Nonlinear Structure Formation Research Articles

Viscous dark matter growth in (neo-)Newtonian cosmology

We assume cold dark matter to possess a small bulk-viscous pressure which typically attenuates the growth of inhomogeneities. Explicit calculations, based on Eckart's theory of dissipative processes, reveal that for viscous cold dark matter the usual Newtonian approximation for perturbation scales smaller than the Hubble scale is no longer valid. We advocate the use of a neo-Newtonian approach which consistently incorporates pressure effects into the fluid dynamics and correctly reproduces the general relativistic dynamics. This result is of interest for numerical simulations of nonlinear structure formation involving nonstandard dark-matter fluids. We obtain upper limits on the magnitude of the viscous pressure by requiring that relevant perturbation amplitudes should grow sufficiently to enter the nonlinear stage.

Warm dark matter primordial spectra and the onset of structure formation at redshiftz

Analytic formulas reproducing the warm dark matter (WDM) primordial spectra are obtained for WDM particles decoupling in and out of thermal equilibrium which provide the initial data for WDM non-linear structure formation. We compute and analyze the corresponding WDM overdensities and compare them to the CDM case. We consider the ratio of the WDM to CDM primordial spectrum and the WDM to CDM overdensities: they turn to be self-similar functions of k/k_{1/2} and R/R_{1/2} respectively, k_{1/2} and R_{1/2} being the wavenumber and length where the WDM spectrum and overdensity are 1/2 of the respective CDM magnitudes. Both k_{1/2} and R_{1/2} show scaling as powers of the WDM particle mass m while the self-similar functions are independent of m. The WDM primordial spectrum sharply decreases around k_{1/2} with respect to the CDM spectrum, while the WDM overdensity slowly decreases around R_{1/2}. The nonlinear regions where WDM structure formation takes place are shown and compared to those in CDM: the WDM non-linear structures start to form later than in CDM, and as a general trend, decreasing the DM particle mass delays the onset of the non-linear regime. The non-linear regime starts earlier for smaller objects than for larger ones; smaller objects can form earlier both in WDM and CDM. We compute and analyze the differential mass function dN/dM for WDM at redshift z in the Press-Schechter approach. The WDM suppression effect of small scale structure increases with the redshift z. Our results for dN/dM are useful to be contrasted with observations, in particular for 4 < z < 12. We perfom all these studies for the most popular WDM particle physics models. Contrasting them to observations should point out the precise value of the WDM particle mass in the keV scale, and help to single out the best WDM particle physics model (Abridged).

Generation of Primordial Magnetic Fields on Linear Overdensity Scales

Magnetic fields appear to be present in all galaxies and galaxy clusters. Recent measurements indicate that a weak magnetic field may be present even in the smooth low density intergalactic medium. One explanation for these observations is that a seed magnetic field was generated by some unknown mechanism early in the life of the Universe, and was later amplified by various dynamos in nonlinear objects like galaxies and clusters. We show that a primordial magnetic field is expected to be generated in the early Universe on purely linear scales through vorticity induced by scale-dependent temperature fluctuations, or equivalently, a spatially varying speed of sound of the gas. Residual free electrons left over after recombination tap into this vorticity to generate magnetic field via the Biermann battery process. Although the battery operates even in the absence of any relative velocity between dark matter and gas at the time of recombination, the presence of such a relative velocity modifies the predicted spatial power spectrum of the magnetic field. At redshifts of order a few tens, we estimate a root mean square field strength of order 10(-25)-10(-24) G on comoving scales ~10 kpc. This field, which is generated purely from linear perturbations, is expected to be amplified significantly after reionization, and to be further boosted by dynamo processes during nonlinear structure formation.

