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We consider a general dynamical, spherically symmetric background in the cubic subclass of Horndeski theory and obtain the quadratic action for the perturbations using the DPSV approach. We analyse the stability conditions for high-energy modes and study the issue of the no-go theorem in the current subclass of Horndeski theory. We formulate the no-go theorem for weak dependence on one variable (time or radial) and derive its generalization to the cases which could be reduced by coordinate transformation to scenarios where the scalar field has weak dependence on one of the coordinates. Moreover we show that wide class of singular solutions are also prohibited within the cubic subclass of Horndeski theory.

This article gives a concise overview of the development and current status of studies on healthy models of the early Universe without an initial singularity, namely the cosmological bounce and Genesis scenarios, constructed within a broad class of scalar-tensor theories, specifically Horndeski theories and their generalizations. The review focuses on the topics related to linear stability at the perturbation level over the non-singular background solutions: 1) the no-go theorem, valid for non-singular cosmologies within Horndeski theory, 2) the updates on possible approaches to evade the no-go theorem, 3) the role of disformal transformations relating the Horndeski subclasses with the generalized theories like DHOST, 4) the effects on stability caused by additional matter coupling and potential emergence of superluminal perturbation modes in the multi-component setting., Comment: This review was prepared for Physics-Uspekhi (Advances in Physical Sciences) Special Issue in Honor of V.A. Rubakov 70th Birthday

We revisit the models recently derived from a Kaluza-Klein compactification of higher dimensional Horndeski theory, where the resulting electromagnetic sector features non-trivial couplings to Horndeski scalar. In particular, this class of theories admits the electromagnetic waves propagating at non-unit speed, which in turn allows to relax the constraints on Horndeski theories following from multi-messenger speed test. In this work we prove that both gravitational wave and its electromagnetic counterpart propagate at the same, although non-unit, speed above an arbitrarily time-dependent, spherically symmetric background within the theories in question. Hence, we support the statement that several subclasses of Horndeski theories are not necessarily ruled out after the GW170817 event provided the photon-Galileon couplings are allowed. We also formulate the set stability conditions for an arbitraty solution within the discussed theoretical setting., Comment: 8 pages

It was recently pointed out that some precise Photon-Galileon couplings in four dimensions (4D) -- inspired by a higher dimensional reduction -- are enough to obtain a Horndeski theory that is less constrained by the stringent experimental bounds on the speed of Gravitational Waves. They imply the constancy of the ratio of speed of gravity to light throughout cosmic evolution. This holds without fine tuning, even if one includes the general $G_4 (\pi,X)$ and $G_5 (\pi)$ scalar potentials. In this paper we go into the details of this 4D Luminal extension of Horndeski theory including its scalar sector. We also present the complete action including the general $G_5(\pi,X),\, G_6(\pi,X)$ scalar potentials. Thus we show all the $U(1)$ gauge invariant vector Galileons in 4D that result from a Kaluza-Klein dimensional reduction from 5D Horndeski. They provide a consistent coupling of a higher derivative vector to scalar modifications of gravity -- namely, without inducing Ostrogradsky ghosts and keeping gauge invariance -- in the aim to explore more universal couplings of dark energy to other matter, such as vectors and in particular the Photon., Comment: 22 pages. Fixed typos, results unchanged. Added references

We address a dynamical, spherically symmetric background in beyond Horndeski theory and formulate a set of linear stability conditions for high energy perturbation modes above an arbitrary solution. In this general setting we derive speeds of propagation in both radial and angular directions for gravity waves and compare them with the speed of light in the case of minimally coupled photon. In particular, we find that the class of beyond Horndeski theories, which satisfy the equality of gravity waves' speed to the speed of light over a cosmological background, feature gravity waves propagating at luminal speeds above a time-dependent inhomogeneous background as well., Comment: 8 pages

We show that the interplay between spin-orbit coupling (SOC) and the paramagnetic response of itinerant electrons in proximitized superconductor/paramagnet systems gives rise to the inverse spin galvanic effect, i.e. generation of magnetic moment under the influence of the charge current. Depending on the sign of the SOC constant and the system temperature, the corresponding contribution to the magnetic response of the superconductor can be either diamagnetic or paramagnetic. We discuss the relevance between the discovered phenomena and the recent experiments on Pt/Nb heterostructures as well as the puzzling sign change of the magnetic response observed in clean Ag coated Nb cylinders., Comment: 6 pages, 3 figures

