Perturbations in the interacting vacuum

We consider the evolution of linear perturbations in models with a nonminimal coupling between dark matter and scalar field dark energy. Growth of matter inhomogeneities in two examples of such models proposed in the literature are investigated in detail. Both of these models are based on a low-energy limit of effective string theory action, and have been previously shown to naturally lead to late acceleration of the universe. However, we find that these models can be ruled out by taking properly into account the impact of the scalar field coupling on the formation of structure in the dark matter density. In particular, when the transition to acceleration in these models begins, the interaction with dark energy enchances the small scale clustering in dark matter much too strongly. We discuss the the role of an effective small scale sound speed in such models with a coupled dark sector.

We consider the linear growth of matter perturbations on low redshifts in some f(R) dark energy (DE) models. We discuss the definition of dark energy (DE) in these models and show the differences with scalar-tensor DE models. For the f(R) model recently proposed by Starobinsky we show that the growth parameter γ0≡γ(z = 0) takes the value γ0 ≃ 0.4 for Ωm,0 = 0.32 and γ0 ≃ 0.43 for Ωm,0 = 0.23, allowing for a clear distinction from ΛCDM. Though a scale-dependence appears in the growth of perturbations on higher redshifts, we find no dispersion for γ(z) on low redshifts up to z ∼ 0.3, γ(z) is also quasi-linear in this interval. At redshift z = 0.5, the dispersion is still small with Δγ ≃ 0.01.As for some scalar-tensor models, we find here too a large value for γ′0≡(dγ/dz)(z = 0), γ′0 ≃ −0.25 for Ωm,0 = 0.32 and γ′0 ≃ −0.18 for Ωm,0 = 0.23. These values are largely outside the range found for DE models in General Relativity (GR). This clear signature provides a powerful constraint on these models.

We experimentally and numerically study the dynamics of a liquid jet issued from a rotating orifice, whose breakup is regulated by a vibrating piezo element. The helical trajectory of the spiralling jet yields fictitious forces varying along the jet whose longitudinal projections stretch and thin the jet, affecting the growth of perturbations. We show that by quantifying these fictitious forces, one can estimate the jet intact length and size distribution of drops formed at jet breakup. The presence of the locally varying fictitious forces may render high-frequency perturbations, that would otherwise be stable in the abscence of stretching, unstable, as observed similarly in the case of straight jets stretching under gravity. The perturbation amplitude then dictates how strong the perturbation is coupled to the jet compared with random noise that is inherently present in any experimental set-up. In the present study we exploit the slenderness of the jet to separate the calculation of the base flow and the growth of perturbations. The fictitious forces calculated from the base flow trajectory are then used in a nonlinear slender-jet model, which treats the spiralling jet as a quasi-straight jet with locally varying body forces. We show both experimentally and numerically that jet breakup characteristics (e.g. intact length and drop size distribution) can be controlled by finite-amplitude perturbations created by mechanically induced pressure modulations. Finally, we revisit the integrated net gain approach developed for straight jets under gravity and we provide simple analogous relations for spiralling jets.

The Met Office Unified Model is run for a case observed during Intensive Observation Period 18 (IOP18) of the Convective Storms Initiation Project (CSIP). The aims are to identify the physical processes that lead to perturbation growth at the convective scale in response to model‐state perturbations and to determine their sensitivity to the character of the perturbations. The case is strongly upper‐level forced but with detailed mesoscale/convective‐scale evolution that is dependent on smaller‐scale processes. Potential temperature is perturbed within the boundary layer. The effects on perturbation growth of both the amplitude and typical scale length of the perturbations are investigated, and perturbations are applied either sequentially (every 30 minutes throughout the simulation) or at specific times.The direct effects (within one time step) of the perturbations are to generate propagating Lamb and acoustic waves and produce generally small changes in cloud parameters and convective instability. In exceptional cases a perturbation at a specific grid point leads to switching of the diagnosed boundary‐layer type or discontinuous changes in convective instability, through the generation or removal of a lid. The indirect effects (during the entire simulation) are changes in the intensity and location of precipitation and in the cloud‐size distribution. Qualitatively different behaviour is found for strong (1 K amplitude) and weak (0.01 K amplitude) perturbations, with faster growth after sunrise found only for the weaker perturbations. However, the overall perturbation growth (as measured by the root‐mean‐square error of accumulated precipitation) reaches similar values at saturation, regardless of the perturbation characterization. Copyright © 2010 Royal Meteorological Society and Crown Copyright.

