Growth Of Linear Perturbations Research Articles

Another path for the emergence of modified galactic dynamics from dark matter superfluidity

In recent work we proposed a novel theory of dark matter (DM) superfluidity that matches the successes of the LambdaCDM model on cosmological scales while simultaneously reproducing MOdified Newtonian Dynamics (MOND) phenomenology on galactic scales. The agents responsible for mediating the MONDian force law are superfluid phonons that couple to ordinary (baryonic) matter. In this paper we propose an alternative way for the MOND phenomenon to emerge from DM superfluidity. The central idea is to use higher-gradient corrections in the superfluid effective theory. These next-to-leading order terms involve gradients of the gravitational potential, and therefore effectively modify the gravitational force law. In the process we discover a novel mechanism for generating the non-relativistic MOND action, starting from a theory that is fully analytic in all field variables. The idea, inspired by the symmetron mechanism, uses the spontaneous breaking of a discrete symmetry. For large acceleration, the symmetry is unbroken and the action reduces to Einstein gravity. For small acceleration, the symmetry is spontaneously broken and the action reduces to MONDian gravity. Cosmologically, however, the universe is always in the Einstein-gravity, symmetry-restoring phase. The expansion history and linear growth of density perturbations are therefore indistinguishable from LambdaCDM cosmology.

Evolution of non-interacting entropic dark energy and its phantom nature

Assuming the form of the entropic dark energy (EDE) as it arises from the surface term in the Einstein–Hilbert’s action, its evolution was analyzed in an expanding flat universe. The model parameters were evaluated by constraining the model using the Union data on Type Ia supernovae. We found that in the non-interacting case, the model predicts an early decelerated phase and a later accelerated phase at the background level. The evolutions of the Hubble parameter, dark energy (DE) density, equation of state parameter and deceleration parameter were obtained. The model hardly seems to be supporting the linear perturbation growth for the structure formation. We also found that the EDE shows phantom nature for redshifts z [Formula: see text] 0.257. During the phantom epoch, the model predicts big rip effect at which both the scale factor of expansion and the DE density become infinitely large and the big rip time is found to be around 36 Giga years from now.

Rapid simulation rescaling from standard to modified gravity models

We develop and test an algorithm to rescale a simulated dark-matter particle distribution or halo catalogue from a standard gravity model to that of a modified gravity model. This method is based on that of Angulo & White but with some additional ingredients to account for (i) scale-dependent growth of linear density perturbations and (ii) screening mechanisms that are generic features of viable modified gravity models. We attempt to keep the method as general as possible, so that it may plausibly be applied to a wide range of modified theories, although tests against simulations are restricted to a subclass of $f(R)$ models at this stage. We show that rescaling allows the power spectrum of matter to be reproduced at the $\sim 3$ per cent level in both real and redshift space up to $k=0.1h\,\mathrm{Mpc}^{-1}$ if we change the box size and alter the particle displacement field; this limit can be extended to $k=1h\,\mathrm{Mpc}^{-1}$ if we additionally alter halo internal structure. We simultaneously develop an algorithm that can be applied directly to a halo catalogue, in which case the halo mass function and clustering can be reproduced at the $\sim 5$ per cent level. Finally we investigate the clustering of halo particle distributions, generated from rescaled halo catalogues, and find that a similar accuracy can be reached.