In this work we suggest a phenomenological theory of photogalvanic phenomena in superconducting materials and structures revealing the diode effect. Starting from a generalized London model including the quadratic nonlinearity in the relation between the supercurrent and superfluid velocity we show that the electromagnetic wave incident on the superconductor can generate a nontrivial superconducting phase difference between the ends of the sample. Being enclosed in a superconducting loop such phase battery should generate a dc supercurrent circulating in the loop. Increasing the electromagnetic wave intensity one can provoke the switching between the loop states with different vorticities., Comment: 6 pages, 2 figures

We show that the full Horndeski theory with both curvature and torsion can support nonsingular, stable and subluminal cosmological solutions at all times. Thus, with torsion, the usual No-Go theorem that holds in a curved spacetime is avoided. In particular, it is essential to include the nonminimal derivative couplings of the $\mathcal{L}_{5}$ part of the Horndeski action ($G^{\mu\nu}\,\nabla_\mu \nabla_\nu \phi,$ and $(\nabla^2 \phi)^3$). Without the latter a No-Go already impedes the eternal subluminality of nonsingular, stable cosmologies., Comment: 21 pages, 13 Figures. Version accepted for publication in JCAP. Results unchanged. Added references

The application of Horndeski theory/ Galileons for late time cosmology is heavily constrained by the strict coincidence in the speed of propagation of gravitational and electromagnetic waves. These constraints presuppose that the minimally coupled photon is not modified, not even at the scales where General Relativity (GR) may need modification. We find that the 4D Galileon obtained from a Kaluza-Klein compactification of its higher dimensional version is a natural simultaneous modification of GR and electromagnetism with automatically "luminal" gravitational waves. This property follows without any fine tuning of Galileon potentials for a larger class of theories than previously thought. In particular, the $G_4$ potential is not constrained by the speed test and $G_5$ may also be present. In other words, some Galileon models that have been ruled out since the event GW170817 are, in fact, not necessarily constrained if they arise in 4D from compactifications of their higher dimensional Galileon counterparts. Besides their compelling luminality, the resulting vector Galileons are naturally $U(1)$ gauge invariant. We also argue that the Vainshtein screening that allows to recover GR predictions for solar system tests is also at work for electrodynamics in the dense region of laboratory tests., Comment: 5 pages. Matches the version published in PLB. Results unchanged

We consider a general static, spherically symmetric background in the quadratic beyond Horndeski theory and analyse the behaviour of linear perturbations in both parity odd and parity even sectors. We derive a full set of stability conditions for an arbitrary static, spherically symmetric solution which guarantees absence of ghosts, gradient instabilities, tachyons and superluminal modes in both sectors., Comment: 16 pages, submitted to IJMPA ICNFP2022 Special Issue

We suggest a theoretical description of the photogalvanic phenomena arising in superconducting condensates in the field of electromagnetic wave. The ac Hall effect and photon drag are shown to originate from the second-order nonlinear response of superconducting carriers caused by the suppression of their concentration due to the combined influence of the electron - hole asymmetry and charge imbalance generated by the incident electromagnetic wave. Starting from the time-dependent Ginzburg-Landau theory with the complex relaxation constant we develop a phenomenological description of these phenomena and investigate the resulting behavior of the dc supercurrent and second harmonic induced by microwave radiation incident on a superconductor surface., Comment: 7 pages, 2 figures

We show that spin-orbit coupling at the interface between a superconducting film of the finite lateral size and the underlying ferromagnetic insulator with in-plane exchange field gives rise to a series of non-reciprocal effects provided the superconducting pairing is enhanced near the boundaries of the superconductor due to, e.g., variation of the film thickness or of the interlayer electron transparency. Specifically, the critical temperature and the critical depairing current are shown to depend on the relative orientation between the exchange field in the ferromagnet and the superconducting film boundaries. The discovered anisotropy of the superconducting properties is promising for the design of diode-type elements in superconducting spintronics., Comment: Accepted to Phys. Rev. B, 20Dec2023 8 pages, 4 figures

Generic models in Galileons or Horndeski theory do not have cosmological solutions that are free of instabilities and singularities in the entire time of evolution. We extend this No-Go theorem to a spacetime with torsion. On this more general geometry the No-Go argument now holds provided the additional hypothesis that the graviton is also subluminal throughout the entire evolution. Thus, critically different for Galileons' stability on a torsionful spacetime, an arguably unphysical although arbitrarily short (deep UV) phase occurring at an arbitrary time, when the speed of gravity $(c_g)$ is slightly higher than luminal $(c)$, and by at least an amount $c_g\geq \,\sqrt{2}\,c $, can lead to an all-time linearly stable and nonsingular cosmology. As a proof of principle we build a stable model for a cosmological bounce that is almost always subluminal, where the short-lived superluminal phase occurs before the bounce and that transits to General Relativity in the asymptotic past and future., Comment: 8 pages, 4 figures. Matches the version accepted for publication in PRD. Added clarifying comments in the proof of the No-Go, references added, results unchanged