Supernova constraints on multi-coupled dark energy

The persisting consistency of ever more accurate observational datawith the predictions of the standard ΛCDM cosmological modelputs severe constraints on possible alternative scenarios, but stilldoes not shed any light on the fundamental nature of the cosmic darksector. As large deviations from a ΛCDM cosmology are ruledout by data, the path to detect possible features of alternative modelsgoes necessarily through the definition of cosmological scenariosthat leave almost unaffected the background and — to a lesser extent — the linear perturbations evolution of the universe. In this context,the Multi-coupled DE (McDE) model was proposed by Baldi [9]as a particular realization of an interacting Dark Energy field characterizedby an effective screening mechanism capable of suppressing the effectsof the coupling at the background and linear perturbation level. Inthe present paper, for the first time, we challenge the McDE scenariothrough a direct comparison with real data, in particular with theluminosity distance of Type Ia supernovae. By studying the existenceand stability conditions of the critical points of the associatedbackground dynamical system, we select only the cosmologically consistentsolutions, and confront their background expansion history with data.Confirming previous qualitative results, the McDE scenario appearsto be fully consistent with the adopted sample of Type Ia supernovae,even for coupling values corresponding to an associated scalar fifth-forceabout four orders of magnitude stronger than standard gravity. Ouranalysis demonstrates the effectiveness of the McDE background screening,and shows some new non-trivial asymptotic solutions for the futureevolution of the universe. Clearly, linear perturbation data and,even more, nonlinear structure formation properties are expected toput much tighter constraints on the allowed coupling range. Nonetheless,our results show how the background expansion history might be highlyinsensitive to the fundamental nature and to the internal complexityof the dark sector.

Magnetoacoustic solitons in dense astrophysical electron-positron-ion plasmas

Nonlinear magnetoacoustic waves in dense electron-positron-ion plasmas are investigated by using three fluid quantum magnetohydrodynamic model. The quantum mechanical effects of electrons and positrons are taken into account due to their Fermionic nature (to obey Fermi statistics) and quantum diffraction effects (Bohm diffusion term) in the model. The reductive perturbation method is employed to derive the Korteweg-de Vries (KdV) equation for low amplitude magnetoacoustic soliton in dense electron-positron-ion plasmas. It is found that positron concentration has significant impact on the phase velocity of magnetoacoustic wave and on the formation of single pulse nonlinear structure. The numerical results are also illustrated by taking into account the plasma parameters of the outside layers of white dwarfs and neutron stars/pulsars.

Systematic simulations of modified gravity: chameleon models

In this work we systematically study the linear and nonlinear structure formation in chameleon theories of modified gravity, using a generic parameterisation which describes a large class of models using only 4 parameters. For this we have modified the N-body simulation code ecosmog to perform a total of 65 simulations for different models and parameter values, including the default ΛCDM. These simulations enable us to explore a significant portion of the parameter space. We have studied the effects of modified gravity on the matter power spectrum and mass function, and found a rich and interesting phenomenology where the difference with the ΛCDM paradigm cannot be reproduced by a linear analysis even on scales as large as k ∼ 0.05 hMpc−1, since the latter incorrectly assumes that the modification of gravity depends only on the background matter density. Our results show that the chameleon screening mechanism is significantly more efficient than other mechanisms such as the dilaton and symmetron, especially in high-density regions and at early times, and can serve as a guidance to determine the parts of the chameleon parameter space which are cosmologically interesting and thus merit further studies in the future.

Direct determination of expansion history using redshift distortions

We investigate the direct determination of expansion history using redshift distortions without plugging into detailed cosmological parameters. The observed spectra in redshift space include a mixture of information: fluctuations of density-density and velocity-velocity spectra, and distance measures of perpendicular and parallel components to the line of sight. Unfortunately it is hard to measure all the components simultaneously without any specific prior assumption. Common prior assumptions include a linear/quasi-linear model of redshift distortions or a model for the shape of the power spectra, which eventually breaks down on small scales at later epochs where nonlinear structure formation disturbs coherent growth. The degeneracy breaking, between the effect of cosmic distances and redshift distortions for example, depends on the prior we assume. An alternative approach is to utilize the cosmological principle inscribed in the heart of the Friedmann-Lematre-Robertson-Walker (hereafter FLRW) universe, that is, the specific relation between the angular diameter distance and the Hubble parameter, in this degeneracy breaking. We show that utilizing this FLRW prior early in the step of distinguishing the distance effect from redshift distortions helps us improve the detectability of power spectra and distance measures with no leaning on a combination of other experiments.

