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Project titleNonlinear solutions in field theory and their role in astrophysics and cosmology

Research area 02 - PHYSICS AND SPACE SCIENCES, 02-101 - Physics of elementary particles

Annotation
Research in astrophysics and cosmology is rapidly expanding nowadays as a precision science and became deeply interconnected with particle physics. In particular, we know that the major part of matter in the Universe consists of Dark Matter, which is the substance of unknown nature signaling a new physics. At present, scientists consider several different models and possible candidates for the role of Dark Matter, attempts are made to find them in direct and indirect experiments. For example, the Dark Matter could be composed of new weak-interacting massive particles – WIMPs, which are predicted by different supersymmetric extensions of the Standard Model. However, at present, such models are strongly restricted by the experiments on the Large Hadron Collider, which have not discovered any new particles beyond the Standard Model yet. Axion or similar light scalar particle represent another class of possible Dark Matter candidates, which, as a primary motivation, provide natural dynamical solution for the strong CP problem. In another promising class of models the Dark Matter consists of Q-balls. The present project is devoted to the study of axion Dark Matter models and theories with Q-balls, both are related by the existence of specific non-linear field configurations which may help to discover this form of matter. In contrast to a supersymmetric scenario, these classes of models are much less studied. Axion models predict very high density of particles in the Galaxy halo. As a consequence, such Dark Matter can form the Bose-Einstein condensate, in cosmological context this condensate represents a gravitationally bound ensemble of axions – the Bose stars. At present, there is no any exact quantitative answer to the question whether the axion-like Dark Matter had time to condense, and if the answer is positive, what is mass fraction of Bose stars in the total matter balance, despite this question is very important in choosing the strategy of experimental search for this form of Dark Matter. This situation is related to the absence of a strict quantitative description of the process of Bose-Einstein condensate formation in the cosmological context, as well as to the lack of understanding of the general properties of coherent field configurations in the form of non-topological solitons like Bose stars. Our group is planning to make a considerable contribution to the theory of non-topological solitons, such as Bose stars and Q-balls, as well as to study possible strategy of their search in astrophysical and cosmological observations in the framework of models where such objects can play a role of the Dark Matter in our Universe. In order to achieve this, we are planning the following. First, we plan to examine the properties of these objects, such as existence of upper bounds on their charge and energy, study the question of stability, which are important for their description in the cosmological context. Second, we plan to examine different regimes and stages of their evolution, starting from the epoch of their formation in the early Universe and ending at the present time. And third, we plan to obtain quantitative estimates for those known effects which are discussed in the literature only qualitatively so far, as well as to consider some less examined processes, which can affect the results of the experimental search for Bose stars and Q-balls.

Expected results
A strict quantitative theory of Bose-Einstein condensation in cosmological context will be developed. In particular, axion-like particles interacting in different ways, including purely gravitational, will be studied. Different stages of cosmological non-linear evolution of axions will be considered, starting from the QCD epoch. Reliable estimate for the number density of Bose stars and analogous gravitationally bound objects will be found. Recommendations for the experimental search of such form of Dark Matter will be formulated. Rapid instability of Bose stars made up of axions or axion-like particles will be thoroughly examined. This is another important processes, which is less studied in the literature but may have important observational signatures. Key role in the development of this instability is played by the negative axion self-coupling and was not studied previously. Instability should result in some heating of axion matter, reducing its number density. Corresponding cosmological consequences will be identified and studied. In addition, some fraction of axions may be converted into radio-photons either in the process of the above instability or in the Bose-star collisions with young magnetized neutron stars. Efficiency of this conversion will be quantified and feasibility of possible connection to the mysterious astrophysical phenomena, Fast Radio Bursts, as was recently suggested in the literature, will be decided. Thorough examination of general properties of coherent field configurations in the scalar field theory, represented by non-topological solitons such as Q-balls (Coleman, 1985), their generalizations to the case of U(1) gauge theory (Lee, Stein-Schabes, Watkins and Widrow, 1989), and by Bose stars will be provided. Though the literature devoted to Q-balls is extensive, the general theory of Q-balls contain essential gaps (which are based, for example, on the unjustified use of the “thin-wall approximation”), as well as incorrect statements. E.g., the well-known restriction on the maximal charge of stable U(1) gauged Q-ball used in many phenomenological models in astrophysics and cosmology, is, in fact, incorrect (Gulamov, Nugaev, Smolyakov, 2014). The general properties of such field configurations will be examined and stability of the corresponding classical solutions will be analyzed and clarified. We expect that the results obtained in the project will be at the world level of research in this field. It should be noted also that though the project is focused on the soliton-like solutions in cosmology and astrophysics, large fraction of the expected general results will be relevant for other areas of physics related to the wave processes, such as nonlinear optics, solid-state physics, etc.

