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Negative kinetic energies correspond to ghost degrees of freedom, which are potentially of relevance for cosmology, quantum gravity, and high energy physics. We present a novel wide class of stable mechanical systems where a positive energy degree of freedom interacts with a ghost. These theories have Hamiltonians unbounded from above and from below, are integrable, and contain free functions. We show analytically that their classical motion is bounded for all initial data. Moreover, we derive conditions allowing for Lyapunov stable equilibrium points. A subclass of these stable systems has simple polynomial potentials with stable equilibrium points entirely due to interactions with the ghost. All these findings are fully supported by numerical computations which we also use to gather evidence for stability in various nonintegrable systems., Comment: modified discussion with regards to ref [55]

We propose a new non-trivial way to combine mimetic dark matter with the mimetic formulation of unimodular gravity. This yields a Weyl-invariant higher-derivative scalar-vector-tensor theory. We demonstrate that on-shell its behavior mimics GR with an additional k-essence scalar. The overall scale of the k-essence arises as an integration constant -- a global degree of freedom. Interestingly, we find that the resulting fluid cannot make transition through ultra-relativistic equation of state. We develop a method to find a mimetic theory corresponding to any eligible k-essence and identify, which k-essences can or cannot be reproduced this way. Finally, we show that abandoning the Weyl symmetry of the setup allows us to obtain both unimodular gravity and mimetic dark matter simultaneously, from one conformal redefinition of the metric., Comment: 16 pages + references, 1 figure, Happy New Year!

We show that invertible transformations of dynamical variables can change the number of dynamical degrees of freedom. Moreover, even in cases when the number of dynamical degrees of freedom remains unchanged, the resulting dynamics can be essentially different from the one of the system prior to transformation. After giving concrete examples in point particle cases, we discuss changes in dynamics due to invertible disformal transformations of the metric in gravitational theories, Comment: 21 pages, plus references, plus 2 figures, added a discussion on spontaneous symmetry breaking

We analyse the dynamical properties of disformally transformed theories of gravity. We show that disformal transformation typically introduces novel degrees of freedom, equivalent to the mimetic dark matter, which possesses a Weyl-invariant formulation. We demonstrate that this phenomenon occurs in a wider variety of disformal transformations than previously thought., Comment: 18 pages + bibliography, no figures; V3: minor changes, updated bibliography, published version

We present a simple class of mechanical models where a canonical degree of freedom interacts with another one with a negative kinetic term, i.e. with a ghost. We prove analytically that the classical motion of the system is completely stable for all initial conditions, notwithstanding that the conserved Hamiltonian is unbounded from below and above. This is fully supported by numerical computations. Systems with negative kinetic terms often appear in modern cosmology, quantum gravity and high energy physics and are usually deemed as unstable. Our result demonstrates that for mechanical systems this common lore can be too naive and that living with ghosts can be stable., Comment: 4 pages + refs, 4 figures

We discuss recently introduced scale-free Einstein equations, where the information from their trace part is lost. These equations are classically equivalent to General Relativity, yet the Newton constant becomes a constant of integration or a global dynamical degree of freedom. Thus, from the point of view of standard quantization, this effective Newton constant is susceptible to quantum fluctuations. This is similar to what happens to the cosmological constant in the unimodular gravity where the trace part of the Einstein equations is lost in a different way. Using analogy with the Henneaux-Teitelboim covariant action for the unimodular gravity, we consider different general-covariant actions resulting in these dynamics. This setup allows one to formulate the Heisenberg uncertainty relations for the Newton constant and canonically conjugated quantities. Unexpectedly, one of such theories also promotes the Planck's quantum constant to a global degree of freedom, which is subject to quantum fluctuations. Following analogy with the unimodular gravity, we discuss non-covariant "unimatter" and "unicurvature" gravities describing the scale-free Einstein equations. Finally, we show that in some limit of the Yang-Mills gauge theory a "frozen" axion-like field can emulate the gravitational Newton constant or even of the quantum Planck constant., Comment: Contribution to the 2021 Gravitation session of the 55th Rencontres de Moriond