An efficient implementation of massive neutrinos in non-linear structure formation simulations

Massive neutrinos make up a fraction of the dark matter, but due to their large thermal velocities, cluster significantly less than cold dark matter (CDM) on small scales. An accurate theoretical modelling of their effect during the non-linear regime of structure formation is required in order to properly analyse current and upcoming high-precision large-scale structure data, and constrain the neutrino mass. Taking advantage of the fact that massive neutrinos remain linearly clustered up to late times, this paper treats the linear growth of neutrino overdensities in a non-linear CDM background. The evolution of the CDM component is obtained via N-body computations. The smooth neutrino component is evaluated from that background by solving the Boltzmann equation linearised with respect to the neutrino overdensity. CDM and neutrinos are simultaneously evolved in time, consistently accounting for their mutual gravitational influence. This method avoids the issue of shot-noise inherent to particle-based neutrino simulations, and, in contrast with standard Fourier-space methods, properly accounts for the non-linear potential wells in which the neutrinos evolve. Inside the most massive late-time clusters, where the escape velocity is larger than the neutrino thermal velocity, neutrinos can clump non-linearly, causing the method to formally break down. It is shown that this does not affect the total matter power spectrum, which can be very accurately computed on all relevant scales up to the present time.

Systematic simulations of modified gravity: symmetron and dilaton models

We study the linear and nonlinear structure formation in the dilaton and symmetron models of modified gravity using a generic parameterisation which describes a large class of scenarios using only a few parameters, such as the coupling between the scalar field and the matter, and the range of the scalar force on very large scales. For this we have modified the N-body simulation code ECOSMOG, which is a variant of RAMSES working in modified gravity scenarios, to perform a set of 110 simulations for different models and parameter values, including the default ΛCDM. These simulations enable us to explore a large portion of the parameter space. We have studied the effects of modified gravity on the matter power spectrum and mass function, and found a rich and interesting phenomenology where the difference with the ΛCDM template cannot be reproduced by a linear analysis even on scales as large as k ∼ 0.05 hMpc−1.Our results show the full effect of screening on nonlinear structure formation and the associated deviation from ΛCDM. We also investigate how differences in the force mediated by the scalar field in modified gravity models lead to qualitatively different features for the nonlinear power spectrum and the halo mass function, and how varying the individual model parameters changes these observables. The differences are particularly large in the nonlinear power spectra whose shapes for f(R), dilaton and symmetron models vary greatly, and where the characteristic bump around 1 hMpc−1 of f(R) models is preserved for symmetrons, whereas an increase on much smaller scales is particular to symmetrons. No bump is present for dilatons where a flattening of the power spectrum takes place on small scales. These deviations from ΛCDM and the differences between modified gravity models, such as dilatons and symmetrons, could be tested with future surveys.

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.

The 6dF Galaxy Survey: z≈ 0 measurements of the growth rate and σ8

We present a detailed analysis of redshift-space distortions in the two-point correlation function of the 6dF Galaxy Survey (6dFGS). The K-band selected sub-sample which we employ in this study contains 81971 galaxies distributed over 17000deg^2 with an effective redshift z = 0.067. By modelling the 2D galaxy correlation function, xi(r_p,pi), we measure the parameter combination f(z)sigma_8(z) = 0.423 +/- 0.055. Alternatively, by assuming standard gravity we can break the degeneracy between sigma_8 and the galaxy bias parameter, b. Combining our data with the Hubble constant prior from Riess et al (2011), we measure sigma_8 = 0.76 +/- 0.11 and Omega_m = 0.250 +/- 0.022, consistent with constraints from other galaxy surveys and the Cosmic Microwave Background data from WMAP7. Combining our measurement of fsigma_8 with WMAP7 allows us to test the relationship between matter and gravity on cosmic scales by constraining the growth index of density fluctuations, gamma. Using only 6dFGS and WMAP7 data we find gamma = 0.547 +/- 0.088, consistent with the prediction of General Relativity. We note that because of the low effective redshift of 6dFGS our measurement of the growth rate is independent of the fiducial cosmological model (Alcock-Paczynski effect). We also show that our conclusions are not sensitive to the model adopted for non-linear redshift-space distortions. Using a Fisher matrix analysis we report predictions for constraints on fsigma_8 for the WALLABY survey and the proposed TAIPAN survey. The WALLABY survey will be able to measure fsigma_8 with a precision of 4-10%, depending on the modelling of non-linear structure formation. This is comparable to the predicted precision for the best redshift bins of the Baryon Oscillation Spectroscopic Survey (BOSS), demonstrating that low-redshift surveys have a significant role to play in future tests of dark energy and modified gravity.

