Halo Mass Function Research Articles

Ultralight DM bosons with an axion-like potential: scale-dependent constraints revisited

A scalar field ϕ endowed with a trigonometric potential has been proposed to play the role of Dark Matter. A deep study of the cosmological evolution of linear perturbations, and its comparison to the Cold Dark Matter (CDM) and Fuzzy Dark Matter (FDM) cases (scalar field with quadratic potential), reveals an enhancement in the amplitude of the mass power spectrum for large wave numbers due to the non-linearity of the axion-like potential. For the first time, we study the scale-dependence on physical quantities such as the growth factor Dk, the velocity growth factor fk, and fk σ8. We found that for z<10, all these quantities recover the CDM evolution, whereas for high redshift there is a clear distinction between each model (FDM case, and axion-like potential) depending on the wavenumber k and on the decay parameter of the axion-like potential as well. A semi-analytical Halo Mass Function is also revisited, finding a suppression of the number of low mass halos, as in the FDM case, but with a small increment in the amplitude of the variance and halo mass function due to the non-linearity of the axion-like potential. Finally, we present constraints on the axion mass and the axion decay parameter by using data of the Planck Collaboration 2018 and Lyman-α forest.

OUP accepted manuscript

We study and model the properties of galaxy clusters in the normal-branch Dvali–Gabadadze–Porrati (nDGP) model of gravity, which is representative of a wide class of theories that exhibit the Vainshtein screening mechanism. Using the first cosmological simulations that incorporate both full baryonic physics and nDGP, we find that, despite being efficiently screened within clusters, the fifth force can raise the temperature of the intracluster gas, affecting the scaling relations between the cluster mass and three observable mass proxies: the gas temperature, the Compton Y-parameter of the Sunyaev–Zel’dovich effect, and the X-ray analogue of the Y-parameter. Therefore, unless properly accounted for, this could lead to biased measurements of the cluster mass in tests that use cluster observations, such as cluster number counts, to probe gravity. Using a suite of dark-matter-only simulations, which span a wide range of box sizes and resolutions, and which feature very different strengths of the fifth force, we also calibrate general fitting formulae that can reproduce the nDGP halo concentration at percent accuracy for 0 ≤ z ≤ 1, and halo mass function with |${\lesssim}3{{\ \rm per\ cent}}$| accuracy at 0 ≤ z ≤ 1 (increasing to |${\lesssim}5{{\ \rm per\ cent}}$| for 1 ≤ z ≤ 2), over a halo mass range spanning four orders of magnitude. Our model for the concentration can be used for converting between halo mass overdensities and predicting statistics such as the non-linear matter power spectrum. The results of this work will form part of a framework for unbiased constraints of gravity using the data from ongoing and upcoming cluster surveys.

First constraints on small-scale non-Gaussianity from UV galaxy luminosity functions

UV luminosity functions provide a wealth of information on the physics of galaxy formation in the early Universe. Given that this probe indirectly tracks the evolution of the mass function of dark matter halos, it has the potential to constrain alternative theories of structure formation. One of such scenarios is the existence of primordial non-Gaussianity at scales beyond those probed by observations of the Cosmic Microwave Background. Through its impact on the halo mass function, such small-scale non-Gaussianity would alter the abundance of galaxies at high redshifts. In this work we present an application of UV luminosity functions as measured by the Hubble Space Telescope to constrain the non-Gaussianity parameter fNL for wavenumbers above a cut-off scale kcut. After marginalizing over the unknown astrophysical parameters and accounting for potential systematic errors, we arrive at a 2σ bound of fNL=71+426−237 for a cut-off scale kcut=0.1 Mpc−1 in the bispectrum of the primordial gravitational potential. Moreover, we perform forecasts for the James Webb Space Telescope and the Nancy Grace Roman Space Telescope, finding an expected improvement of a factor 3–4 upon the current bound.