We show that promoting the trace part of the Einstein equations to a trivial identity results in the Newton constant being an integration constant. Thus, in this formulation the Newton constant is a global dynamical degree of freedom which is also a subject to quantization and quantum fluctuations. This is similar to what happens to the cosmological constant in the unimodular gravity where the trace part of the Einstein equations is lost in a different way. We introduce a constrained variational formulation of these modified Einstein equations. Then, drawing on analogies with the Henneaux-Teitelboim action for unimodular gravity, we construct different general-covariant actions resulting in these dynamics. The inverse of dynamical Newton constant is canonically conjugated to the Ricci scalar integrated over spacetime. Surprisingly, instead of the dynamical Newton constant one can formulate an equivalent theory with a dynamical Planck constant. Finally, we show that an axion-like field can play a role of the gravitational Newton constant or even of the quantum Planck constant., Comment: 13 pages+refs, no figures, updated refs, corrected typos, extended discussion

Primordial magnetic fields are often thought to be the early Universe seeds that have bloomed into what we observe today as galactic and extra-galactic magnetic fields. Owing to their minuscule strength, primordial magnetic fields are very hard to detect in cosmological and astrophysical observations. We show how this changes if a part of neutral Dark Matter has a magnetic susceptibility. In this way, by studying Dark Matter one can obtain information about the properties of primordial magnetic fields, even if the latter have a comoving amplitude $B_0 \lesssim0.01~\mbox{nG}$. In our model Dark Matter is a stable singlet scalar $\chi$, which interacts with electromagnetism through the Rayleigh operator as $\chi^2 F_{\mu \nu} F^{\mu \nu}/\Lambda^2$. For primordial magnetic fields present in the early Universe this operator forces the $Z_2$-symmetry of the model to be spontaneously broken. Later, when the primordial magnetic field redshifts below a critical value, the symmetry is restored through an "inverse phase transition". At that point the field $\chi$ begins to oscillate and acts as a "magnetomorphic" Dark Matter component, inheriting the properties of the primordial magnetic field space distribution. In particular, for a nearly flat spectrum of magnetic field fluctuations, the scalar $\chi$ carries a statistically anisotropic isocurvature mode. We discuss the parameter space of the model and consider the possibility that the bulk of the Dark Matter is composed of the same particles $\chi$ produced via the freeze-in mechanism., Comment: 29 pages and 4 figures, v2 with updated references

We propose a novel, higher-derivative, Weyl-invariant and generally-covariant theory for the cosmological constant. This theory is a mimetic construction with gauge fields playing the role of dynamical variables. These fields compose the Chern-Simons current instead of the vector field used in the Henneaux and Teitelboim formulation of the unimodular gravity. The equations of motion exactly reproduce the traceless Einstein equations. We demonstrate that, reformulated in Weyl-invariant variables, this novel theory reduces to standard general relativity with the cosmological constant as a Lagrange multiplier. This Lagrange multiplier has an axion-like coupling., Comment: 15 pages+refs, no figures, comments welcome!

We introduce a new Weyl-invariant and generally-covariant vector-tensor theory with higher derivatives. This theory can be induced by extending the mimetic construction to vector fields of conformal weight four. We demonstrate that in gauge-invariant variables this novel theory reduces to the Henneaux-Teitelboim description of the unimodular gravity. Hence, compared with the standard general relativity, our new higher derivative vector-tensor theory has only one new global degree of freedom - the cosmological constant. Finally we discuss potential extensions of this vector-tensor theory., Comment: 9 pages+references, comments are welcome

We study the correspondence between models of a self-interacting canonical complex scalar field and P(X)-theories/shift-symmetric k-essence. Both describe the same background cosmological dynamics, provided that the amplitude of the complex scalar is frozen modulo the Hubble drag. We compare perturbations in these two theories on top of a fixed cosmological background. The dispersion relation for the complex scalar has two branches. In the small momentum limit, one of these branches coincides with the dispersion relation of the P(X)-theory. Hence, the low momentum phase velocity agrees with the sound speed in the corresponding P(X)-theory. The behavior of high frequency modes associated with the second branch of the dispersion relation depends on the value of the sound speed. In the subluminal case, the second branch has a mass gap. On the contrary, in the superluminal case, this branch is vulnerable to a tachyonic instability. We also discuss the special case of the P(X)-theories with an imaginary sound speed leading to the catastrophic gradient instability. The complex field models provide with a cutoff on the momenta involved in the instability., Comment: 16 pages+appendices, references added, matches the published version