Alternative to particle dark matter

We propose an alternative to particle dark matter that borrows ingredients of MOdified Newtonian Dynamics (MOND) while adding new key components. The first new feature is a dark matter fluid, in the form of a scalar field with small equation of state and sound speed. This component is critical in reproducing the success of cold dark matter for the expansion history and the growth of linear perturbations, but does not cluster significantly on non-linear scales. Instead, the missing mass problem on non-linear scales is addressed by a modification of the gravitational force law. The force law approximates MOND at large and intermediate accelerations, and therefore reproduces the empirical success of MOND at fitting galactic rotation curves. At ultra-low accelerations, the force law reverts to an inverse-square-law, albeit with a larger Newton's constant. This latter regime is important in galaxy clusters and is consistent with their observed isothermal profiles, provided the characteristic acceleration scale of MOND is mildly varying with scale or mass, such that it is ~12 times higher in clusters than in galaxies. We present an explicit relativistic theory in terms of two scalar fields. The first scalar field is governed by a Dirac-Born-Infeld action and behaves as a dark matter fluid on large scales. The second scalar field also has single-derivative interactions and mediates a fifth force that modifies gravity on non-linear scales. Both scalars are coupled to matter via an effective metric that depends locally on the fields. The form of this effective metric implies the equality of the two scalar gravitational potentials, which ensures that lensing and dynamical mass estimates agree. Further work is needed in order to make both the acceleration scale of MOND and the fraction at which gravity reverts to an inverse-square law explicitly dynamical quantities, varying with scale or mass.

Transient growth in strongly stratified shear layers

AbstractWe investigate numerically transient linear growth of three-dimensional perturbations in a stratified shear layer to determine which perturbations optimize the growth of the total kinetic and potential energy over a range of finite target time intervals. The stratified shear layer has an initial parallel hyperbolic tangent velocity distribution with Reynolds number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Re}=U_0 h/\nu =1000$ and Prandtl number $\nu /\kappa =1$, where $\nu $ is the kinematic viscosity of the fluid and $\kappa $ is the diffusivity of the density. The initial stable buoyancy distribution has constant buoyancy frequency $N_0$, and we consider a range of flows with different bulk Richardson number ${\mathit{Ri}}_b=N_0^2h^2/U_0^2$, which also corresponds to the minimum gradient Richardson number ${\mathit{Ri}}_g(z)=N_0^2/(\mathrm{d}U/\mathrm{d} z)^2$ at the midpoint of the shear layer. For short target times, the optimal perturbations are inherently three-dimensional, while for sufficiently long target times and small ${\mathit{Ri}}_b$ the optimal perturbations are closely related to the normal-mode ‘Kelvin–Helmholtz’ (KH) instability, consistent with analogous calculations in an unstratified mixing layer recently reported by Arratia et al. (J. Fluid Mech., vol. 717, 2013, pp. 90–133). However, we demonstrate that non-trivial transient growth occurs even when the Richardson number is sufficiently high to stabilize all normal-mode instabilities, with the optimal perturbation exciting internal waves at some distance from the midpoint of the shear layer.

LINEAR ANALYSIS ON THE GROWTH OF NON-SPHERICAL PERTURBATIONS IN SUPERSONIC ACCRETION FLOWS

We analyzed the growth of non-spherical perturbations in supersonic accretion flows. We have in mind the application to the post-bounce phase of core-collapse supernovae (CCSNe). Such non-spherical perturbations have been suggested by a series of papers by Arnett, who has numerically investigated violent convections in the outer layers of pre-collapse stars. Moreover, Couch & Ott (2013) demonstrated in their numerical simulations that such perturbations may lead to a successful supernova even for a progenitor that fails to explode without the fluctuations. This study investigated the linear growth of perturbations during the infall onto a stalled shock wave. The linearized equations are solved as an initial and boundary value problem with the use of Laplace transform. The background is a Bondi accretion flow whose parameters are chosen to mimic the 15 $\mathrm{M_\odot}$ progenitor model by Woosley & Heger (2007), which is supposed to be a typical progenitor of CCSNe. We found that the perturbations that are given at a large radius grow as they flow down to the shock radius; the density perturbations can be amplified by a factor of 30, for example. We analytically showed that the growth rate is proportional to $l$, the index of the spherical harmonics. We also found that the perturbations oscillate in time with frequencies that are similar to those of the standing accretion shock instability. This may have an implication for shock revival in CCSNe, which will be investigated in our forthcoming paper in more detail.