We discuss the approach suggested by Deffayet et al. (DPSV) to analysing the linearized perturbations in Horndeski theory in the case of a static, spherically symmetric background. In $\mathcal{L}_3$ subclass of Horndeski theories we prove the validity of the DPSV approach by showing that the original method corresponds to a specific gauge choice in the quadratic action for perturbations. We also show that in the case of a spherically symmetric background the DPSV trick does not work in a more general $\mathcal{L}_4$ Horndeski theory., Comment: 5 pages

Considering an anisotropic cosmological background is an interesting and simultaneously challenging problem of theoretical physics, since we not only assume a high degree of anisotropy in the early stages of the Universe, but also observe it to a small degree until now. In this paper we have constructed the unconstrained action for the perturbations above Bianchi I type background in the most general scalar-tensor theory of gravity, the Horndeski theory, and evaluate the effect of the deviation from the anisotropic background on the previously established stable solution obtained in previous works.

We consider the Quartic Horndeski theory with torsion on a FLRW background in the second order formalism. We show that there is a one parameter family of Quartic Horndeski Cartan Lagrangians and all such theories only modify the dispersion relations of the graviton and the scalar perturbation that are usually found in the standard Horndeski theory on a torsionless spacetime. In other words, for the theories in this class torsion does not induce new degrees of freedom but it only modifies the propagation. This holds for first order perturbations in spite of a kinetic mixing between the Horndeski scalar with the torsion field in the action. We also show that for most Lagrangians within the family of Quartic Horndeski Cartan theories the dispersion relation of the scalar mode is radically modified. We find only one theory within the family whose scalar mode has a regular wave-like dispersion relation., Comment: 25 pages, 3 figures. Matches version published in PRD. Expanded discussions, references added, results unchanged

We consider the issue of stability at the linearized level for static, spherically symmetric wormhole solutions within a subclass of scalar-tensor theories of beyond Horndeski type. In this class of theories we derive a set of stability conditions ensuring the absence of ghosts and both radial and angular gradient instabilities about a static, spherically-symmetric background. This set of constraints extends the existing one and completes the stability analysis for high energy modes in both parity odd and parity even sectors, while "slow" tachyonic instabilities remain unconstrained. We give an example of beyond Horndeski Lagrangian admitting a wormhole solution which complies with all stability constraints for the high energy modes., Comment: 30 pages, 2 figures

It is known that the construction of a completely stable solution in Horndeski theory is restricted very strongly by the so-called no-go theorem. Previously, various techniques have been used to avoid the conditions of the theorem. In this paper a new way of constructing stable solutions are shown in the general Horndeski theory. We considered the situation in which the unitary gauge studied earlier turns out to be singular. On this basis we construct a spatially flat, stable bouncing and genesis Universe solutions which are described by General Relativity with non-conventional scalar field.

We study the Mana and Magic for quantum states. They have a standard definition through the Clifford group, which is finite and thus classically computable. We introduce a modified Mana and Magic, which keep their main property of classical computability, while making other states classically computable. We also apply these new definitions to the studies of knot states of 2-strand knots., Comment: 9 pages, 6 figures

In this note we collect, systemise and generalise the existing results for relations between general Horndeski theories and beyond Horndeski theories via disformal transformations of metric. We derive additional disformal transformation rules relating Lagrangian functions of beyond Horndeski theory and corresponding Horndeski theory and demonstrate that some of them become singular at some moments(s) once one constructs a non-singular cosmological solution in beyond Horndeski theory that is free from ghost, gradient instabilities and strong gravity regime during the entire evolution of the system. The key issue here is that such solutions are banned in Horndeski theory due to existing no-go theorem. The proof of singular behaviour of disformal relations in this case resolves the apparent contradiction between the fact that Horndeski and beyond Horndeski theories appear related by field redefinition but describe different physics in the context of non-singular cosmologies.

