Initial Power Spectrum Research Articles

Information content of higher order galaxy correlation functions

ABSTRACT The shapes of galaxy N-point correlation functions can be used as standard rulers to constrain the distance–redshift relationship. The cosmological density fields traced by late-time galaxy formation are initially nearly Gaussian, and hence, all the cosmological information can be extracted from their two-point correlation function. Subsequent non-linear evolution under gravity, as well as halo and then galaxy formation, generates higher order correlation functions. Since the mapping of the initial to the final density field is, on large scales, invertible, it is often claimed that the information content of the initial field’s power spectrum is equal to that of all the higher order functions of the final, non-linear field. This claim implies that reconstruction of the initial density field from the non-linear field renders analysis of higher order correlation functions of the latter superfluous. We show that this claim is false when the N-point functions are used as standard rulers. Constraints available from joint analysis of the two and three-point correlation functions can, in some cases, exceed those offered by the initial power spectrum. We provide a mathematical justification for this claim and demonstrate it using a large suite of N-body simulations. In particular, we show that for the z = 0 real-space matter field in the limit of vanishing shot-noise, taking modes up to kmax = 0.2 h Mpc−1, using the bispectrum alone offers a factor of 2 reduction in the variance on the cosmic distance scale relative to that available from the linear power spectrum.

Axion miniclusters made easy

We use a modified version of the peak patch excursion set formalism to compute the mass and size distribution of QCD axion miniclusters from a fully non-Gaussian initial density field obtained from numerical simulations of axion string decay. We find strong agreement with $N$-body simulations at significantly lower computational cost. We employ a spherical collapse model, and provide fitting functions for the modified barrier in the radiation era. The halo mass function at $z=629$ has a power-law distribution ${M}^{\ensuremath{-}0.6}$ for masses within the range ${10}^{\ensuremath{-}15}\ensuremath{\lesssim}M\ensuremath{\lesssim}{10}^{\ensuremath{-}10}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, with all masses scaling as $({m}_{a}/50\text{ }\text{ }\ensuremath{\mu}\mathrm{eV}{)}^{\ensuremath{-}0.5}$. We construct merger trees to estimate the collapse redshift and concentration mass relation, $C(M)$, which is well described using analytical results from the initial power spectrum and linear growth. Using the calibrated analytic results to extrapolate to $z=0$, our method predicts a mean concentration $C\ensuremath{\sim}\mathcal{O}(\mathrm{few})\ifmmode\times\else\texttimes\fi{}{10}^{4}$. The low computational cost of our method makes future investigation of the statistics of rare, dense miniclusters easy to achieve.

Initial fluctuations and power spectrum of flow anisotropies in relativistic heavy-ion collisions

Flow has emerged as a crucial probe for the properties of the thermalized medium produced in relativistic heavy-ion collisions. The evolution of initial state fluctuations leaves imprints on the power spectrum of flow coefficients. Therefore, flow coefficients are a crucial probe of initial state fluctuations arising from the parton distributions of the colliding nuclei. This has a very strong correspondence with the physics of power spectrum of cosmic microwave background radiation (CMBR) anisotropies which directly probes initial inflationary fluctuations. Much work has been done to probe these interesting interconnections, in particular, in developing techniques for the measurements of higher flow coefficients. We present a short review of these developments. The effect of initial magnetic field on these features will also be reviewed. All this acquires special importance in view of upcoming electron-ion collider which will directly probe initial parton distribution of the colliding nucleus.

Constraining the primordial magnetic field with dwarf galaxy simulations

Using a set of cosmological hydro-dynamical simulations, we constrained the properties of primordial magnetic fields by studying their impact on the formation and evolution of dwarf galaxies. We performed a large set of simulations (8 dark matter only and 72 chemo-hydrodynamical) including primordial magnetic fields through the extra density fluctuations they induce at small length scales (k ≥ 10 h Mpc−1) in the matter power spectrum. Our sample of dwarfs includes nine systems selected out of the initial (3.4 Mpc h−1)3 parent box, resimulated from z = 200 to z = 0 using a zoom-in technique and including the physics of baryons. We explored a wide variety of primordial magnetic fields with strength Bλ ranging from 0.05 to 0.50 nG and magnetic energy spectrum slopes nB from −2.9 to −2.1. Strong magnetic fields characterized by a high amplitude (Bλ = 0.50, 0.20 nG with nB = −2.9) or by a steep initial power spectrum slope (nB = −2.1, −2.4, with Bλ = 0.05 nG) induce perturbations on mass scales from 107 to 109 M⊙. In this context emerging galaxies see their star formation rates strongly boosted. They become more luminous and metal rich than their counterparts without primordial magnetic fields. Such strong fields are ruled out by their inability to reproduce the observed scaling relations of dwarf galaxies. They predict that dwarf galaxies are at the origin of an unrealistically early reionization of the Universe and that they also overproduce luminous satellites in the Local Group. Weaker magnetic fields impacting the primordial density field at corresponding masses ≲106 M⊙, produce a large number of mini dark matter halos orbiting the dwarfs, however out of reach for current lensing observations. This study allows us, for the first time, to constrain the properties of primordial magnetic fields based on realistic cosmological simulations of dwarf galaxies.