The Evolution of Star Formation Rate Density of Galaxies

We present a semi-analytical calculation of the global star formation density (SFD) by using the well constrained cold dark matter (CDM) halo mass function. Both, halo masses <I>M<SUB>H</SUB></I>(<i>z</i>) and stellar masses <I>M</I>_*(<i>z</i>) are taken from observations of Lyα emitter (LAEs) and/or Lyman break galaxies (LBGs). Most of them, spectroscopically selected, are characterized by high star formation rates. The view of galaxy formation is mainly based on the hierarchical (“botton-up”) cold dark matter model for structure formation. We have used the connection between the halo mass and the star formation rate in galaxies of the halo mass <I>M<SUB>H</SUB></I> at redshift <i>z</i>. Our model has the advantage that we are able to calculate the global star formation rate <i>ρ</i>_*(<i>z</i>) (in <I>M</I>ʘ<i>y</i>-1<i>Mpc</i>-3) by a closed equation. All parameters (<I>M<SUB>H</SUB></I>; <I>M</I>_* and <i>n</i>) have a well-defined physical meaning. From the CDM spectrum, the power law index of the halo mass function is well constrained. Our results are compiled in Table 1 and Figure 1. Here our results are compared with observations and hydrodynamical simulations. The physical meaning of the evolution of comoving cosmic star density as a function of redshift with three epochs is discussed. We find a good agreement between the SFD inferred from observations and our model in the range of redshifts <i>z</i> = 0 - 7.

OUP accepted manuscript

We present a Markov chain Monte Carlo pipeline that can be used for robust and unbiased constraints of $f(R)$ gravity using galaxy cluster number counts. This pipeline makes use of a detailed modelling of the halo mass function in $f(R)$ gravity, which is based on the spherical collapse model and calibrated by simulations, and fully accounts for the effects of the fifth force on the dynamical mass, the halo concentration and the observable-mass scaling relations. Using a set of mock cluster catalogues observed through the thermal Sunyaev-Zel'dovich effect, we demonstrate that this pipeline, which constrains the present-day background scalar field $f_{R0}$, performs very well for both $\Lambda$CDM and $f(R)$ fiducial cosmologies. We find that using an incomplete treatment of the scaling relation, which could deviate from the usual power-law behaviour in $f(R)$ gravity, can lead to imprecise and biased constraints. We also find that various degeneracies between the modified gravity, cosmological and scaling relation parameters can significantly affect the constraints, and show how this can be rectified by using tighter priors and better knowledge of the cosmological and scaling relation parameters. Our pipeline can be easily extended to other modified gravity models, to test gravity on large scales using galaxy cluster catalogues from ongoing and upcoming surveys.

Accelerating computation of the density-field filtering scale σ(R) and non-linear mass by an order of magnitude

ABSTRACT The non-linear mass is a characteristic scale in halo formation that has many applications across cosmology. Naively, computing it requires repeated numerical integration to calculate the variance of the power spectrum on different scales and determine which scales exceed the threshold for non-linear collapse. We accelerate calculation of both the non-linear mass and the rms amplitude of the power spectrum σ(R) by working in configuration space and approximating the correlation function as a polynomial at r ≤ 5 h−1 Mpc. This enables an analytic rather than numerical solution for the non-linear mass, accurate across a variety of cosmologies to 0.1–$1{{\ \rm per\ cent}}$ in mass (depending on redshift) and 20–60× faster than the standard numerical method. We also present a further acceleration of the non-linear mass (400–1000× faster than the standard method) in which we determine the polynomial coefficients using a Taylor expansion in the cosmological parameters rather than re-fitting a polynomial to the correlation function. Our method is also 500× faster than the standard method for σ(R) for a typical case of NR = 100 desired R values, with timing essentially independent of NR. Our approach can be used for quick calculation of the halo mass function, halo mass–bias relation, and cosmological calculations involving the non-linear mass.

Testing dark matter halo properties using self-similarity

ABSTRACT We use self-similarity in N-body simulations of scale-free models to test for resolution dependence in the mass function and two-point correlation functions of dark matter haloes. We use 10243 particle simulations performed with abacus , and compare results obtained with two halo finders: friends-of-friends (fof ), and rockstar . The fof mass functions show a systematic deviation from self-similarity which is explained by resolution dependence of the fof mass assignment previously reported in the literature. Weak evidence for convergence is observed only starting from haloes of several thousand particles, and mass functions are overestimated by at least as much as $20-25{{\ \rm per\ cent}}$ for haloes of 50 particles. The mass function of the default rockstar halo catalogue (with bound virial spherical overdensity mass), on the other hand, shows good convergence of the order of 50 to 100 particles per halo, with no detectable evidence at the few percent level of any systematic dependence for larger particle number. Tests show that the mass unbinding procedure in rockstar is the key factor in obtaining this much improved resolution. Applying the same analysis to the halo–halo two point correlation function, we find again strong evidence for convergence only for rockstar haloes, at separations sufficiently large so that haloes do not overlap. At these separations, we can exclude dependence on resolution at the $5-10{{\ \rm per\ cent}}$ level once haloes have of the order of 50 to 100 particles. At smaller separations results are not converged even at significantly larger particle number, and bigger simulations would be required to establish the resolution required for convergence.