Annotation of the results obtained in 2018
1) We studied resonance production of soft photons in the field of axion Bose star. To this end we formulated one-dimensional boundary problem which specifies whether a given configuration of axion field is unstable with respect to production of photons via parametric resonance. We considered static and collapsing Bose stars. Parametric resonance occurs in these cases if coupling of axions to photons is amplified 100 and 10 times, respectively, as compared to QCD axions. These results were reported at “14th AxionWIMP conference (Patras workshop),” June 18-22, Hamburg, Germany. Now, we are preparing them for publication. 2) We performed numerical simulation which for the first time showed Bose-Einstein condensation of light dark matter in virialized halo / miniclusters caused by universal gravitational interactions. Immediately after formation the condensate formed spherical gravitationally bound objects — Bose stars. We showed that this new phenomenon of gravitational Bose condensation is described by the Landau kinetic equation, and we derived expression for the condensation time. Our results suggest that Bose stars can form during the lifetime of the Universe in two popular models with light dark matter. Our results are published in D.G. Levkov, A.G. Panin, I.I. Tkachev, "Gravitational Bose-Einstein condensation in the kinetic regime", Phys. Rev. Lett. 121 (2018) 151301 [arXiv: 1804.05857]. 2) Vibrational modes of nontopological solitons are studied in two models where the solutions themselves and linear perturbations around them can be obtained analytically. For the first time, the spectrum of the classical solutions of this type is obtained in analytic form. The results are published in Phys. Rev. D98 (2018) 096016 [arxiv: 1805.03518].

Publications

1. A. Belokon, A. Tokareva Light scalar dark matter coupled to a trace of energy-momentum tensor Journal of Cosmology and Astroparticle Physics, - (year - 2019)

2. A. Kovtun, E. Nugaev, A. Shkerin Vibrational modes of Q-balls Physical Review D, Phys. Rev. D 98, 096016 (year - 2018) https://doi.org/10.1103/PhysRevD.98.096016

3. A.G. Panin, M.N. Smolyakov Classical behaviour of Q-balls in the Wick-Cutkosky model The European Physical Journal C, - (year - 2019)

4. D.G. Levkov, A.G. Panin, I.I. Tkachev Gravitational Bose-Einstein condensation in the kinetic regime Physical Review Letters, Volume 121, Issue 15, id.151301 (year - 2018) https://doi.org/10.1103/PhysRevLett.121.151301

5. A. Kovtun, E. Nugaev, A. Shkerin Characteristic modes of vibration of Q-balls EPJ Web Conf., Volume 191, 2018, 06018 (year - 2018) https://doi.org/10.1051/epjconf/201819106018

6. E. Nugaev Metastable Q-balls EPJ Web Conf., Volume 191, 2018, 06017 (year - 2018) https://doi.org/10.1051/epjconf/201819106017

7. - Российские физики увидели, как темная материя образует капли ГАЗЕТА.РУ, - (year - )

8. - Российские физики открыли новое необычное свойство темной материи РИА НОВОСТИ, - (year - )