Constraints on primordial gravitational waves from the cosmic microwave background

Searches for primordial gravitational waves have resulted in constraints in a large frequency range from a variety of sources. The standard Cosmic Microwave Background (CMB) technique is to parameterise the tensor power spectrum in terms of the tensor-to-scalar ratio, r, and spectral index, nt, and constrain these using measurements of the temperature and polarization power spectra. Another method, applicable to modes well inside the cosmological horizon at recombination, uses the shortwave approximation, under which gravitational waves behave as an effective neutrino species. In this paper we give model-independent CMB constraints on the energy density of gravitational waves, Ωgw h2, for the entire range of observable frequencies. On large scales, f ≲ 10−16 Hz, we reconstruct the initial tensor power spectrum in logarithmic frequency bins, finding maximal sensitivity for scales close to the horizon size at recombination. On small scales, f ≳10−15 Hz, we use the shortwave approximation, finding Ωgw h2 < 1.7 ×10−6 for adiabatic initial conditions and Ωgw h2 < 2.9 ×10−7 for homogeneous initial conditions (both 2σ upper limits). For scales close to the horizon size at recombination, we use second-order perturbation theory to calculate the back-reaction from gravitational waves, finding Ωgw h2 < 8.4 ×10−7, in the absence of neutrino anisotropic stress and Ωgw h2 < 8.6 ×10−7 when including neutrino anisotropic stress. These constraints are valid for 10−15 Hz ≳ f ≳ 3 × 10−16 Hz.

Voronoi volume function: a new probe of cosmology and galaxy evolution

ABSTRACT We study the Voronoi volume function (VVF) – the distribution of cell volumes (or inverse local number density) in the Voronoi tessellation of any set of cosmological tracers (galaxies/haloes). We show that the shape of the VVF of biased tracers responds sensitively to physical properties such as halo mass, large-scale environment, substructure, and redshift-space effects, making this a hitherto unexplored probe of both primordial cosmology and galaxy evolution. Using convenient summary statistics – the width, median, and a low percentile of the VVF as functions of average tracer number density – we explore these effects for tracer populations in a suite of N-body simulations of a range of dark matter models. Our summary statistics sensitively probe primordial features such as small-scale oscillations in the initial matter power spectrum (as arise in models involving collisional effects in the dark sector), while being largely insensitive to a truncation of initial power (as in warm dark matter models). For vanilla cold dark matter (CDM) cosmologies, the summary statistics display strong evolution and redshift-space effects, and are also sensitive to cosmological parameter values for realistic tracer samples. Comparing the VVF of galaxies in the Galaxies &amp; Mass Assembly (GAMA) survey with that of abundance-matched CDM (sub)haloes tentatively reveals environmental effects in GAMA beyond halo mass (modulo unmodelled satellite properties). Our exploratory analysis thus paves the way for using the VVF as a new probe of galaxy evolution physics as well as the nature of dark matter and dark energy.

Modified initial power spectrum and too big to fail problem

ABSTRACT The galactic scale challenges of dark matter such as ‘missing satellite’ problem and ‘too big to fail’ problem are the main caveats of standard model of cosmology. These challenges could be solved either by implementing the complicated baryonic physics or it could be considered as an indication to a new physics beyond the standard model of cosmology. The modification of collisionless dark matter models or the standard initial conditions are two promising venues for study. In this work, we investigate the effects of the deviations from scale invariant initial curvature power spectrum on number density of dark matter haloes. We develop the non-Markov extension of the excursion set theory to calculate the number density of dark matter substructures and dark matter halo progenitor mass distribution. We show that the plausible solution to ‘too big to fail’ problem could be obtained by a Gaussian excess in initial power in the scales of k* ∼ 3 h Mpc−1 that is related to the mass scale of M* ∼ 1011 M⊙. We show that this deviation leads to the decrement of dark matter subhaloes in galactic scale, which is consistent with the current status of the non-linear power spectrum. Our proposal also has a prediction that the number density of Milky Way-type galaxies must be higher than the standard case.

