field collapse with self-interaction potential

We examine a one-parameter family of analytical solutions representing spherically symmetric collapse of a nonlinear massless scalar field with self-interaction in an asymptotically flat spacetime. The time evolution exhibits a type of critical behavior. Depending on the scalar charge parameter $q$ as compared to a critical value ${q}^{*}$, the incoming scalar wave collapses either to a globally naked central singularity if $q&lt;{q}^{*}$ (weak field) or to a scalar-hairy black hole if $q&gt;{q}^{*}$ (strong field), both having finite asymptotic masses. Near the critical evolution, the black hole mass follows a product-logarithmic scaling law: $\ensuremath{-}{M}^{2}\mathrm{ln}M\ensuremath{\sim}q\ensuremath{-}{q}^{*}$ with $0&lt;M\ensuremath{\ll}1$ and $q&gt;{q}^{*}$. The solution admits no self-similarity and satisfies the null and the strong energy conditions.

Multiplicity of solutions of nonlinear scalar field equations

In this Note we present new multiplicity results for the solutions of nonlinear elliptic problems of the form -\Delta u +a(x)u=|u|^{p-1}u in \mathbb R^N , u\in H^1(\mathbb R^N) , where N\ge 2 , p&gt;1 , p&lt;{N+2\over N-2} if N\ge 3 , a\in L^{N/2}_{\mathrm {loc}} (\mathbb R^N) , \inf_{\mathbb R^N}a&gt;0 . In particular, we have infinitely many positive solutions when there exists a_\infty&gt;0 such that \lim_{|x|\to\infty}a(x)=a_\infty and \lim_{|x|\to\infty}[a(x)-a_\infty]\,e^{\eta|x|}=+\infty \forall\eta&gt;0 .

Strictly Finite Range Forces from the Signum-Gordon Field: Exact Results in two Spatial Dimensions

Exact formula for the force between two identical static point charges coupled to the nonlinear scalar field of two-dimensional signum-Gordon model is obtained. Pertinent solution of the field equation is found in the form of one-dimensional integral. The force exactly vanishes when the distance between the charges exceeds certain critical value.

Covariant and gauge-invariant linear scalar perturbations in multiple scalar field cosmologies

We derive a set of equations monitoring the evolution of covariant and gauge-invariant linear scalar perturbations of Friedman-Lema\^itre-Robertson-Walker models with multiple interacting non-linear scalar fields. We use a dynamical systems' approach in order to perform a stability analysis for some classes of scalar field potentials. In particular, using a recent approximation for the inflationary dynamics of the background solution, we derive conditions under which homogenization occurs for chaotic (quadratic and quartic potentials) and new inflation. We also prove a cosmic no-hair result for power-law inflation and its generalisation for two scalar fields with independent exponential potentials (assisted power-law inflation).

Lichnerowicz-type theorems for self-gravitating systems with nonlinear electromagnetic fields

We consider a self-gravitating system containing a globally timelike Killing vector and a nonlinear Born-Infeld electromagnetic field and scalar fields. We prove that under certain boundary conditions (asymptotically flat/AdS) there can't be any nontrivial field configurations in the spacetime. To explore nontrivial solutions one should break any of the conditions we imposed. The case with another type of nonlinear electromagnetic field is also analyzed, and similar conclusions have been obtained under certain conditions.

Nonlinear scalar field equations: Existence of a positive solution with infinitely many bumps

In this paper we consider the equation(E)−Δu+a(x)u=|u|p−1uin RN, where N⩾2, p>1, p<2⁎−1=N+2N−2, if N⩾3. During last thirty years the question of the existence and multiplicity of solutions to (E) has been widely investigated mostly under symmetry assumptions on a. The aim of this paper is to show that, differently from those found under symmetry assumption, the solutions found in [6] admit a limit configuration and so (E) also admits a positive solution of infinite energy having infinitely many 'bumps’.

Gravitational waves from oscillon preheating

Oscillons are long-lived, localized excitations of nonlinear scalar fields which may be copiously produced during preheating after inflation, leading to a possible oscillon-dominated phase in the early Universe. For example, this can happen after axion monodromy inflation, on which we run our simulations. We investigate the stochastic gravitational wave background associated with an oscillon-dominated phase. An isolated oscillon is spherically symmetric and does not radiate gravitational waves, and we show that the flux of gravitational radiation generated between oscillons is also small. However, a significant stochastic gravitational wave background may be generated during preheating itself (i.e, when oscillons are forming), and in this case the characteristic size of the oscillons is imprinted on the gravitational wave power spectrum, which has multiple, distinct peaks.