Large scale structure formation in Eddington-inspired Born-Infeld gravity

We study the large scale structure formation in Eddington-inspired Born-Infeld (EiBI) gravity. It is found that the linear growth of scalar perturbations in EiBI gravity deviates from that in general relativity for modes with large wave numbers ($k$), but the deviation is largely suppressed with the expansion of the Universe. We investigate the integrated Sachs-Wolfe effect in EiBI gravity, and find that its effect on the angular power spectrum of the anisotropy of the cosmic microwave background (CMB) is almost the same as that in the Lambda-cold dark matter ($\Lambda$CDM) model. We further calculate the linear matter power spectrum in EiBI gravity and compare it with that in the $\Lambda$CDM model. Deviation is found on small scales ($k\gtrsim 0.1 h$ Mpc$^{-1}$), which can be tested in the future by observations from galaxy surveys.

Entropic-force dark energy reconsidered

We reconsider the entropic-force model in which both kinds of Hubble terms, $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{H}$ and ${H}^{2}$, appear in the effective dark energy (DE) density affecting the evolution of the main cosmological functions, namely, the scale factor, deceleration parameter, matter density, and growth of linear matter perturbations. However, we find that the entropic-force model is not viable at the background and perturbation levels due to the fact that the entropic formulation does not add a constant term in the Friedmann equations. On the other hand, if on mere phenomenological grounds we replace the $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{H}$ dependence of the effective DE density with a linear term $H$ without including a constant additive term, we find that the transition from deceleration to acceleration becomes possible, but the recent structure formation data strongly disfavor this cosmological scenario. Finally, we briefly compare the entropic-force models with some related DE models (based on dynamical vacuum energy) which overcome these difficulties and are compatible with the present observations.

Millennial Variability in an Idealized Ocean Model: Predicting the AMOC Regime Shifts

AbstractA salient feature of paleorecords of the last glacial interval in the North Atlantic is pronounced millennial variability, commonly known as Dansgaard–Oeschger events. It is believed that these events are related to variations in the Atlantic meridional overturning circulation and heat transport. Here, the authors formulate a new low-order model, based on the Howard–Malkus loop representation of ocean circulation, capable of reproducing millennial variability and its chaotic dynamics realistically. It is shown that even in this chaotic model changes in the state of the meridional overturning circulation are predictable. Accordingly, the authors define two predictive indices which give accurate predictions for the time the circulation should remain in the on phase and then stay in the subsequent off phase. These indices depend mainly on ocean stratification and describe the linear growth of small perturbations in the system. Thus, monitoring particular indices of the ocean state could help predict a potential shutdown of the overturning circulation.

CDM and baryons as distinct fluids in a linear approximation for the growth of structure

A single fluid approximation which treats perturbations in baryons and dark matter as equal has sometimes been used to calculate the growth of linear matter density perturbations in the Universe. We demonstrate that properly accounting for the separate growth of baryon and dark matter fluctuations can change some predictions of structure formation in the linear domain in a way that can alter conclusions about the consistency between predictions and observations for $\ensuremath{\Lambda}\mathrm{CDM}$ models vs modified gravity scenarios. Our results may also be useful for 21 cm tomography constraints on alternative cosmological models for the formation of large scale structure.

Linear perturbations in Galileon gravity models

We study the cosmology of Galileon modified gravity models in the linear perturbation regime. We derive the fully covariant and gauge invariant perturbed field equations using two different methods, which give consistent results, and solve them using a modified version of the {\tt CAMB} code. We find that, in addition to modifying the background expansion history and therefore shifting the positions of the acoustic peaks in the cosmic microwave background (CMB) power spectrum, the Galileon field can cluster strongly from early times, and causes the Weyl gravitational potential to grow, rather than decay, at late times. This leaves clear signatures in the low-$l$ CMB power spectrum through the modified integrated Sachs-Wolfe effect, strongly enhances the linear growth of matter density perturbations and makes distinctive predictions for other cosmological signals such as weak lensing and the power spectrum of density fluctuations. The quasi-static approximation is shown to work quite well from small to the near-horizon scales. We demonstrate that Galileon models display a rich phenomenology due to the large parameter space and the sensitive dependence of the model predictions on the Galileon parameters. Our results show that some Galileon models are already ruled out by present data and that future higher significance galaxy clustering, ISW and lensing measurements will place strong constraints on Galileon gravity.