Tripolar vortex formation in dense quantum plasma with ion-temperature-gradients

We have derived system of nonlinear equations governing the dynamics of low-frequency electrostatic toroidal ion-temperature-gradient mode for dense quantum magnetoplasma. For some specific profiles of the equilibrium density, temperature, and ion velocity gradients, the nonlinear equations admit a stationary solution in the form of a tripolar vortex. These results are relevant to understand nonlinear structure formation in dense quantum plasmas in the presence of equilibrium ion-temperature and density gradients.

WiggleZ Dark Energy Survey: Cosmological neutrino mass constraint from blue high-redshift galaxies

The absolute neutrino mass scale is currently unknown, but can be constrained from cosmology. The WiggleZ high redshift star-forming blue galaxy sample is less sensitive to systematics from non-linear structure formation, redshift-space distortions and galaxy bias than previous surveys. We obtain a upper limit on the sum of neutrino masses of 0.60eV (95% confidence) for WiggleZ+Wilkinson Microwave Anisotropy Probe. Combining with priors on the Hubble Parameter and the baryon acoustic oscillation scale gives an upper limit of 0.29eV, which is the strongest neutrino mass constraint derived from spectroscopic galaxy redshift surveys.

A gradient expansion for cosmological backreaction

We address the issue of cosmological backreaction from non-linearstructure formation by constructing an approximation for the time evolved metric of a dust dominated universe based on a gradient expansion. Our metric begins as a perturbation of a flat Friedmann-Robertson-Walker state described by a nearly scale invariant, Gaussian, power-law distribution, and evolves in time until non-linear structures have formed. After describing and attempting to control for certain complications in the implementation of this approach, this metric then forms a working model of the universe. We numerically calculate the evolution of the average scale factor in this model and hence the backreaction. We argue that, despite its limitations, this model is more realistic than previous models that have confronted the issue of backreaction. We find that the instantaneous effects of backreaction in this model could be as large as ∼ 10% of the background. This suggests that a proper understanding of the cumulative effects of backreaction could be crucial for precision cosmology and any future exploration of the dark sector.

Neutrinos in non-linear structure formation — a simple SPH approach

We present a novel method for implementing massive neutrinos in N-body simulations. Instead of sampling the neutrino velocity distribution by individual point particles we take neutrino free-streaming into account by treating it as an effective redshift dependent sound speed in a perfect isothermal fluid, and assume a relation between the sound speed and velocity dispersion of the neutrinos. Although the method fails to accurately model the true neutrino power spectrum, it is able to calculate the total matter power spectrum to the same accuracy as more complex hybrid neutrino methods, except on very small scales. We also present an easy way to update the publicly available GADGET-2 version with this neutrino approximation.

Simulation studies of dark energy clustering induced by the formation of dark matter halos

In this paper, we present a simulation method within the two-component spherical collapse model to investigate dark energy perturbations associated with the formation of dark matter halos. The realistic mass accretion history of a dark matter halo taking into account its fast and slow growth is considered by imposing suitable initial conditions and isotropized virializations for the spherical collapse process. The dark energy component is treated as a perfect fluid described by two important parameters, the equation of state parameter $w$ and the sound speed $c_s$. Quintessence models with $w>-1$ are analyzed. We adopt the Newtonian gauge to describe the spacetime which is perturbed mainly by the formation of a dark matter halo. It is found that the dark energy density perturbation $\delta_{DE}$ depends on $w$ and $c_s$, and its behavior follows closely the gravitational potential $\Phi$ of the dark matter halo with $\delta_{DE}\approx -(1+w)\Phi/c_s^2$. For $w>-1$, the dark energy perturbation presents a clustering behavior with $\delta_{DE}>0$ during the entire formation of the dark matter halo, from linear to nonlinear and virialized stages. The value of $\delta_{DE}$ increases with the increase of the halo mass. For a cluster of mass $M\sim 10^{15} M_{\odot}$, $\delta_{DE}\sim 10^{-5}$ within the virialized region for $c_s^2 \in [0.5, 1]$, and it can reach $\delta_{DE}=O(1)$ with $c_s^2=0.00001$. For a scalar-field dark energy model, we find that with suitably modeled $w$ and $c_s$, its perturbation behavior associated with the nonlinear formation of dark matter halos can well be analyzed using the fluid approach, demonstrating the validity of the fluid description for dark energy even considering its perturbation in the stage of nonlinear dark matter structure formation.