On the impact of baryons on the halo mass function, bias, and cluster cosmology

ABSTRACT Luminous matter produces very energetic events, such as active galactic nuclei and supernova explosions, that significantly affect the internal regions of galaxy clusters. Although the current uncertainty in the effect of baryonic physics on cluster statistics is subdominant as compared to other systematics, the picture is likely to change soon as the amount of high-quality data is growing fast, urging the community to keep theoretical systematic uncertainties below the ever-growing statistical precision. In this paper, we study the effect of baryons on galaxy clusters, and their impact on the cosmological applications of clusters, using the magneticum suite of cosmological hydrodynamical simulations. We show that the impact of baryons on the halo mass function can be recast in terms on a variation of the mass of the haloes simulated with pure N-body, when baryonic effects are included. The halo mass function and halo bias are only indirectly affected. Finally, we demonstrate that neglecting baryonic effects on haloes mass function and bias would significantly alter the inference of cosmological parameters from high-sensitivity next-generations surveys of galaxy clusters.

Universal at Last? The Splashback Mass Function of Dark Matter Halos

Abstract The mass function of dark matter halos is one of the most fundamental statistics in structure formation. Many theoretical models (such as Press–Schechter theory) are based on the notion that it could be universal, meaning independent of redshift and cosmology, when expressed in the appropriate variables. However, simulations exhibit persistent nonuniversalities in the mass functions of the virial mass and other commonly used spherical overdensity definitions. We systematically study the universality of mass functions over a wide range of mass definitions, for the first time including the recently proposed splashback mass, . We confirm that, in ΛCDM cosmologies, all mass definitions exhibit varying levels of nonuniversality that increase with peak height and reach between 20% and 500% at the highest masses we can test. , , and exhibit similar levels of nonuniversality. There are, however, two regimes where the splashback mass functions are significantly more universal. First, they are universal to 10% at , whereas spherical overdensity definitions experience an evolution due to dark energy. Second, when additionally considering self-similar cosmologies with extreme power spectra, splashback mass functions are remarkably universal (to between 40% and 60%), whereas their spherical overdensity counterparts reach nonuniversalities between 180% and 450%. These results strongly support the notion that the splashback radius is a physically motivated definition of the halo boundary. We present a simple and universal fitting formula for splashback mass functions that accurately reproduces our simulation data.

A Stochastic Theory of the Hierarchical Clustering. I. Halo Mass Function

Abstract We present a new theory for the hierarchical clustering of dark matter (DM) halos, based on stochastic differential equations, that constitutes a change of perspective with respect to existing frameworks (e.g., the excursion set approach); this work is specifically focused on the halo mass function. First, we present a stochastic differential equation that describes fluctuations in the mass growth of DM halos, as driven by a multiplicative white (Gaussian) noise dependent on the spherical collapse threshold and on the power spectrum of DM perturbations. We demonstrate that such a noise yields an average drift of the halo population toward larger masses, that quantitatively renders the standard hierarchical clustering. Then, we solve the Fokker–Planck equation associated to the stochastic dynamics, and obtain the Press &amp; Schechter mass function as a (stationary) solution. Moreover, generalizing our treatment to a mass-dependent collapse threshold, we obtain an exact analytic solution capable of fitting remarkably well the N-body mass function over a wide range in mass and redshift. All in all, the new perspective offered by the theory presented here can contribute to a better understanding of the gravitational dynamics leading to the formation, evolution, and statistics of DM halos across cosmic times.

Spoon or slide? The non-linear matter power spectrum in the presence of massive neutrinos

Numerical simulations of massive neutrino cosmologies consistently find a spoon-like feature in the non-linear matter power spectrum ratios of cosmological models that differ only in the neutrino mass fraction fN. Typically, the ratio approaches unity at low wave numbers k, decreases by ∼ 10 fN at k ∼ 1 h/Mpc, and turns up again at large k. Using the halo model of large-scale structure, we show that this spoon feature originates in the transition from the two-halo power spectrum to the one-halo power spectrum. The former's sensitivity to fN rises with k, while that of the latter decreases with k. The presence of this spoon feature is robust with respect to different choices of the halo mass function and the halo density profile, and does not require any parameter tuning within the halo model. We demonstrate that a standard halo model calculation is already able to predict the depth, width, and position of this spoon as well as its evolution with redshift z with remarkable accuracy. Predictions at z ≳ 1 can be further improved using non-linear perturbative inputs.