Annotation of the results obtained in 2016
1) In 2016 we studied a collapse of the axion Bose stars due to attractive self-interaction of the axion-like particles. For the first time we completely investigated the mechanism of this phenomenon. We demonstrated that it involves two alternating subprocesses: infall of the axion-like particles into the star center and relativistic evolution in the center. As a result of these subprocesses, collapsing stars emit a flux of mildly relativistic axion-like particles with universal spectrum. We studied possible astrophysical and cosmological implications of the Bose star collapse. These results are published in D.G. Levkov, A.G. Panin and I.I. Tkachev, “Relativistic axions from collapsing Bose stars”, arXiv:1609.03611, accepted for publication in Physical Review Letters. 2) We estimated the flux of radiophotons emanating from the collapsing Bose stars composed of the standard QCD axions. We demonstrated that this flux is unobservably small. One can hope, however, to obtain observable radiofluxes in special models of axion-like particles involving enhanced interaction of axions and photons. Solution to this additional problem will be obtained and published in 2017 when a collapse of Bose stars in special axion-like models will be investigated. 3) Q-ball solutions in the Wick-Cutkosky model are examined in detail. The energy-charge dependencies for Q-balls in this model are obtained analytically, explicit solutions for the Q-ball scalar fields are obtained numerically. A method for estimating the binding energy of the Q-ball is proposed, which can be used in the general case. This method is tested on the Q-ball in the Wick-Cutkosky model against the analytical solution of the Bete-Salpeter equation obtained for this model earlier. Direct comparison reveals very good agreement between the results obtained in the two different approaches. 4) A detailed study of the problem of classical stability of U(1) gauged Q-balls is performed. We showed that the stability criterion for ordinary (nongauged) one-field and two-field Q-balls (stating that Q-balls with dQ/d\omega<0, where Q is the Q-ball charge and \omega is its frequency, are classically stable), is inapplicable in the case of U(1) gauged Q-balls, although all the technical steps of the derivation remain the same as for the ordinary Q-balls. We performed explicit numerical simulations in models with different scalar field potentials, which explicitly demonstrate that in general the regions of stability of U(1) gauged Q-balls cannot be identified in the same way as in the case of the ordinary Q-balls. Our results imply that in the general case the classical stability criterion for ordinary Q-balls is not valid for U(1) gauged Q-balls. 5) We obtained an upper bound on the charge of nontopological solitons in the case when fermions are added to the model. This result was obtained using the analysis of Coleman-Weinberg for inhomogeneous configurations. Our bound is nonlinear in coupling constant. It may nevertheless play an important role in phenomenology, since the Q-balls with global changes 10^{22}-10^{28} are considered in literature.

Publications

1. A.G. Panin, M.N. Smolyakov Classical (in)stability of U(1) gauged Q-balls submitted to Physical Review D, - (year - 2017)

2. A.V. Kovtun, E.Ya. Nugaev Radiative corrections and instability of large Q-balls submitted to Physical Review D, - (year - 2017)

3. D.G. Levkov, A.G. Panin, I.I. Tkachev Relativistic axions from collapsing Bose stars Physical Review Letters, - (year - 2016)

4. E.Y. Nugaev, M.N. Smolyakov Q-balls in the Wick-Cutkosky model submitted to European Physical Journal C, - (year - 2017)