Ion-acoustic vortex formation in a non-uniform two-electron-temperature magnetoplasma with sheared ion flow

AbstractWe have investigated some linear as well as nonlinear properties of ion-acoustic wave (IAW) propagation in a non-uniform two-electron-temperature magnetoplasma in the presence of ion-sheared flows. In the linear limit, new dispersion relation has been derived and analyzed in some interesting limiting cases. It is shown that ion-sheared flow can drive the IAW unstable under a certain limit.Whereas, in the nonlinear case, dipolar and vortex street type solutions can appear. It is observed that by choosing some typical parameters of Earth's auroral region, the scalelength of the nonlinear structures are significantly modified. The present investigation might be very useful to explain various types of nonlinear structure formation which has been observed in space environments where two-electron-temperature plasma exist.

Turbulence in fluid and plasma: search for a new paradigm

A first principle explanation of the origin of intermittency and nonlinear structure formation in the Lagrangian velocity increments of a turbulent flow is presented in the context of a scale-invariant analytical formalism that is being developed recently. The copious generation of power laws and nonlinear exponents in the structure functions are shown to follow quite naturally in the present formalism.

Galaxy bias and non-linear structure formation in general relativity

Length scales probed by the large scale structure surveys are becoming closerand closer to the horizon scale. Further, it has been recently understood thatnon-Gaussianity in the initial conditions could show up in a scale dependence ofthe bias of galaxies at the largest possible distances. It is thereforeimportant to take General Relativistic effects into account. Here we providea General Relativistic generalization of the bias that is valid both forGaussian and for non-Gaussian initial conditions. The collapse of objectshappens on very small scales, while long-wavelength modes are always in thequasi linear regime. Around every small collapsing region, it is thereforepossible to find a reference frame that is valid for arbitrary times and wherethe space time is almost flat: the Fermi frame. Here the Newtonianapproximation is applicable and the equations of motion are the ones of thestandard N-body codes. The effects of long-wavelength modes are encoded in themapping from the cosmological frame to the local Fermi frame. At the level ofthe linear bias, the effect of the long-wavelength modes on the dynamics of theshort scales is all encoded in the local curvature of the Universe, which allowsus to define a General Relativistic generalization of the bias in the standardNewtonian setting. We show that the bias due to this effect goes tozero as the square of the ratio between the physical wavenumber and the Hubblescale for modes longer than the horizon, confirming the intuitive picture thatmodes longer than the horizon do not have any dynamical effect. On the otherhand, the bias due to non-Gaussianities does not need to vanish for modes longerthan the Hubble scale, and for non-Gaussianities of the local kind it goes to aconstant. As a further application of our setup, we show that it is notnecessary to perform large N-body simulations to extract information aboutlong-wavelength modes: N-body simulations can be done on small scales andlong-wavelength modes are encoded simply by adding curvature to thesimulation, as well as rescaling the time and the scale.

Prospects for detecting dark matter halo substructure with pulsar timing

One of the open questions of modern cosmology is the nature and properties of the dark matter halo and its substructures. In this work we study the gravitational effect of dark matter substructures on pulsar timing observations. Since millisecond pulsars are stable and accurate emitters, they have been proposed as plausible astrophysical tools to probe the gravitational effects of dark matter structures. We study this effect on pulsar timing through Shapiro time delay (or integrated Sachs-Wolfe (ISW) effect) and Doppler effects statistically, showing that the latter dominates the signal. For this task, we relate the power spectrum of pulsar frequency change to the matter power spectrum on small scales, which we compute using the stable clustering hypothesis, as well as other models of nonlinear structure formation. We compare this power spectrum with the reach of current and future observations of pulsar timing designed for gravitational wave detection. Our results show that while current observations are unable to detect these signals, the sensitivity of the upcoming square kilometer array is only a factor of few weaker than our optimistic predictions.