We extend recently proposed mimetic dark matter (DM) and dust of dark energy (DE) models to a U(1)-charged gauged scalar field. This extension yields a mass to the photon via the Higgs mechanism. The square of this photon mass is proportional to the DM energy density. Thus dense DM environments can screen the dark vector force. There is a substantial freedom in this gauged extension of the irrotational fluid-like DM. This freedom enables one to model the classical London equation of superconductivity or to obtain the photon mass which remains constant during the matter-dominated \'epoque., Comment: 11 pages

We study a particular realization of the cosmological bounce scenario proposed recently by Ijjas and Steinhardt. First, we find that their bouncing solution starts from a divergent sound speed and ends with its vanishing. Thus, the solution connects two strongly coupled configurations. These pathologies are separated from the bouncing regime by only a few Planck times. We then reveal the exact structure of the Lagrangian, which reproduces this bouncing solution. This reconstruction allowed us to consider other cosmological solutions of the theory and analyze the phase space. In particular, we find other bouncing solutions and solutions with superluminal sound speed. These stable superluminal states can be continuously transformed into the solution constructed by Ijjas and Steinhardt. We discuss the consequences of this feature for a possible UV-completion., Comment: published version. 16 pages + references, 4 figures, new section on Conformal Transformations, Gauges and Acoustic Geometry, new figure. Corrected typos, added references

We study a recently proposed new cosmological phase where a scalar field moves periodically in an expanding spatially-flat Friedmann universe. This phase corresponds to a limiting cycle of the equations of motion and can be considered as a cosmological realization of a "time-crystal". We show that this phase is only possible, provided the Null Energy Condition is violated and the so-called Phantom divide is crossed. We prove that in general k-essence models: i) this crossing causes infinite growth of quantum perturbations on short scales, and ii) exactly periodic solutions are only possible, provided the limiting cycle encircles a singularity in the phase plane. The configurations neighboring this singular curve in the phase space are linearly unstable on one side of the curve and superluminal on the other side. Moreover, the increment of the instability is infinitely growing for each mode by approaching the singularity, while for the configurations on the other side, the sound speed is growing without limit. We illustrate our general results by analytical and numerical studies of a particular class of such k-essence models., Comment: 15 pages, 3 figures, plus references

We consider the recently introduced mimetic gravity, which is a Weyl-symmetric extension of the General Relativity and which can play a role of an imperfect fluid-like Dark Matter with a small sound speed. In this paper we discuss in details how this higher- derivative scalar-tensor theory goes beyond the construction by Horndeski, keeping only one scalar degree of freedom on top of two standard graviton polarizations. In particular, we consider representations of the theory in different sets of Weyl-invariant variables and connect this framework to the singular Brans-Dicke theory. Further, we find solution of equations of motion for the mimetic gravity in the synchronous reference frame in a general curved spacetime. This solution is exact in the test-field approximation or in the case of a shear-free spacetime without any other matter., Comment: 10 pages, no figures

We consider cosmology of the recently introduced mimetic matter with higher derivatives (HD). Without HD this system describes irrotational dust - Dark Matter (DM) as we see it on cosmologically large scales. DM particles correspond to the shift-charges - Noether charges of the shifts in the field space. Higher derivative corrections usually describe a deviation from the thermodynamical equilibrium in the relativistic hydrodynamics. Thus we show that mimetic matter with HD corresponds to an imperfect DM which: i) renormalises the Newton's constant in the Friedmann equations, ii) has zero pressure when there is no extra matter in the universe, iii) survives the inflationary expansion which puts the system on a dynamical attractor with a vanishing shift-charge, iv) perfectly tracks any external matter on this attractor, v) can become the main (and possibly the only) source of DM, provided the shift-symmetry in the HD terms is broken during some small time interval in the radiation domination era. In the second part of the paper we present a hydrodynamical description of general anisotropic and inhomogeneous configurations of the system. This imperfect mimetic fluid has an energy flow in the field's rest frame. We find that in the Eckart and in the Landau-Lifshitz frames the mimetic fluid possesses nonvanishing vorticity appearing already at the first order in the HD. Thus, the structure formation and gravitational collapse should proceed in a rather different fashion from the simple irrotational DM models., Comment: updated refs, corrected typos, expanded discussion on the Eckart frame, matches the published version

We consider minimal extensions of the recently proposed Mimetic Dark Matter and show that by introducing a potential for the mimetic non-dynamical scalar field we can mimic nearly any gravitational properties of the normal matter. In particular, the mimetic matter can provide us with inflaton, quintessence and even can lead to a bouncing nonsingular universe. We also investigate the behaviour of cosmological perturbations due to a mimetic matter. We demonstrate that simple mimetic inflation can produce red-tilted scalar perturbations which are largely enhanced over gravity waves., Comment: 19 pages