The influence of initial perturbation power spectra on the growth of a turbulent mixing layer induced by Richtmyer–Meshkov instability

This paper investigates the influence of different broadband perturbations on the evolution of a Richtmyer–Meshkov turbulent mixing layer initiated by a Mach 1.84 shock traversing a perturbed interface separating gases with a density ratio of 3:1. Both the bandwidth of modes in the interface perturbation, as well as their relative amplitudes, are varied in a series of carefully designed numerical simulations at grid resolutions up to 3.2×109 cells. Three different perturbations are considered, characterised by a power spectrum of the form P(k)∝km where m=−1, −2 and −3. The growth of the mixing layer is shown to strongly depend on the initial conditions, with the growth rate exponent θ found to be 0.5, 0.63 and 0.75 for each value of m at the highest grid resolution. The asymptotic values of the molecular mixing fraction Θ are also shown to vary significantly with m; at the latest time considered Θ is 0.56, 0.39 and 0.20 respectively. Turbulent kinetic energy (TKE) is also analysed in both the temporal and spectral domains. The temporal decay rate of TKE is found not to match the predicted value of n=2−3θ, which is shown to be due to a time-varying normalised dissipation rate Cϵ. In spectral space, the data follow the theoretical scaling of k(m+2)∕2 at low wavenumbers and tend towards k−3∕2 and k−5∕3 scalings at high wavenumbers for the spectra of transverse and normal velocity components respectively. The results represent a significant extension of previous work on the Richtmyer–Meshkov instability evolving from broadband initial perturbations and provide useful benchmarks for future research.

Does spatial flatness forbid the turnaround epoch of collapsing structures?

Cosmological observational analysis frequently assumes that the Universe is spatially flat. We aim to non-perturbatively check the conditions under which a flat or nearly flat expanding dust universe, including the Λ-cold-dark-matter (ΛCDM) model if interpreted as strictly flat, forbids the gravitational collapse of structure. We quantify spatial curvature at turnaround. We use the Hamiltonian constraint to determine the pointwise conditions required for an overdensity to reach its turnaround epoch in an exactly flat spatial domain. We illustrate this with a plane-symmetric, exact, cosmological solution of the Einstein equation, extending earlier work. More generally, for a standard initial power spectrum, we use the relativistic Zel'dovich approximation implemented in INHOMOG to numerically estimate how much positive spatial curvature is required to allow turnaround at typical epochs/length scales in almost-Einstein-de Sitter (EdS)/ΛCDM models with inhomogeneous curvature. We find that gravitational collapse in a spatially exactly flat, irrotational, expanding, dust universe is relativistically forbidden pointwise. In the spatially flat plane-symmetric model considered here, pancake collapse is excluded both pointwise and in averaged domains. In an almost-EdS/ΛCDM model, the per-domain average curvature in collapsing domains almost always becomes strongly positive prior to turnaround, with the expansion-normalised curvature functional reaching Ωℛ\U0001d49f∼−5. We show analytically that a special case gives Ωℛ\U0001d49f=−5 exactly (if normalised using the EdS expansion rate) at turnaround. An interpretation of ΛCDM as literally 3-Ricci flat would forbid structure formation. The difference between relativistic cosmology and a strictly flat ΛCDM model is fundamental in principle, but we find that the geometrical effect is weak.

Inhomogeneous universe from group field theory condensate

One of the fundamental challenges for quantum cosmology is to explain the emergence of our macroscopic Universe from physics at the Planck scale. In the group field theory (GFT) approach to quantum gravity, such a macroscopic universe results from the formation of a “condensate” of fundamentally discrete degrees of freedom. It has been shown that the effective dynamics of such GFT condensates follows the classical Friedmann dynamics at late times, while avoiding the classical singularity by a bounce akin to the one of loop quantum cosmology (LQC). It was also shown how quantum fluctuations in a GFT condensate provide an initial power spectrum of volume fluctuations around exact homogeneity. Here we connect the results for quantum fluctuations in GFT to the usual formalism for cosmological perturbations within quantum field theory in curved spacetime. We consider a bouncing universe filled with a massless scalar field, in which perturbations are generated by vacuum fluctuations in the contracting phase. Matching conditions at the bounce are provided by working within LQC. We then compare the results to the GFT condensate scenario for quantum gravity with massless scalar matter. Here, instead, an initial quantum phase described by a GFT condensate generates initial scalar perturbations through quantum fluctuations. We show general agreement in the predictions of both approaches, suggesting that GFT condensates can provide a physical mechanism for the emergence of a slightly inhomogeneous universe from full quantum gravity.