The growth of density contrasts of collisionless particles and nucleonic matter is pursued from the decoupling era up to the present in the Newtonian mechanics. The negative density perturbation of collisionles particles grows quickly to the void and surrounding ridge. Meanwhile, the shell-crossing occurs. The nucleonic matter, which is set uniformly at the decoupling epoch, is enforced to concentrate into the ridge by the gravitational force at this shell-crossing epoch. At the same time, the temperature of nucleonic matter increases rapidly due to the dissipation of kinetic energy by the pressure force. The dependence of results upon the amplitude of the initial density perturbation is made clear. If the galaxies were formed after the shell-crossing, the initial amplitude of density perturbation of collisionless particles must be higher than 0.03 in the Einstein-de Sitter universe. Through the analysis of gravitational instability of ridges, a possible scenario for the formation of the large-scale structure of the universe within the adiabatic theory is presented.

We investigate the formation of the large-scale structures in the present accelerated era in the f(R) gravity background. This is done by considering the linear growth of matter perturbations at low redshift z < 1. The effect of f(R) alters the behavior of the matter density perturbations from the matter-dominated universe to the late-time accelerated universe, which is encoded in the Newtonian gravitational constant as G → G eff. The modified gravitational constant (G eff) depends on the form of f(R). The late-time accelerated expansion affects the formation of large-scale structures by slowing down the growth of matter density. On the other hand, f(R) increases the growth rate of the matter density perturbations. We have found that the source term in the f(R) background, G effΩ m , overcomes the accelerated expansion and the effect of accelerated expansion suppresses the formation of the large-scale structures in the asymptotic future.

The linear baroclinic and parametric instabilities of boundary currents with piecewise-constant potential vorticity are studied in a two-layer quasi-geostrophic model. The growth rates of both the exponential modes and of the optimal perturbations are calculated for the baroclinic instability of steady coastal currents. We show that the growth rates of the exponential modes are maximal for a vertically symmetric flow. Furthermore, the vertical asymmetries induced by different layer thicknesses, the presence of a barotropic potential vorticity or bottom topography, all act to dampen the growth rates and favor growth at shorter wavelengths. It is shown that this behavior can be predicted from the conditions for vertical resonance of Rossby waves on the two potential vorticity fronts. Also, the baroclinic instability of the optimal perturbations has larger growth rates at shorter wavelengths and shorter time scales. As well, the presence of a sloping bottom of moderate amplitude favors the growth of these optimal perturbations. Finally, we compute the growth rates of parametric instability of oscillatory coastal flows. We show that subharmonic resonance is the most unstable mode of growth. In addition, a second region of parametric instability is found (for the first time) away from marginality of exponential-mode baroclinic instability. It is shown that the functional dependency of the growth rates of parametric instability, for optimal excitation, are similar to that of the optimal perturbations of baroclinic instability. To explain this a mechanism for parametric instability, involving the rapid growth of short-wave optimal perturbations, is proposed.

Certain characteristics of the perturbations which grow most rapidly over a finite time interval in a primitiveequation atmospheric model are discussed. They are the singular vectors of a linear approximation of the European Centre for Medium‐Range Weather Forecasts primitive‐equation model. They are computed using the adjoint technique at horizontal spectral truncation T21 with 19 vertical levels. Linear combinations of singular vectors, named optimal perturbations, can be used in ensemble prediction to generate the initial conditions of perturbed integrations.Firstly, having specified the initial amplitude to be comparable with the amplitude of analysis‐error estimates, the nonlinear time evolution of optimal perturbations when added to the control initial conditions are studied. In particular, estimates are made of the time limit, TNL, after which nonlinear processes cannot be neglected. Considering optimal perturbations generated using singular vectors with maximum growth over a 36‐hour time interval, and characterized by amplitudes comparable with analysis‐error estimates, two different methods estimate TNL ≈︁ 2‐2.5 days.Secondly, the sensitivity of ensemble predictions to the optimal perturbation amplitude is analysed. This sensitivity study suggests that an increase of the root‐mean‐square amplitude of the initial perturbation can give a more realistic ensemble spread.Lastly, an estimate of the possible impact of the reduction of the amplitude of analysis errors on the skill of numerical weather prediction is deduced from the comparison of ensemble experiments run with T21 initial perturbations characterized by different amplitudes. Results indicate that a reduction of the root‐mean‐square amplitude of the analysis error by a factor √2 may lead to an improvement of medium‐range predictability up to 1 day, and that a reduction by a factor 2√2 may reduce the errors of the 7‐day forecast to values shown, at present, at forecast‐day 5.