We show that in superlattices with alternating superconducting (S) and ferromagnetic (F) layers the spontaneous magnetic field induced in the superconducting layers due to the electromagnetic proximity effect becomes dramatically enhanced compared to the previously studied S/F bilayers. The effect reveals itself for the in-plane orientation of the magnetic moments both for ferromagnetic and anti-ferromagnetic ordering of the moments in the F layers. In the finite size samples the magnetic field decays from the sample surface towards the bulk of the structure, and the decay length strongly depends on the relative orientation of the sample surface, the layers planes and magnetic moments in the F layers. The obtained results provide additional insights into experimental data on the neutron scattering in Nb/Gd superlattices., Comment: 6 figures

We show that Josephson $\psi$ junctions with the half-metallic (HM) weak link coupled to the superconducting (S) electrodes through the ferromagnetic (F) layers host collective excitations of magnetic moment and the Josephson phase. This results in the shift of the ferromagnetic resonance frequency, anomalies in the current-voltage characteristics and the appearance of additional magnetic anisotropy in the F layers. In contrast to the previously studied S/F/S junctions, the coupling between magnetic and plasma modes emerges even in the long-wavelength limit. Such coupling is shown to enable the controllable magnetization reversal in the F layer governed by the d.c. current pulse which provides the effective mechanism for magnetic moment manipulation in the devices of superconducting spintronics., Comment: 7 pages, 2 figures

We show that a ferromagnetic (F) slab with the in-plane magnetization sandwiched between two superconducting (S) films experiences strong demagnetization effect due to the Meissner screening of the stray magnetic field by the superconductors. In the extreme case the transition of the S films from normal to the superconducting state can switch the demagnetization factor from 0 to 1 which is in a sharp contrast with the S/F bilayers where such transition affects the magnetic field inside the F film only slightly. The giant demagnetization effect is shown to be qualitatively robust against the decreasing of the superconducting film thickness and may provide a hint towards the explanation of the anomalously large ferromagnetic resonance frequency shift recently observed for the S/F/S structures [I. A. Golovchanskiy, N. N. Abramov, V. S. Stolyarov, V. I. Chichkov, M. Silaev, I. V. Shchetinin, A. A. Golubov, V. V. Ryazanov, A. V. Ustinov, and M. Yu. Kuprianov, Phys. Rev. Appl. 14, 024086 (2020)]., Comment: 7 pages, 3 fugures

The Cooper pairs in superconducting condensates are shown to acquire a temperature-dependent dc magnetic moment under the effect of the circularly polarized electromagnetic radiation. The mechanisms of this inverse Faraday effect are investigated within the simplest version of the phenomenological dynamic theory for superfluids, namely, the time-dependent Ginzburg-Landau (GL) model. The light-induced magnetic moment is shown to be strongly affected by the nondissipative oscillatory contribution to the superconducting order parameter dynamics which appears due to the nonzero imaginary part of the GL relaxation time. The relevance of the latter quantity to the Hall effect in superconducting state allows to establish the connection between the direct and inverse Faraday phenomena., Comment: 11 pages, 3 figures

We investigate superconducting phase transition in superconductor(S)/ferromagnet(F) bilayer with Rasba spin-orbit interaction at S/F interface. This spin-orbit coupling produces spontaneous supercurrents flowing inside the atomic-thickness region near the interface, which are compensated by the screening Meissner currents [S. Mironov and A. Buzdin, Phys. Rev. Lett \textbf{118}, 077001 (2017)]. In the case of thin superconducting film the emergence of the spontaneous surface currents causes the increase of the superconducting critical temperature and we calculate the actual value of the critical temperature shift. We also show that in the case of type-I superconducting film this phase transition can be of the first order. In the external magnetic field the critical temperature depends on the relative orientation of the external magnetic field and the exchange field in the ferromagnet. Also we predict the in-plane anisotropy of the critical current which may open an alternative way for the experimental observation of the spontaneous supercurrents generated by the SOC.

We consider DHOST Ia theory interacting gravitationally with an additional conventional scalar field minimally coupled to gravity. At the linearized level of perturbations about cosmological background, we find that in the presence of a slowly rolling extra scalar field, one of the modes generically propagates at superluminal speed. This result is valid for any stable cosmological background. We identify a subclass of DHOST Ia theories in which this superluminality property is absent, and all modes may propagate (sub)luminally. We discuss possible implications for the interacting DHOST Ia theories.