New cosmic accelerating scenario without dark energy

We propose an alternative, nonsingular, cosmic scenario based on gravitationally induced particle production. The model is an attempt to evade the coincidence and cosmological constant problems of the standard model ($\Lambda$CDM) and also to connect the early and late time accelerating stages of the Universe. Our space-time emerges from a pure initial de Sitter stage thereby providing a natural solution to the horizon problem. Subsequently, due to an instability provoked by the production of massless particles, the Universe evolves smoothly to the standard radiation dominated era thereby ending the production of radiation as required by the conformal invariance. Next, the radiation becomes sub-dominant with the Universe entering in the cold dark matter dominated era. Finally, the negative pressure associated with the creation of cold dark matter (CCDM model) particles accelerates the expansion and drives the Universe to a final de Sitter stage. The late time cosmic expansion history of the CCDM model is exactly like in the standard $\Lambda$CDM model, however, there is no dark energy. This complete scenario is fully determined by two extreme energy densities, or equivalently, the associated de Sitter Hubble scales connected by $\rho_I/\rho_f=(H_I/H_f)^{2} \sim 10^{122}$, a result that has no correlation with the cosmological constant problem. We also study the linear growth of matter perturbations at the final accelerating stage. It is found that the CCDM growth index can be written as a function of the $\Lambda$ growth index, $\gamma_{\Lambda} \simeq 6/11$. In this framework, we also compare the observed growth rate of clustering with that predicted by the current CCDM model. Performing a $\chi^{2}$ statistical test we show that the CCDM model provides growth rates that match sufficiently well with the observed growth rate of structure.

Structure formation in multiple dark matter cosmologies with long-range scalar interactions

(Abridged) An interaction between Cold Dark Matter (CDM) and a classical scalar field playing the role of the cosmic dark energy (DE) might provide long-range dark interactions without conflicting with solar system bounds. Although presently available observations allow to constrain such interactions to a few percent of the gravitational strength, some recent studies have shown that if CDM is composed by two different particle species having opposite couplings to the DE field, such tight constraints can be considerably relaxed, allowing for long-range scalar forces of order gravity without significantly affecting observations both at the background and at the linear perturbations level. In the present work, we extend the investigation of such Multiple Dark Matter scenarios to the nonlinear regime of structure formation, by presenting the first N-body simulations ever performed for these cosmologies. Our results highlight some characteristic footprints of long-range scalar forces that arise only in the nonlinear regime for specific models that would be otherwise practically indistinguishable from the standard LCDM scenario both in the background and in the growth of linear density perturbations. Among these effects, the formation of "mirror" cosmic structures in the two CDM species, the suppression of the nonlinear matter power spectrum at k > 1 h/Mpc, and the fragmentation of collapsed halos, represent peculiar features that might provide a direct way to constrain this class of cosmological models.

Multiple dark matter as a self‐regulating mechanism for dark sector interactions

AbstractA wide range of astrophysical and cosmological observations support the evidence that the energy density of the Universe is presently largely dominated by particles and fields that do not belong to the standard model of particle physics. Such cosmic dark sector appears to be made of two distinct entities capable to account for the growth of large‐scale structures and for the observed acceleration of the expansion rate of the Universe, respectively dubbed dark matter and dark energy. Nevertheless, the fundamental nature of these two dark components has so far remained mysterious. In the currently accepted scenario dark matter is associated to a single new massive and weakly interacting particle beyond the standard model, while dark energy is assumed to be a simple cosmological constant. However, present cosmological constraints and the absence of a direct detection and identification of any dark matter particle candidate leave room to the possibility that the dark sector of the Universe be actually more complex than it is normally assumed. In particular, more than one new fundamental particle could be responsible for the observed dark matter density in the Universe, and possible new interactions between dark energy and dark matter might characterize the dark sector. In the present work, the possibility that two dark matter particles may exist in nature is investigated. These different species are assumed to have identical physical properties except for the sign of their coupling constant to dark energy. Extending previous works on similar scenarios, the evolution of the background cosmology as well as the growth of linear density perturbations for a wide range of parameters of such multiple dark matter model is studied. Interestingly, the results show how the simple assumption that dark matter particles carry a “charge” with respect to their interaction with the dark energy field allows for new long‐range scalar forces of gravitational strength in the dark sector without conflicting with present observations both at the background and linear levels. The presented scenario does not introduce new parameters with respect to the case of a single dark matter species for which such strong dark interactions have been already ruled out. Therefore, the present investigation suggests that only a detailed study of nonlinear structure formation processes might possibly provide effective constraints on new scalar interactions of gravitational strength in the dark sector.