Void halo mass function: A promising probe of neutrino mass

Cosmic voids, the underdense regions in the universe, are particularly sensitive to diffuse density components such as cosmic neutrinos. This sensitivity is enhanced by the match between void sizes and the free-streaming scale of massive neutrinos. Using the massive neutrino simulations massivenus, we investigate the effect of neutrino mass on dark matter halos as a function of environment. We find that the halo mass function depends strongly on neutrino mass and that this dependence is more pronounced in voids than in high-density environments. An observational program that measured the characteristic mass of the most massive halos in voids should be able to place novel constraints on the sum of the masses of neutrinos $\ensuremath{\sum}{m}_{\ensuremath{\nu}}$. The neutrino mass effect in the simulations is quite strong: In a ${512}^{3}\text{ }\text{ }{h}^{\ensuremath{-}3}\text{ }{\mathrm{Mpc}}^{3}$ survey, the mean mass of the 1000 most massive halos in the void interiors is $(4.82\ifmmode\pm\else\textpm\fi{}0.11)\ifmmode\times\else\texttimes\fi{}{10}^{12}\text{ }\text{ }{h}^{\ensuremath{-}1}\text{ }{M}_{\ensuremath{\bigodot}}$ for $\ensuremath{\sum}{m}_{\ensuremath{\nu}}=0.6\text{ }\text{ }\mathrm{eV}$ and $(8.21\ifmmode\pm\else\textpm\fi{}0.13)\ifmmode\times\else\texttimes\fi{}{10}^{12}\text{ }\text{ }{h}^{\ensuremath{-}1}\text{ }{M}_{\ensuremath{\bigodot}}$ for $\ensuremath{\sum}{m}_{\ensuremath{\nu}}=0.1\text{ }\text{ }\mathrm{eV}$. Subaru (SuMIRe), Euclid and WFIRST will have both spectroscopic and weak lensing surveys. Covering volumes at least 50 times larger than our simulations, they should be sensitive probes of neutrino mass through void substructure.

An efficient hybrid method to produce high-resolution large-volume dark matter simulations for semi-analytic models of reionization

ABSTRACT Resolving faint galaxies in large volumes is critical for accurate cosmic reionization simulations. While less demanding than hydrodynamical simulations, semi-analytic reionization models still require very large N-body simulations in order to resolve the atomic cooling limit across the whole reionization history within box sizes ${\gtrsim}100 \, h^{-1}\, \rm Mpc$. To facilitate this, we extend the mass resolution of N-body simulations using a Monte Carlo algorithm. We also propose a method to evolve positions of Monte Carlo haloes, which can be an input for semi-analytic reionization models. To illustrate, we present an extended halo catalogue that reaches a mass resolution of $M_\text{halo} = 3.2 \times 10^7 \, h^{-1} \, \text{M}_\odot$ in a $105 \, h^{-1}\, \rm Mpc$ box, equivalent to an N-body simulation with ∼68003 particles. The resulting halo mass function agrees with smaller volume N-body simulations with higher resolution. Our results also produce consistent two-point correlation functions with analytic halo bias predictions. The extended halo catalogues are applied to the meraxes semi-analytic reionization model, which improves the predictions on stellar mass functions, star formation rate densities, and volume-weighted neutral fractions. Comparison of high-resolution large-volume simulations with both small-volume and low-resolution simulations confirms that both low-resolution and small-volume simulations lead to reionization ending too rapidly. Lingering discrepancies between the star formation rate functions predicted with and without our extensions can be traced to the uncertain contribution of satellite galaxies.