We study the superluminality issue in beyond Horndeski theory with additional scalar field, which is minimally coupled to gravity and has no second derivatives in the Lagrangian. We present the quadratic action for perturbations in cosmological backgrounds, stability conditions and expressions for sound speeds. We find that in the case of conventional additional scalar whose flat-space propagation speed is that of light, one of the modes in interacting theory is necessarily superluminal when this scalar rolls, even arbitrarily slowly. This result holds in any theory of the beyond Horndeski class (with 6 arbitrary functions in the Lagrangian) and for any stable rolling background. More generally, the requirement of the absence of superluminality imposes non-trivial constraints on the structure of the theory., Comment: A contribution to Physica Scripta Special Issue "Focus on New Frontiers in Physics - Selected Papers from ICNFP 2019"; the journal version

We demonstrate that a Josephson junction with a half-metallic weak link integrated into the superconducting loop enables the pumping of magnetic flux piercing the loop. In such junctions, the ground state phase $\psi$ is determined by the mutual orientation of magnetic moments in two ferromagnets surrounding the half-metal. Thus, the precession of magnetic moment in one of two ferromagnets controlled, e.g., by the microwave radiation, results in the accumulation of the phase $\psi$ and subsequent switching between the states with different vorticities. The proposed flux pumping mechanism does not require the application of voltage or external magnetic field which enables the design of electrically decoupled memory cells in superconducting spintronics., Comment: 5 pages, 5 figures

We address the issue of potential superluminal propagation of gravitational waves in backgrounds neighboring the previously suggested bounce [arXiv:1807.08361] in beyond Horndeski theory. We find that the bouncing solution lies right at the boundary of the region where the gravitational waves propagate at speed exceeding that of light, i.e. that solution suffers superluminality problem. We suggest a novel version of a completely stable bouncing model where both scalar and tensor perturbations remain safely subluminal not only on the solution itself but also in its neighbourhood. The model remains free of superluminality when extra matter in the form of radiation or, more generally, ideal fluid with equation of state parameter $w\leq 1/3$ (and also somewhat higher) is added. Superluminality reappears when extra matter is added whose sound velocity is equal or close to 1 in flat space; an example is scalar field minimally coupled to metric. The latter property is characteristic of all beyond Horndeski cosmologies; we briefly discuss its significance., Comment: 24 pages, 12 figures. In v3: Major revision. A section on (the absence of) superluminality in the presence of additional matter added. Journal version, to appear in JCAP

Spin-singlet Cooper pairs consisting of two electrons with opposite spins cannot directly penetrate from a superconductor to a half-metal (fully spin polarized ferromagnets) which blocks the superconducting proximity effect between these materials. In this paper we demonstrate that, nevertheless, two half-metallic layers electrically coupled to the superconducting film substantially affect its critical temperature and produce the spin valve effect. Within the tight-binding model for the atomically thin multilayered spin valves we show that depending on the details of the electron energy spectra in half-metals the critical temperature as a function of the angle between the spin quantization axes in half-metals can be either monotonically increasing or decreasing. This finding highlights the crucial role of the band structure details in the proximity effect with half-metals which cannot be adequately treated in the quasiclassical theories.

The spin-triplet correlations in superconducting spin valve structures arising in the presence of noncollinear textures of magnetic moment are shown to enhance strongly the electromagnetic proximity effect, i. e. the long-range leakage of the magnetic field from the ferromagnet (F) to the superconducting (S) layer. Both the dirty and clean limits are studied on the basis of the Usadel and Eilenberger theory, correspondingly. Our results suggest a natural explanation for the puzzling enhancement of the spontaneous magnetic fields induced by the noncollinear magnetic structures observed by the muon spin rotation techniques in a wide class of layered S/F systems. We show that the electromagnetic proximity effect causes the shift of the Fraunhofer dependence of the critical current on the external magnetic field in the Josephson junction with one superconducting electrode covered by the ferromagnetic layer. This provides an alternative way to measure both the magnitude and the direction of the spontaneous magnetic field induced in the superconductor. We also demonstrate the possibility of the long ranged superconductivity control of the magnetic state in F$_1$/S/F$_2$ structures.

This essay is a brief review of the recent studies of non-singular cosmological scenarios with bounce and Genesis and their stability in a subclass of scalar-tensor theories with higher derivatives -- beyond Horndeski theories. We discuss the general results of stability analysis of the non-singular cosmological solutions in beyond Horndeski theories, as well as other closely related topics: 1) the no-go theorem, which is valid in the general Horndeski theories but not in their extensions, 2) singularities in disformal transformations relating beyond Horndeski theories with general ones, 3) healthy behaviour of the scalar sector in the unitary gauge despite divergencies of coefficients in the quadratic action for perturbations ("$\gamma$-crossing"). We describe several specific examples of bouncing cosmologies and models with Genesis epoch which have neither ghosts nor gradient instabilities among the linearized perturbations about the homogeneous isotropic background during entire evolution., Comment: This essay was prepared for JETP Special Issue in Honor of I.M. Khalatnikov 100th Birthday