Nonlinear dynamics of corrugated doping fronts in organic optoelectronic devices

Recently, it was demonstrated that electrochemical doping fronts in organic semiconductors exhibit a new fundamental instability growing from multidimensional perturbations [Bychkov et al., Phys. Rev. Lett. 107, 016103 (2011)]. In the instability development, linear growth of tiny perturbations goes over into a nonlinear stage of strongly distorted doping fronts. Here we develop the nonlinear theory of the doping front instability and predict the key parameters of a corrugated doping front, such as its velocity, in close agreement with the experimental data. We show that the instability makes the electrochemical doping process considerably faster. We obtain the self-similar properties of the front shape corresponding to the maximal propagation velocity, which allows for a wide range of controlling the doping process in the experiments. The developed theory provides the guide for optimizing the performance of organic optoelectronic devices such as light-emitting electrochemical cells.

Hydrodynamic and thermodiffusive instability effects on the evolution of laminar planar lean premixed hydrogen flames

AbstractNumerical simulations with single-step chemistry and detailed transport are used to study premixed hydrogen/air flames in two-dimensional channel-like domains with periodic boundary conditions along the horizontal boundaries as a function of the domain height. Both unity Lewis number, where only hydrodynamic instability appears, and subunity Lewis number, where the flame propagation is strongly affected by the combined effect of hydrodynamic and thermodiffusive instabilities are considered. The simulations aim at studying the initial linear growth of perturbations superimposed on the planar flame front as well as the long-term nonlinear evolution. The dispersion relation between the growth rate and the wavelength of the perturbation characterizing the linear regime is extracted from the simulations and compared with linear stability theory. The dynamics observed during the nonlinear evolution depend strongly on the domain size and on the Lewis number. As predicted by the theory, unity Lewis number flames are found to form a single cusp structure which propagates unchanged with constant speed. The long-term dynamics of the subunity Lewis number flames include steady cell propagation, lateral flame movement, oscillations and regular as well as chaotic cell splitting and merging.

Non-normal dynamics of time-evolving co-rotating vortex pairs

AbstractTransient energy growth of disturbances to co-rotating pairs of vortices with axial core flows is investigated in an analysis where vortex core expansion and vortex merging are included by adopting a time-evolving base flow. The dynamics of pairs are compared with those of individual vortices in order to highlight the effect of vortex interaction. Three typical vortex pair cases are studied, with the pairs comprised respectively of individually inviscidly unstable vortices at the streamwise wavenumber that maximizes the individual instabilities, viscously unstable vortices also at the streamwise wavenumber maximizing the individual instabilities and asymptotically stable vortices at streamwise wavenumber zero. For the inviscidly unstable case, the optimal perturbation takes the form of a superposition of two individual helical unstable modes and the optimal energy growth is similar to that predicted for an individual inviscid unstable vortex, while where the individual vortices are viscously unstable, the optimal disturbances within each core have similar spatial distributions to the individually stable case. For both of these cases, time horizons considered are much lower than those required for the merger of the undisturbed vortices. However, for the asymptotically stable case, large linear transient energy growth of optimal perturbations occurs for time horizons corresponding to vortex merging. Linear transient disturbance energy growth exhibited by pairs in this stable case is two to three orders of magnitude larger than that for a corresponding individual vortex. The superposition of the perturbation and the base flow shows that the perturbation has a displacement effect on the vortices in the base flow. Direct numerical simulations of stable pairs seeded by optimal initial perturbations have been carried out and acceleration/delay of vortex merging associated with a dual vortex meandering and vortex breakup related to axially periodic acceleration and delay of vortex merging are observed. For axially invariant cases, the sign of perturbation has an effect, as well as magnitude; the sign dependence relates to whether or not the perturbation adds to or subtracts from the swirl of the base flow. For a two-dimensional perturbation that adds to the swirl of the base flow, seeding with the linear optimal disturbance at a relative energy level $1\ensuremath{\times} 1{0}^{\ensuremath{-} 4} $ induces the pair to move towards each other and approximately halves the time required for merger. Direct numerical simulation shows that the optimal three-dimensional perturbation can induce the vortex system to break up before merging occurs, since the two-dimensional nature of vortex merging is broken by the development of axially periodic perturbations.