The Universe at z &amp;gt; 10: predictions for JWST from the universemachine DR1

ABSTRACT The James Webb Space Telescope (JWST) is expected to observe galaxies at z &amp;gt; 10 that are presently inaccessible. Here, we use a self-consistent empirical model, the universemachine, to generate mock galaxy catalogues and light-cones over the redshift range z = 0−15. These data include realistic galaxy properties (stellar masses, star formation rates, and UV luminosities), galaxy–halo relationships, and galaxy–galaxy clustering. Mock observables are also provided for different model parameters spanning observational uncertainties at z &amp;lt; 10. We predict that Cycle 1 JWST surveys will very likely detect galaxies with M* &amp;gt; 107 M⊙ and/or M1500 &amp;lt; −17 out to at least z ∼ 13.5. Number density uncertainties at z &amp;gt; 12 expand dramatically, so efforts to detect z &amp;gt; 12 galaxies will provide the most valuable constraints on galaxy formation models. The faint-end slopes of the stellar mass/luminosity functions at a given mass/luminosity threshold steepen as redshift increases. This is because observable galaxies are hosted by haloes in the exponentially falling regime of the halo mass function at high redshifts. Hence, these faint-end slopes are robustly predicted to become shallower below current observable limits (M* &amp;lt; 107 M⊙ or M1500 &amp;gt; −17). For reionization models, extrapolating luminosity functions with a constant faint-end slope from M1500 = −17 down to M1500 = −12 gives the most reasonable upper limit for the total UV luminosity and cosmic star formation rate up to z ∼ 12. We compare to three other empirical models and one semi-analytic model, showing that the range of predicted observables from our approach encompasses predictions from other techniques. Public catalogues and light-cones for common fields are available online.

Constraints on primordial power spectrum from galaxy luminosity functions

We derive constraints on primordial power spectrum, for the first time, from galaxy UV luminosity functions (LFs) at high redshifts. Since the galaxy LFs reflect an underlying halo mass function which depends on primordial fluctuations, one can constrain primordial power spectrum, particularly on small scales. We perform a Markov Chain Monte Carlo analysis by varying parameters for primordial power spectrum as well as those describing astrophysics. We adopt the UV LFs derived from Hubble Frontier Fields data at $z = 6 -10$, which enable us to probe primordial fluctuations on the scales of $k \sim 10 - 10^3~{\rm Mpc}^{-1}$. Our analysis also clarifies how the assumption on cosmology such as primordial power spectrum affects the determination of astrophysical parameters.

On the Mass Distribution of the Intracluster Light in Galaxy Groups and Clusters

Abstract We take advantage of a semianalytic model with a state-of-art implementation of the formation of the intracluster light (ICL) to study the mass distribution of the ICL in galaxy groups and clusters, at different redshifts. We assume the ICL to follow a Navarro–Frenk–White (NFW) profile with a different concentration, linked to that of the dark matter by the relation c ICL = γ c DM, where the parameter γ is set to reproduce the observed relation between the stellar mass in the brightest cluster galaxy (BCG) and ICL in the innermost 100 kpc and the halo mass (M * 100 − M 500) at z = 0. The model is then tested against several theoretical and observational results, from the present time to z ∼ 1.5. Our analysis shows that the fraction of stellar mass in the BCG and ICL within the innermost 100 kpc is an increasing function of redshift, parameter γ, and a decreasing function of the halo mass. The value of γ required to match the observed M * 100 − M 500 is γ = 3 at z = 0, but there are indications that it might be a function of redshift and halo mass. This result indicates that the distribution of the ICL is more concentrated than the dark matter one, but less concentrated than previously found by other studies. We suggest that a modified version of the NFW is a good description of the distribution of the diffuse light in groups and clusters, which makes the ICL a reliable tracer of the dark matter, in good agreement with recent observational findings.

Dynamic zoom simulations: A fast, adaptive algorithm for simulating light-cones

ABSTRACT The advent of a new generation of large-scale galaxy surveys is pushing cosmological numerical simulations in an uncharted territory. The simultaneous requirements of high resolution and very large volume pose serious technical challenges, due to their computational and data storage demand. In this paper, we present a novel approach dubbed dynamic zoom simulations – or dzs – developed to tackle these issues. Our method is tailored to the production of light-cone outputs from N-body numerical simulations, which allow for a more efficient storage and post-processing compared to standard comoving snapshots, and more directly mimic the format of survey data. In dzs, the resolution of the simulation is dynamically decreased outside the light-cone surface, reducing the computational work load, while simultaneously preserving the accuracy inside the light-cone and the large-scale gravitational field. We show that our approach can achieve virtually identical results to traditional simulations at half of the computational cost for our largest box. We also forecast this speedup to increase up to a factor of 5 for larger and/or higher resolution simulations. We assess the accuracy of the numerical integration by comparing pairs of identical simulations run with and without dzs. Deviations in the light-cone halo mass function, in the sky-projected light-cone, and in the 3D matter light-cone always remain below 0.1 per cent. In summary, our results indicate that the dzs technique may provide a highly valuable tool to address the technical challenges that will characterize the next generation of large-scale cosmological simulations.