We study a recently proposed scenario for the early universe: Subluminal Galilean Genesis. We prove that without any other matter present in the spatially flat Friedmann universe, the perturbations of the Galileon scalar field propagate with a speed at most equal to the speed of light. This proof applies to all cosmological solutions -- to the whole phase space. However, in a more realistic situation, when one includes any matter which is not directly coupled to the Galileon, there always exists a region of phase space where these perturbations propagate superluminally, indeed with arbitrarily high speed. We illustrate our analytic proof with numerical computations. We discuss the implications of this result for the possible UV completion of the model., Comment: 16 pages, 3 figures. v2 reflects version accepted for publication in JCAP. Changes include a reorganisation of section order, a new figure 1 and additional references

We point out that theories of cosmological acceleration which have equation of state, w, such that 1+w is small but positive may still secretly violate the null energy condition. This violation implies the existence of observers for whom the background has infinitely negative energy densities, despite the fact that the perturbations are free of ghosts and gradient instabilities., Comment: 5 pages, 1 figure. v2 reflects version accepted for publication in PRD. Changes: additional discussion of gauge-dependence in perturbed cosmologies

We study vacuum quantum fluctuations of simple Nambu-Goldstone bosons - derivatively coupled single scalar-field theories possessing shift-symmetry in field space. We argue that quantum fluctuations of the interacting field can be drastically suppressed with respect to the free-field case. Moreover, the power-spectrum of these fluctuations can soften to become red for sufficiently small scales. In quasiclassical approximation, we demonstrate that this suppression can only occur for those theories that admit such classical static backgrounds around which small perturbations propagate faster than light. Thus, a quasiclassical softening of quantum fluctuations is only possible for theories which classicalize instead of having a usual Lorentz invariant and local Wilsonian UV- completion. We illustrate our analysis by estimating the quantum fluctuations for the DBI-like theories., Comment: 6 pages, no figures, published version, more general discussion of uncertainty relation in QFT, improved and more general derivation of the main result

We ask whether the recent OPERA results on neutrino superluminality could be an environmental effect characteristic of the local neighborhood of our planet, without the need of violation of the Poincar\'e-invariance at a fundamental level. This explanation requires the existence of a new spin-2 field of a planetary Compton wave-length that is coupled to neutrinos and the rest of the matter asymmetrically, both in the magnitude and in the sign. Sourced by the earth this field creates an effective metric on which neutrinos propagate superluminally, whereas other species are much less sensitive to the background. Such a setup, at an effective field theory level, passes all immediate phenomenological tests and its natural prediction is an inevitable appearance of a testable long-range gravity-type fifth force. We then prove that under the assumption of the weakly-coupled Poincar\'e-invariant physics, the asymmetrically-coupled second massive graviton is the only possible environmental explanation. Despite phenomenological viability, the sign asymmetry of the coupling we identify as the main potential obstacle for a consistent UV-completion. We also discuss the possible identification of this field with a Kaluza-Klein state of an extra dimension in which neutrino can propagate., Comment: 5 pages, added references and discussion of strong coupling, corrected typos, matches the published version

We present a wide class of models which realise a bounce in a spatially flat Friedmann universe in standard General Relativity. The key ingredient of the theories we consider is a noncanonical, minimally coupled scalar field belonging to the class of theories with Kinetic Gravity Braiding / Galileon-like self-couplings. In these models, the universe smoothly evolves from contraction to expansion, suffering neither from ghosts nor gradient instabilities around the turning point. The end-point of the evolution can be a standard radiation-domination era or an inflationary phase. We formulate necessary restrictions for Lagrangians needed to obtain a healthy bounce and illustrate our results with phase portraits for simple systems including the recently proposed Galilean Genesis scenario., Comment: 28 pages. v2 reflects version accepted for publication in JCAP. References and minor comments added