Growth factor and galaxy bias from future redshift surveys: a study on parametrizations

Many experiments in the near future will test dark energy through its effects on the linear growth of matter perturbations. In this paper we discuss the constraints that future large-scale redshift surveys can put on three different parameterizations of the linear growth factor and how these constraints will help ruling out different classes of dark energy and modified gravity models. We show that a scale-independent bias can be estimated to a few percent per redshift slice by combining redshift distortions with power spectrum amplitude, without the need of an external estimation. We find that the growth rate can be constrained to within 2-4% for each $\Delta z=0.2$ redshift slice, while the equation of state $w$ and the index $\gamma$ can be simultaneously estimated both to within 0.02. We also find that a constant dimensionless coupling between dark energy and dark matter can be constrained to be smaller than 0.14.

Dynamic of the Accelerated Expansion of the Universe in the DGP Model

According to experimental data of SNe Ia (Supernovae type Ia), we will discuss in detial dynamics of the DGP model and introduce a simple parametrization of matter $\omega$, in order to analyze scenarios of the expanding universe and the evolution of the scale factor. We find that the dimensionless matter density parameter at the present epoch $\Omega^0_m=0.3$, the age of the universe $t_0= 12.48$ Gyr, $\frac{a}{a_0}=-2.4e^{\frac{-t}{25.56}}+2.45$. The next we study the linear growth of matter perturbations, and we assume a definition of the growth rate, $f \equiv \frac{dln\delta}{dlna}$. As many authors for many years, we have been using a good approximation to the growth rate $f \approx \Omega^{\gamma(z)}_m$, we also find that the best fit of the growth index, $\gamma(z)\approx 0.687 - \frac{40.67}{1 + e^{1.7. (4.48 + z)}}$, or $\gamma(z)= 0.667 + 0.033z$ when $z\ll1$. We also compare the age of the universe and the growth index with other models and experimental data. We can see that the DGP model describes the cosmic acceleration as well as other models that usually refers to dark energy and Cold Dark Matter (CDM).

Data compression of measurements of peculiar velocities of supernovae type Ia

We study the compression of information present in the correlated perturbations to the luminosity distance in the low-redshift ($z<0.1$) supernovae Ia due to peculiar velocities of these supernovae. We demonstrate that the na\"{\i}ve compression into angular velocity power spectrum does not work efficiently, due to thickness of the spherical shell over which the supernovae are measured. Instead, we show that measurements can be compressed into measurements of ${f}^{2}P(k)$, where $f$ is the logarithmic rate of growth of linear perturbations and $P(k)$ is their power spectrum. We develop an optimal quadratic estimator and show that it recovers all information for $\ensuremath{\Lambda}\mathrm{CDM}$ models for surveys of $N\ensuremath{\sim}10,000$ or more supernovae. We explicitly demonstrate robustness with respect to the assumed fiducial model and the number of power spectrum bins. Using mock catalogues of supernovae Ia we estimate that future low-redshift surveys will be able to probe ${\ensuremath{\sigma}}_{8}$ to 6% accuracy with 10 000 supernovae Ia.