Thermal Sunyaev–Zel’dovich Effect in the IGM due to Primordial Magnetic Fields

In the present universe, magnetic fields exist with various strengths and on various scales. One possible origin of these cosmic magnetic fields is the primordial magnetic fields (PMFs) generated in the early universe. PMFs are considered to contribute to matter density evolution via Lorentz force and the thermal history of intergalactic medium (IGM) gas due to ambipolar diffusion. Therefore, information about PMFs should be included in the temperature anisotropy of the Cosmic Microwave Background through the thermal Sunyaev–Zel’dovich (tSZ) effect in IGM. In this article, given an initial power spectrum of PMFs, we show the spatial fluctuation of mass density and temperature of the IGM and tSZ angular power spectrum created by the PMFs. Finally, we find that the tSZ angular power spectrum induced by PMFs becomes significant on small scales, even with PMFs below the observational upper limit. Therefore, we conclude that the measurement of tSZ anisotropy on small scales will provide the most stringent constraint on PMFs.

Gravitational lensing and the power spectrum of dark matter substructure: Insights from the ETHOS N -body simulations

Strong gravitational lensing has been identified as a promising astrophysical probe to study the particle nature of dark matter. In this paper we present a detailed study of the power spectrum of the projected mass density (convergence) field of substructure in a Milky Way-sized halo. This power spectrum has been suggested as a key observable that can be extracted from strongly-lensed images and yield important clues about the matter distribution within the lens galaxy. We use two different $N$-body simulations from the ETHOS framework: one with cold dark matter and another with self-interacting dark matter and a cutoff in the initial power spectrum. Despite earlier works that identified $k\ensuremath{\gtrsim}100\text{ }\text{ }{\mathrm{kpc}}^{\ensuremath{-}1}$ as the most promising scales to learn about the particle nature of dark matter we find that even at lower wave numbers---which are actually within reach of observations in the near future---we can gain important information about dark matter. Comparing the amplitude and slope of the power spectrum on scales $0.1\ensuremath{\lesssim}k/{\mathrm{kpc}}^{\ensuremath{-}1}\ensuremath{\lesssim}10$ from lenses at different redshifts can help us distinguish between cold dark matter and other exotic dark matter scenarios that alter the abundance and central densities of subhalos. Furthermore, by considering the contribution of different mass bins to the power spectrum we find that subhalos in the mass range $1{0}^{7}\ensuremath{-}{10}^{8}\text{ }\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}$ are on average the largest contributors to the power spectrum signal on scales $2\ensuremath{\lesssim}k/{\mathrm{kpc}}^{\ensuremath{-}1}\ensuremath{\lesssim}15$, despite the numerous subhalos with masses $&gt;{10}^{8}\text{ }\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}$ in a typical lens galaxy. Finally, by comparing the power spectra obtained from the subhalo catalogs to those from the particle data in the simulation snapshots we find that the seemingly-too-simple halo model is in fact a fairly good approximation to the much more complex array of substructure in the lens.

CosmicGrowth Simulations—Cosmological simulations for structure growth studies

I present a large set of high resolution simulations, called CosmicGrowth Simulations, which were generated with either 8.6 billion or 29 billion particles. As the nominal cosmological model that can match nearly all observations on cosmological scales, I have adopted a flat Cold Dark Matter (CDM) model with a cosmological constant $\Lambda$ (${\Lambda}$CDM). The model parameters have been taken either from the latest result of the WMAP satellite (WMAP ${\Lambda}$CDM) or from the first year's result of the Planck satellite (Planck ${\Lambda}$CDM). Six simulations are produced in the ${\Lambda}$CDM models with two in the Planck model and the others in the WMAP model. In order for studying the nonlinear evolution of the clustering, four simulations were also produced with $8.6$ billion particles for the scale-free models of an initial power spectrum $P(k)\propto k^n$ with $n=0$,$-1$,$-1.5$ or $-2.0$. Furthermore, two radical CDM models (XCDM) are simulated with 8.6 billion particles each. Since the XCDM have some of the model parameters distinct from those of the ${\Lambda}$CDM models, they must be unable to match the observations, but are very useful for studying how the clustering properties depend on the model parameters. The Friends-of-Friends (FoF) halos were identified for each snapshot and subhalos were produced by the Hierarchical Branch Tracing (HBT) algorithm. These simulations form a powerful database to study the growth and evolution of the cosmic structures both in theories and in observations.

