Axionic extension of the Einstein-aether theory

Abstract

We extend the Einstein-aether theory to take into account the interaction between a pseudoscalar field, which describes the axionic dark matter, and a time-like dynamic unit vector field, which characterizes the velocity of the aether motion. The Lagrangian of the Einstein-aether-axion theory includes cross-terms based on the axion field and its gradient four-vector, on the covariant derivative of the aether velocity four-vector, and on the Riemann tensor and its convolutions. We follow the principles of the Effective Field theory, and include into the Lagrangian of interactions all possible terms up to the second order in the covariant derivative. Interpretation of new couplings is given in terms of irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. A spatially isotropic and homogeneous cosmological model with dynamic unit vector field and axionic dark matter is considered as an application of the established theory; new exact solutions are discussed, which describe models with a Big Rip, Pseudo Rip and de Sitter-type asymptotic behavior.

Stability of out-of-phase solitons and laser pulse self-compression in active multicore fibers

“…Figure 1 shows schematically an MCF fiber with N = 3. The analysis will be based on the standard theoretical model [7,8,13,16,17,27,37], in the framework of which it is assumed that the fundamental guided modes of the optical cores oriented parallel to the z-axis are weakly coupled. In this case, the propagation of laser pulses in the MCF can be described approximately as a superposition of fundamental modes localized in each core (1) where φ(x, y) is the structure of the lowest spatial mode in the core, E n is the envelope of the electric field strength in the n-th core, which slowly changes along the z-axis.…”

“…Unfortunately, these expectations have failed. As shown by theoretical and experimental studies [6][7][8][9][10][11][12], such systems have its own critical power/energy, at which self-focusing of the quasi-homogeneous distribution of the discrete wave field occurs, and the field disintegrates into a set of incoherent structures [13]. Despite that, a number of interesting results were obtained in this direction related to studying the possibilities of generating a supercontinuum [14,15], reducing the duration of laser pulses [13,[16][17][18][19][20][21][22][23], controlling the structure of the wave field [24][25][26][27][28], and producing light bullets [10-12, 29, 30].…”

New application of the Killing vector field formalism: modified periodic potential and two-level profiles of the axionic dark matter distribution

“…This idea emphasizes that the axion system is not a simple collisionless, pressureless cold gas; the axion system has to be characterized by some internal self-interaction. We also follow the idea that axionic systems are self-interacting, and we think that their internal structures are predetermined by the modified periodic potential (23). Minima of this potential predetermine the equilibrium states of the axions.…”

“…When we deal with the standard and/or conformal Killing vectors ξ (a) , the left-hand side of this equation vanishes, as it was shown in Section IIA. When the axion field is in the equilibrium state, the quantity ∂V ∂Φ * (see (23)) also is equal to zero. In this sense, our scheme of extension of the potential of the pseudoscalar (axion) field using the moduli of the Killing vectors is self-consistent, when we assume that the axion field takes one of the equilibrium values ±Φ * , ±2Φ * , ..., ±nΦ * , ....…”

“…During the last decade new trends in the theory of the axionic dark matter appeared. First of all, we mean the non-minimal extensions of the axion models, which are based on the F (R) modifications of the theory of gravity (see, e.g., [17][18][19][20][21]), on the non-minimal extensions of the theory of the axion-photon coupling [22], and on the axionically extended models of the dynamic aether [23]. The second trend is associated with the recent surge of interest to the black hole mergers and supermassive black holes: the axionic dark matter can play the role of * Electronic address: Alexander.Balakin@kpfu.ru † Electronic address: groshevdmitri@mail.ru a marker revealing specific features of the strong gravitational field (see, e.g., [24,25] as illustrations).…”