We present a standard hydrodynamical description for non-canonical scalar field theories with kinetic gravity braiding. In particular, this picture applies to the simplest galileons and k-essence. The fluid variables not only have a clear physical meaning but also drastically simplify the analysis of the system. The fluid carries charges corresponding to shifts in field space. This shift-charge current contains a spatial part responsible for diffusion of the charges. Moreover, in the incompressible limit, the equation of motion becomes the standard diffusion equation. The fluid is indeed imperfect because the energy flows neither along the field gradient nor along the shift current. The fluid has zero vorticity and is not dissipative: there is no entropy production, the energy-momentum is exactly conserved, the temperature vanishes and there is no shear viscosity. Still, in an expansion around a perfect fluid one can identify terms which correct the pressure in the manner of bulk viscosity. We close by formulating the non-trivial conditions for the thermodynamic equilibrium of this imperfect fluid., Comment: 23 pages plus appendices. New version includes extended discussion on diffusion and dynamics in alternative frames, as well as additional references. v3 reflects version accepted for publication in JHEP: minor comments added regarding suitability to numerical approaches

Numerical simulations of the accretion of test scalar fields with non-standard kinetic terms (of the k-essence type) onto a Schwarzschild black hole are performed. We find a full dynamical solution for the spherical accretion of a Dirac-Born-Infeld type scalar field. The simulations show that the accretion eventually settles down to a well known stationary solution. This particular analytical steady state solution maintains two separate horizons. The standard horizon is for the usual particles propagating with the limiting speed of light, while the other sonic horizon is for the k-essence perturbations propagating with the speed of sound around this accreting background. For the case where the k-essence perturbations propagate superluminally, we show that one can send signals from within a black hole during the approach to the stationary solution. We also find that a ghost condensate model settles down to a stationary solution during the accretion process., Comment: 8 pages, 10 figures

We introduce a large class of scalar-tensor models with interactions containing the second derivatives of the scalar field but not leading to additional degrees of freedom. These models exhibit peculiar features, such as an essential mixing of scalar and tensor kinetic terms, which we have named kinetic braiding. This braiding causes the scalar stress tensor to deviate from the perfect-fluid form. Cosmology in these models possesses a rich phenomenology, even in the limit where the scalar is an exact Goldstone boson. Generically, there are attractor solutions where the scalar monitors the behaviour of external matter. Because of the kinetic braiding, the position of the attractor depends both on the form of the Lagrangian and on the external energy density. The late-time asymptotic of these cosmologies is a de Sitter state. The scalar can exhibit phantom behaviour and is able to cross the phantom divide with neither ghosts nor gradient instabilities. These features provide a new class of models for Dark Energy. As an example, we study in detail a simple one-parameter model. The possible observational signatures of this model include a sizeable Early Dark Energy and a specific equation of state evolving into the final de-Sitter state from a healthy phantom regime., Comment: 41 pages, 7 figures. References and some clarifying language added. This version was accepted for publication in JCAP

We introduce a novel class of field theories where energy always flows along timelike geodesics, mimicking in that respect dust, yet which possess non-zero pressure. This theory comprises two scalar fields, one of which is a Lagrange multiplier enforcing a constraint between the other's field value and derivative. We show that this system possesses no wave-like modes but retains a single dynamical degree of freedom. Thus, the sound speed is always identically zero on all backgrounds. In particular, cosmological perturbations reproduce the standard behaviour for hydrodynamics with vanishing sound speed. Using all these properties we propose a model unifying Dark Matter and Dark Energy in a single degree of freedom. In a certain limit this model exactly reproduces the evolution history of Lambda-CDM, while deviations away from the standard expansion history produce a potentially measurable difference in the evolution of structure., Comment: 13 pages, 3 figures. Added references, corrected language.

We propose a cosmological scenario based on the assumption that the Standard Model possesses a large number of copies. It is demonstrated that baryons in the hidden copies of the standard model can naturally account for the dark matter. The right abundance of the hidden-sector baryons and the correct spectrum of density perturbations are simultaneously generated during modulated reheating. We show that for the natural values of inflaton coupling constants, dictated by unitarity, the dark-matter abundance is predicted to be proportional to the ratio of observed cosmological parameters: the square of the amplitude of cosmological perturbations and the baryon-to-photon number ratio., Comment: 11 pages, 2 figures

In this paper we show that, for general scalar fields, stationary configurations are possible for shift symmetric theories only. This symmetry with respect to constant translations in field space should either be manifest in the original field variables or reveal itself after an appropriate field redefinition. In particular this result implies that neither k-Essence nor Quintessence can have exact steady state / Bondi accretion onto Black Holes. We also discuss the role of field redefinitions in k-Essence theories. Here we study the transformation properties of observables and other variables in k-Essence and emphasize which of them are covariant under field redefinitions. Finally we find that stationary field configurations are necessarily linear in Killing time, provided that shift symmetry is realized in terms of these field variables., Comment: 8 pages