Annotation of the results obtained in 2017
1) Small evaporating black holes were proposed to be dangerous in inducing fast decay of the electroweak false vacuum. We observe that the flat-spectrum matter perturbations growing at the post-inflationary matter dominated stage can produce such black holes in a tiny amount which may nevertheless be sufficient to destroy the vacuum in the visible part of the Universe via the induced process. If the decay probability in the vicinity of Planck-mass black holes was of order one as suggested in literature, the absence of such objects in the early Universe would put severe constraints on inflation and subsequent stages, thus excluding many well-motivated models (e.g. the R^2-inflation) and supporting the need of new physics in the Higgs sector. We give a qualitative argument, however, that exponential suppression of the probability should persist in the limit of small black hole masses. This suppression relaxes our cosmological constraints, and, if sufficiently strong, may cancel them. https://arxiv.org/abs/1704.05399 http://iopscience.iop.org/article/10.1088/1475-7516/2017/10/016/meta 2) The smallest classically stable Q-balls are, in fact, generically metastable: in quantum theory they decay into free particles via collective tunneling. We derive general semiclassical method to calculate the rate of this process in the entire kinematical region of Q-ball metastability. Our method uses Euclidean field-theoretical solutions resembling the Coleman's bounce and fluctuations around them. As an application of the method, we numerically compute the decay rate to the leading semiclassical order in a particular one-field model. We shortly discuss cosmological implications of metastable Q-balls. https://arxiv.org/abs/1711.05279 3) We have performed detailed calculations of the destruction of axion miniclusters in gravitational collisions with Galactic stars by taking into account distribution of minicluster orbits in the Galactic halo. We have investigated two DM halo models, the Navarro-Frenk-White and isothermal density profiles. We have shown that about 2-5% of the axion miniclusters are destroyed by the time corresponding to the current age of the Galaxy, and transform subsequently into axion streams. The expected detection rate of streams in laboratory experiments, with an overdensity exceeding an order of magnitude, is 1-2 in 20 years. https://arxiv.org/abs/1710.09586 https://link.springer.com/article/10.1134%2FS1063776117080039 4) The regions of classical stability of Q-balls in the Wick-Сutkosky model, describing the interacting massive complex scalar field and massless real scalar field, are found. The behavior of classically stable Q-balls in the external real scalar field is examined, taking into account the modification of the Q-ball form in the course of its motion. Nonlinear evolution of the classically unstable Q-balls is also examined. 5) Nonlinear small perturbations against stationary solutions in the theory of complex scalar field (Q-balls) and in the theory described by the nonlinear Schrodinger equation, are examined in the general case. Explicit expressions for the integrals of motion of nonlinear perturbations, which are charge and energy in the case of Q-balls and particle number, energy and momentum in the case of the nonlinear Schrodinger equation, are derived. It is shown that the additivity property is valid for the integrals of motion of different nonlinear modes forming the perturbation. It is also shown that the corresponding nonlinear corrections to the integrals of motion can be taken into account without explicitly solving the nonlinear equations of motion for the perturbations. https://arxiv.org/abs/1710.10445 https://arxiv.org/abs/1711.05730

Publications

1. D. Gorbunov, D. Levkov and A. Panin Fatal youth of the Universe: black hole threat for the electroweak vacuum during preheating IOP Publishing Ltd and Sissa Medialab, JCAP 1710 (2017) no.10, 016 (year - 2017) https://doi.org/10.1088/1475-7516/2017/10/016

2. D. Levkov, E. Nugaev, A. Popescu The fate of small classically stable Q-balls Springer Berlin Heidelberg, - (year - 2017)

3. Emin Nugaev, Alexander Panin, Mikhail Smolyakov U(1) gauged Q-balls and their properties EPJ Web of Conferences, 158, 07003 (year - 2017) https://doi.org/10.1051/epjconf/201715807003

4. Mikhail Smolyakov Perturbations against a stationary solution of the nonlinear Schrodinger equation submitted to Physica D: Nonlinear Phenomena, - (year - 2018)

5. Mikhail Smolyakov Perturbations against a Q-ball: charge, energy and additivity property submitted to Physical Review D, - (year - 2018)

6. V.I. Dokuchaev, Y.N. Eroshenko and I.I. Tkachev Destruction of axion miniclusters in the Galaxy Pleiades Publishing, J.Exp.Theor.Phys. 125 (2017) no.3, 434-442 (year - 2017) https://doi.org/10.1134/S1063776117080039