Nonlinear growth of structure in cosmologies with damped matter fluctuations

We investigate the nonlinear evolution of structure in variants of the standard cosmological model which display damped density fluctuations relative to cold dark matter (e.g. in which cold dark matter is replaced by warm or interacting DM). Using N-body simulations, we address the question of how much information is retained from different scales in the initial linear power spectrum following the nonlinear growth of structure. We run a suite of N-body simulations with different initial linear matter power spectra to show that, once the system undergoes nonlinear evolution, the shape of the linear power spectrum at high wavenumbers does not affect the non-linear power spectrum, while it still matters for the halo mass function. Indeed, we find that linear power spectra which differ from one another only at wavenumbers larger than their half-mode wavenumber give rise to (almost) identical nonlinear power spectra at late times, regardless of the fact that they originate from different models with damped fluctuations. On the other hand, the halo mass function is more sensitive to the form of the linear power spectrum. Exploiting this result, we propose a two parameter model of the transfer function in generic damped scenarios, and show that this parametrisation works as well as the standard three parameter models for the scales on which the linear spectrum is relevant.

Feeding supermassive black holes by collisional cascades

The processes driving gas accretion on to supermassive black holes (SMBHs) are still poorly understood. Angular momentum conservation prevents gas within $\sim10\,$pc of the black hole from reaching radii $\sim10^{-3}\,$pc where viscous accretion becomes efficient. Here we present simulations of the collapse of a clumpy shell of swept-up isothermal gas, which is assumed to have formed as a result of feedback from a previous episode of AGN activity. The gas falls towards the SMBH forming clumps and streams, which intersect, collide, and often form a disc. These collisions promote partial cancellations of angular momenta, resulting in further infall and more collisions. This continued collisional cascade generates a tail of gas with sufficiently small angular momenta and provides a viable route for gas inflow to sub-parsec scales. The efficiency of this process hardly depends on details, such as gas temperature, initial virial ratio and power spectrum of the gas distribution, as long as it is not strongly rotating. Adding star formation to this picture might explain the near-simultaneous formation of the S-stars (from tidally disrupted binaries formed in plunging gas streams) and the sub-parsec young stellar disc around Sgr A$^{\!\star}$.

Silent initial conditions for cosmological perturbations with a change of spacetime signature

Recent calculations in loop quantum cosmology suggest that a transition from a Lorentzian to a Euclidean spacetime might take place in the very early universe. The transition point leads to a state of silence, characterized by a vanishing speed of light. This behavior can be interpreted as a decoupling of different space points, similar to the one characterizing the BKL phase. In this study, we address the issue of imposing initial conditions for the cosmological perturbations at the transition point between the Lorentzian and Euclidean phases. Motivated by the decoupling of space points, initial conditions characterized by a lack of correlations are investigated. We show that the “white noise” gains some support from analysis of the vacuum state in the deep Euclidean regime. Furthermore, the possibility of imposing the silent initial conditions at the trans-Planckian surface, characterized by a vanishing speed for the propagation of modes with wavelengths of the order of the Planck length, is studied. Such initial conditions might result from the loop deformations of the Poincaré algebra. The conversion of the silent initial power spectrum to a scale-invariant one is also examined.

The median density of the Universe

Despite the fact that the mean matter density of the universe has been measured to an accuracy of a few percent within the standard $\Lambda$CDM paradigm, its median density is not known even to order of magnitude. Typical points lie in low-density regions and are not part of a collapsed structure of any scale. Locally, the dark matter distribution is then simply a stretched version of that in the early universe. In this single-stream regime, the distribution of unsmoothed density is sensitive to the initial power spectrum on all scales, in particular on very small scales, and hence to the nature of the dark matter. It cannot be estimated reliably using conventional cosmological simulations because of the enormous dynamic range involved, but a suitable excursion set procedure can be used instead. For the Planck cosmological parameters, a 100 GeV WIMP, corresponding to a free-streaming mass $\sim 10^{-6}M_\odot$, results in a median density of $\sim 4\times 10^{-3}$ in units of the mean density, whereas a 10 $\mu$eV axion with free-streaming mass $\sim 10^{-12}M_\odot$ gives $\sim 3\times 10^{-3}$, and Warm Dark Matter with a (thermal relic) mass of 1 keV gives $\sim 8\times 10^{-2}$. In CDM (but not in WDM) universes, single-stream regions are predicted to be topologically isolated by the excursion set formalism. A test by direct N-Body simulations seems to confirm this prediction, although it is still subject to finite size and resolution effects. Unfortunately, it is unlikely that any of these properties is observable and so suitable for constraining the properties of dark matter.