The k-essence theories admit in general the superluminal propagation of the perturbations on classical backgrounds. We show that in spite of the superluminal propagation the causal paradoxes do not arise in these theories and in this respect they are not less safe than General Relativity., Comment: 34 pages, 5 figures

In this short talk we review our results from the paper hep-th/0604075 with the main stress on the issues of causality and acoustic metric in eikonal approximation. In addition we correct the formula for the redshift of sound signals from our original work. We show that, if there exists a special kind of Born-Infeld type scalar field, then one can send information from inside a black hole. This information is encoded in perturbations of the field propagating in non-trivial scalar field backgrounds, which serve as a "new ether". Although the action of the theory is manifestly Lorentz-invariant the non-trivial solutions break this symmetry spontaneously, allowing, the superluminal propagation of perturbations with respect to this "new ether". We found the stationary solution for background, which describes the accretion of the scalar field onto a black hole. Examining the propagation of small perturbations around this solution we show that the signals emitted inside the Schwarzschild horizon can reach an observer located outside the black hole. Thus the accreting field forms a hydrodynamical analog of a black hole whose horizon is inside of the gravitational black hole drawing in the scalar field., Comment: To appear in the proceedings of 11th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation, and Relativistic Field Theories, Berlin, Germany, 23-29 Jul 2006

It is well known that in manifestly Lorentz invariant theories with nontrivial kinetic terms, perturbations around some classical backgrounds can travel faster than light. These exotic "supersonic" models may have interesting consequences for cosmology and astrophysics. In particular, one can show that in such theories the contribution of the gravitational waves to the CMB fluctuations can be significantly larger than that in standard inflationary models. This increase of the tensor-to-scalar perturbation ratio leads to a larger B-component of the CMB polarization, thus making the prospects for future detection much more promising. Interestingly, the spectral index of scalar perturbations and mass of the scalar field considered in the model are practically indistinguishable from the standard case. Whereas the energy scale of inflation and hence the reheating temperature can be much higher compared to a simple chaotic inflation., Comment: Contributed to XLIst Rencontres de Moriond Workshop on Contents and Structures of the Universe, La Thuile, Italy, March 18-25, 2006

We propose a novel model of inflation based on a large class of covariant effective actions containing only the second derivatives of a scalar field. The initial conditions leading to the inflationary solutions in this model are rather generic. The graceful exit from the inflationary regime is natural once the first order derivative terms are included., Comment: 21 pages,10 figures, references added, Fig.1 slightly corrected, discussion about stability is extended

We discuss classical stability of the cosmological mechanism which is responsible for the ghost condensation. We show that the simplest general covariant effective action which includes two covariant derivatives may lead to an overshoot of the condensation point into the regime, where the model becomes classically unstable. The model exhibits this behaviour for the de Sitter and matter dominated universes when the initial values taken to be in the region of validity of the low-energy effective theory. In the matter dominated case there is a finite time (which can be large enough to exceed the present age of the Universe) during which the model remains in the stable region. In inflationary regime the system does not experience an overshoot only if the Hubble parameter is larger than the characteristic energy scale of the effective field theory (EFT). This latter regime is, however, inconsistent with the EFT description at the condensation point. We discuss the limitations of the use of the truncated action and point out how one can avoid problems due to the overshoot in order to have a viable ghost condensation mechanism., Comment: 16 pages, 7 figures Added references, one figure and additional discussion

Dark energy rapidly evolving from the dustlike state in the close past to the phantomlike state at present has been recently proposed as the best fit for the supernovae Ia data. Assuming that a dark energy component with an arbitrary scalar-field Lagrangian, which has a general dependence on the field itself and its first derivatives, dominates in the flat Friedmann universe, we analyze the possibility of a dynamical transition from the states with w>-1 to those with w<-1 or vice versa. We have found that generally such transitions are physically implausible because they are either realized by a discrete set of trajectories in the phase space or are unstable with respect to the cosmological perturbations. This conclusion is confirmed by a comparison of the analytic results with numerical solutions obtained for simple models. Without the assumption of the dark energy domination, this result still holds for a certain class of dark energy Lagrangians, in particular, for Lagrangians quadratic in field's first derivatives. The result is insensitive to topology of the Friedmann universe as well., Comment: 15 pages, 9 figures, corrected typos, exposition is improved;published version