A de Sitter tachyon thick braneworld

Among the multiple 5D thick braneworld models that have been proposed in the last years,in order to address several open problems in modern physics, there is a specific one involving atachyonic bulk scalar field. Delving into this framework, a thick braneworld with a cosmologicalbackground induced on the brane is here investigated. The respective field equations — derivedfrom the model with a warped 5D geometry — are highly non-linear equations, admitting anon-trivial solution for the warp factor and the tachyon scalar field as well, in a de Sitter 4Dcosmological background. Moreover, the non-linear tachyonic scalar field, that generates the branein complicity with warped gravity, has the form of a kink-like configuration. Notwithstanding, thenon-linear field equations restricting character does not allow one to easily find thick branesolutions with a decaying warp factor which leads to the localization of 4D gravity and othermatter fields. We derive such a thick brane configuration altogether in this tachyon-gravitysetup. When analyzing the spectrum of gravity fluctuations in the transverse traceless sector, the4D gravity is shown to be localized due to the presence of a single zero mode bound state,separated by a continuum of massive Kaluza-Klein (KK) modes by a mass gap. It contrasts withprevious results, where there is a KK massive bound excitation providing no clear physicalinterpretation. The mass gap is determined by the scale of the metric parameter H. Finally, thecorrections to Newton's law in this model are computed and shown to decay exponentially. It is infull compliance to corrections reported in previous results (up to a constant factor) withinsimilar braneworlds with induced 4D de Sitter metric, despite the fact that the warp factor andthe massive modes have a different form.

Screening fifth forces in k-essence and DBI models

New fifth forces have not yet been detected in the laboratory or in the solar system, hence it is typically difficult to introduce new light scalar fields that would mediate such forces. In recent years it has been shown that a number of non-linear scalar field theories allow for a dynamical mechanism, such as the Vainshtein and chameleon ones, that suppresses the strength of the scalar fifth force in experimental environments. This is known as screening, however it is unclear how common screening is within non-linear scalar field theories. k-essence models are commonly studied examples of non-linear models, with DBI as the best motivated example, and so we ask whether these non-linearities are able to screen a scalar fifth force. We find that a Vainshtein-like screening mechanism exists for such models although with limited applicability. For instance, we cannot find a screening mechanism for DBI models. On the other hand, we construct a large class of k-essence models which lead to the acceleration of the Universe in the recent past for which the fifth force mediated by the scalar can be screened.

Scalar field interpretation of the radius in spherically symmetric comoving systems

The physical radius appearing in spherically symmetry co-moving metric is interpreted in terms of a complex scalar field. The corresponding scalar field equation is formulated in the same space-time defined by the physical radius. There follows a highly non-linear scalar field equation that can be reduced to separated radial and time equations. The general integral of the separated radial equation is determined in case of real field. The same for the separated real massless time equation. Particular complex solutions are also given. It is shown that the real solutions of the scheme are not solutions of the Einstein and scalar field equations coupled in the conventional way. They can be interpreted as generating possible cosmologies with self-settling gravitational field. As to the complex solutions, they satisfy an “orthonormality” relation, similar to the one that defines the normal modes of field equation in curved space-time. This suggest the idea of possible quantization of the physical radius field. Owing to non-linearity, the procedure seems difficult to perform and to be set up completely.

A BERESTYCKI–LIONS THEOREM REVISITED

In 1983, Berestycki and Lions [Nonlinear scalar field equations I. Existence of a ground state, Arch. Ration. Mech. Anal.82 (1983) 313–346] studied the following elliptic problem: [Formula: see text] where N ≥ 3, g is subcritical at infinity. They proved the existence of a ground state under some appropriate growth restrictions on g. In the present paper, we improve this result by showing that under the critical growth assumption on g the problem admits a ground state. In addition we study a mountain pass characterization of the least energy solutions of the problem. Without the assumption of the monotonicity of the function [Formula: see text], we show that the mountain pass value gives the least energy level.

The Hamilton-Pontryagin principle and multi-Dirac structures for classical field theories

We introduce a variational principle for field theories, referred to as the Hamilton-Pontryagin principle, and we show that the resulting field equations are the Euler-Lagrange equations in implicit form. Second, we introduce multi-Dirac structures as a graded analog of standard Dirac structures, and we show that the graph of a multisymplectic form determines a multi-Dirac structure. We then discuss the role of multi-Dirac structures in field theory by showing that the implicit Euler-Lagrange equations for fields obtained from the Hamilton-Pontryagin principle can be described intrinsically using multi-Dirac structures. Finally, we show a number of illustrative examples, including time-dependent mechanics, nonlinear scalar fields, Maxwell's equations, and elastostatics.

Entropic measure for localized energy configurations: Kinks, bounces, and bubbles

We construct a configurational entropy measure in functional space. We apply it to several nonlinear scalar field models featuring solutions with spatially-localized energy, including solitons and bounces in one spatial dimension, and critical bubbles in three spatial dimensions, typical of first-order phase transitions. Such field models are of widespread interest in many areas of physics, from high energy and cosmology to condensed matter. Using a variational approach, we show that the higher the energy of a trial function that approximates the actual solution, the higher its relative configurational entropy, defined as the absolute difference between the configurational entropy of the actual solution and of the trial function. Furthermore, we show that when different trial functions have degenerate energies, the configurational entropy can be used to select the best fit to the actual solution. The configurational entropy relates the dynamical and informational content of physical models with localized energy configurations.