We produce lensing potential and deflection-angle maps in order to simulate the weak gravitational lensing of the Cosmic Microwave Background (CMB) via ray-tracing through the COupled Dark Energy Cosmological Simulations (CoDECS), the largest suite of N-body simulations to date for interacting Dark Energy cosmologies. The constructed maps faithfully reflect the N-body cosmic structures on a range of scales going from the arcminute to the degree scale, limited only by the resolution and extension of the simulations. We investigate the variation of the lensing pattern due to the underlying Dark Energy (DE) dynamics, characterised by different background and perturbation behaviours as a consequence of the interaction between the DE field and Cold Dark Matter (CDM). In particular, we study in detail the results from three cosmological models differing in the background and perturbations evolution at the epoch in which the lensing cross section is most effective, corresponding to a redshift of ∼ 1, with the purpose to isolate their imprints in the lensing observables, regardless of the compatibility of these models with present constraints. The scenarios investigated here include a reference ΛCDM cosmology, a standard coupled DE (cDE) scenario, and a ``bouncing" cDE scenario. For the standard cDE scenario, we find that typical differences in the lensing potential result from two effects: the enhanced growth of linear CDM density fluctuations with respect to the ΛCDM case, and the modified nonlinear dynamics of collapsed structures induced by the DE-CDM interaction. As a consequence, CMB lensing highlights the DE impact in the cosmological expansion, even in the degenerate case where the amplitude of the linear matter density perturbations, parametrised through σ8, is the same in both the standard cDE and ΛCDM cosmologies. For the ``bouncing" scenario, we find that the two opposite behaviours of the lens density contrast and of the matter abundance lead to a counter-intuitive effect, making the power of the lensing signal in this model lower by 10% than in the ΛCDM scenario. Moreover, we compare the behaviour of CDM and baryons in CoDECS separately, in order to isolate effects coming from the coupling with the DE component. We find that, in the bouncing scenario, baryons show an opposite trend with respect to CDM, due to the coupling of the latter with the DE component. These results confirm the relevance of CMB lensing as a probe for DE at the early stages of cosmic acceleration, and demonstrate the reliability of N-body based large scale CMB lensing simulations in the context of DE studies.

The cosmic stories : beginning, evolution, and present days of the universe

The stability and formation of structures in lattices of diffusively coupled logistic maps are investigated for high nonlinearity and medium and large coupling. Two stability statements are given that relate the presence of the predominant attractors, i.e., cycles and quasiperiodic traveling waves, to the stability of a few simple periodic structures. They are supported by strong numerical evidence. Furthermore, they are justified through the description of some mechanisms that connect the formation of a stable structure to the cycles of the uncoupled lattice. As an important consequence, for given parameter values, an approximate prediction of the behavior of the lattice is allowed.

In low-density universe models the gravitational growth of density perturbations are slower than that in the Einstein–de Sitter critical model, and larger amplitudes are required at the decoupling time, in order that protoclusters may form to the present epoch. In this paper it is shown that, if the thermal model without secondary heating is assumed, the required amplitudes of entropy perturbations exceed the observational limit derived from the high degree of isotropy of the cosmic background radiation, as well as those of adiabatic perturbations.

A new maximum entropy approach has been applied to analyse three types of transient transport experiments. For sawtooth propagation experiments in the ASDEX Upgrade and ECRH power modulation and power-switching experiments in the Wendelstein 7-AS Stellarator, either the time evolution of the temperature perturbation or the phase and amplitude of the modulated temperature perturbation are used as non-linear constraints to the profile to be fitted. Simultaneously, the constraints given by the equilibrium temperature profile for steady-state power balance are fitted. In the maximum entropy formulation, the flattest profile consistent with the constraints is found. It was found that determined from sawtooth propagation was greater than the power balance value by a factor of five in the ASDEX Upgrade. From power modulation experiments, employing the measurements of four modulation frequencies simultaneously, the power deposition profile as well as the profile could be determined. A comparison of the predictions of a time-independent model and a power-dependent model is made. The power-switching experiments show that the profile must change within a millisecond to a new value consistent with the power balance value at the new input power. Neither power deposition broadening due to suprathermal electrons nor temperature or temperature gradient dependences of can explain this observation.

Nonlinear waves on sheets of dielectric liquid in the presence of an external tangential electric field are studied theoretically. It is shown that waves of arbitrary shape in three-dimensional geometry can propagate along (or against) the electric field direction without distortion, i.e., the equations of motion admit a wide class of exact traveling wave solutions. This unusual situation occurs for nonconducting ideal liquids with high dielectric constants in the case of a sufficiently strong field strength. Governing equations for evolution of plane symmetric waves on fluid sheets are derived using conformal variables. A dispersion relation for the evolution of small perturbations of the traveling wave solutions is obtained. It follows from this relation that, regardless of the wave shape, the amplitudes of small-scale perturbations do not increase with time and, hence, the traveling waves are stable. We also study the interaction of counterpropagating symmetric waves with small but finite amplitudes. The corresponding solution of the equations of motion describes the nonlinear superposition of the oppositely directed waves. The results obtained are applicable for the description of long waves on fluid sheets in a horizontal magnetic field.

We derive the minimal seed magnetic field which unavoidably arises in the radiation and matter eras, prior to recombination, by the rotational velocity of ions and electrons, gravitationally induced by the nonlinear evolution of primordial density perturbations. The resulting magnetic field power spectrum is fully determined by the amplitude and spectral index of density perturbations. The rms amplitude of the seed field at recombination is B≈10-23(λ/Mpc)-2 G, on comoving scales λ≳1 Mpc.