Thermal Sunyaev-Zel’dovich effect in the intergalactic medium with primordial magnetic fields

The presence of ubiquitous magnetic fields in the universe is suggested from observations of radiation and cosmic ray from galaxies or the intergalactic medium (IGM). One possible origin of cosmic magnetic fields is the magnetogenesis in the primordial universe. Such magnetic fields are called primordial magnetic fields (PMFs), and are considered to affect the evolution of matter density fluctuations and the thermal history of the IGM gas. Hence the information of PMFs is expected to be imprinted on the anisotropies of the cosmic microwave background (CMB) through the thermal Sunyaev-Zel'dovich (tSZ) effect in the IGM. In this study, given an initial power spectrum of PMFs as $P(k)\propto B_{\rm 1Mpc}^2 k^{n_{B}}$, we calculate dynamical and thermal evolutions of the IGM under the influence of PMFs, and compute the resultant angular power spectrum of the Compton $y$-parameter on the sky. As a result, we find that two physical processes driven by PMFs dominantly determine the power spectrum of the Compton $y$-parameter; (i) the heating due to the ambipolar diffusion effectively works to increase the temperature and the ionization fraction, and (ii) the Lorentz force drastically enhances the density contrast just after the recombination epoch. These facts result in making the tSZ angular power spectrum induced by the PMFs more remarkable at $\ell >10^4$ than that by galaxy clusters even with $B_{\rm 1Mpc}=0.1$ nG and $n_{B}=-1.0$ because the contribution from galaxy clusters decreases with increasing $\ell$. The measurement of the tSZ angular power spectrum on high $\ell$ modes can provide the stringent constraint on PMFs.

Towards optimal extraction of cosmological information from nonlinear data

One of the main unsolved problems of cosmology is how to maximize the extraction of information from nonlinear data. If the data are nonlinear the usual approach is to employ a sequence of statistics (N-point statistics, counting statistics of clusters, density peaks or voids etc.), along with the corresponding covariance matrices. However, this approach is computationally prohibitive and has not been shown to be exhaustive in terms of information content. Here we instead develop a hierarchical Bayesian approach, expanding the likelihood around the maximum posterior of linear modes, which we solve for using optimization methods. By integrating out the modes using perturbative expansion of the likelihood we construct an initial power spectrum estimator, which for a fixed forward model contains all the cosmological information if the initial modes are gaussian distributed. We develop a method to construct the window and covariance matrix such that the estimator is explicitly unbiased and nearly optimal. We then generalize the method to include the forward model parameters, including cosmological and nuisance parameters, and primordial non-gaussianity. We apply the method in the simplified context of nonlinear structure formation, using either simplified 2-LPT dynamics or N-body simulations as the nonlinear mapping between linear and nonlinear density, and 2-LPT dynamics in the optimization steps used to reconstruct the initial density modes. We demonstrate that the method gives an unbiased estimator of the initial power spectrum, providing among other a near optimal reconstruction of linear baryonic acoustic oscillations.

Effect of enhanced dissipation by shear flows on transient relaxation and probability density function in two dimensions

We report a non-perturbative study of the effects of shear flows on turbulence reduction in a decaying turbulence in two dimensions. By considering different initial power spectra and shear flows (zonal flows, streamers and zonal flows, and streamers combined), we demonstrate how shear flows rapidly generate small scales, leading to a fast damping of turbulence amplitude. In particular, a double exponential decrease in the turbulence amplitude is shown to occur due to an exponential increase in wavenumber. The scaling of the effective dissipation time scale τe, previously taken to be a hybrid time scale τe∝τΩ2/3τη, is shown to depend on types of shear flow as well as the initial power spectrum. Here, τΩ and τη are shearing and molecular diffusion times, respectively. Furthermore, we present time-dependent Probability Density Functions (PDFs) and discuss the effect of enhanced dissipation on PDFs and a dynamical time scale τ(t), which represents the time scale over which a system passes through statistically different states.