A flexible analytic model of cosmic variance in the first billion years

ABSTRACT Cosmic variance is the intrinsic scatter in the number density of galaxies due to fluctuations in the large-scale dark matter density field. In this work, we present a simple analytic model of cosmic variance in the high-redshift Universe (z ∼ 5–15). We assume that galaxies grow according to the evolution of the halo mass function, which we allow to vary with large-scale environment. Our model produces a reasonable match to the observed ultraviolet (UV) luminosity functions in this era by regulating star formation through stellar feedback and assuming that the UV luminosity function is dominated by recent star formation. We find that cosmic variance in the UV luminosity function is dominated by the variance in the underlying dark matter halo population, and not by differences in halo accretion or the specifics of our stellar feedback model. We also find that cosmic variance dominates over Poisson noise for future high-z surveys except for the brightest sources or at very high redshifts (z ≳ 12). We provide a linear approximation of cosmic variance for a variety of redshifts, magnitudes, and survey areas through the public python package galcv. Finally, we introduce a new method for incorporating priors on cosmic variance into estimates of the galaxy luminosity function and demonstrate that it significantly improves constraints on that important observable.

Quantifying the line-of-sight halo contribution to the dark matter convergence power spectrum from strong gravitational lenses

Galaxy-galaxy strong gravitational lenses have become a popular probe of dark matter (DM) by providing a window into structure formation on the smallest scales. In particular, the convergence power spectrum of subhalos within lensing galaxies has been suggested as a promising observable to study DM. However, the distances involved in strong-lensing systems are vast, and we expect the relevant volume to contain line-of-sight (LOS) halos that are not associated with the main lens. We develop a formalism to calculate the effect of LOS halos as an effective convergence power spectrum. The multi-lens plane equation couples the angular deflections of consecutive lens planes, but by assuming that the perturbations due to the LOS halos are small, we show that they can be projected onto the main-lens plane as effective subhalos. We test our formalism by simulating lensing systems using the full multi-plane lens equation and find excellent agreement. We show how the relative contribution of LOS halos and subhalos depends on the source and lens redshift, as well as the assumed halo and subhalo mass functions. For a fiducial system with fraction of DM halo mass in substructure $f_{\rm sub}=0.4\%$ for subhalo masses $[10^5-10^8]\rm{M}_{\odot}$, the interloper contribution to the power spectrum is at least several times greater than that of subhalos for source redshifts $z_s\gtrsim0.5$. Furthermore, it is likely that for the SLACS and BELLS lenses the interloper contribution dominates: $f_{\rm sub}\gtrsim2\%$ ($4\%$) is needed for subhalos to dominate in SLACS (BELLS), which is higher than current upper bounds on $f_{\rm sub}$ for our mass range. Since the halo mass function is better understood from first principles, the dominance of interlopers in galaxy-galaxy lenses with high-quality imaging can be seen as a significant advantage when translating this observable into a constraint on DM.

Enhanced spectrum of primordial perturbations, galaxy formation, and small-scale structure

The standard structure formation scenario is successful on linear scales. Several apparent problems affect it however at galactic scales, such as the small scale problems at low redshift and more recent issues involving early massive galaxy and black hole formation. As these problems arise where complex baryonic physics becomes important, the associated unknowns are often assumed to be behind the problems. But the same scales are also those where the primordial spectrum is relatively unconstrained, and there are several ways in which it can be modified. We focus on that arising from effects possibly associated with the crossing of high energy cutoff scale by fluctuation modes during inflation. Elementary arguments show that adiabatic evolution cannot modify the near scale invariance, we thus discuss a simple model for the contrary extreme of sudden transition. Numerical calculations and simple arguments suggest that its predictions, for parameters considered here, are more generic than may be expected, with significant modifications requiring a rapid transition. We examine the implications of such a scenario, in this simplest form of sudden jump, on the matter power spectrum and halo mass function in light of the limitations imposed by particle production. We show that enhancement and oscillation in the power spectrum on currently nonlinear scales can potentially simultaneously alleviate both the apparent problem of early structure formation and, somewhat counterintuitively, problems at low redshift such as the apparent dearth of dwarf galaxies. We discuss consequences that can observationally constrain the scenario and its parameters, including an inflationary Hubble scale $\lesssim 10^{-8} M_{\rm Pl}$, while touching on the possibility of simultaneous modification of power on the largest scales.