Steen Hannestad, Yvonne Y. Y. Wong
We propose an alternative approach to the construction of fitting functions to the nonlinear matter power spectrum extracted from $N$-body simulations based on the relative matter power spectrum $δ(k,a)$, defined as the fractional deviation in the absolute matter power spectrum produced by a target cosmology away from a reference $Λ$CDM prediction. From the computational perspective, $δ(k,a)$ is fairly insensitive to the specifics of the simulation settings, and numerical convergence at the 1%-level can be readily achieved without the need for huge computing capacity. Furthermore, $δ(k,a)$ exhibits several interesting properties that enable a piece-wise construction of the full fitting function, whereby component fitting functions are sought for single-parameter variations and then multiplied together to form the final product. Then, to obtain 1%-accurate absolute power spectrum predictions for any target cosmology only requires that the community as a whole invests in producing one single ultra-precise reference $Λ$CDM absolute power spectrum, to be combined with the fitting function to produce the desired result. To illustrate the power of this approach, we have constructed the fitting function RelFit using only five relatively inexpensive $w$CDM simulations (box length $L=256 h^{-1}$Mpc, $N=1024^3$ particles, initialised at $z_i=49$). In a 6-parameter space spanning $\{ω_m,A_s,n_s,w,ω_b,h\}$, the output relative power spectra of RelFit are consistent with the predictions of the CosmicEmu emulator to 1% or better for a wide range of cosmologies up to $k\simeq 10$/Mpc. Thus, our approach could provide an inexpensive and democratically accessible route to fulfilling the 1%-level accuracy demands of the upcoming generation of large-scale structure probes, especially in the exploration of "non-standard" or "exotic" cosmologies on nonlinear scales.
Jack J. Bennett, Gilles Buldgen, Marco Drewes, Yvonne Y. Y. Wong
We revisit several aspects of Standard Model physics at finite temperature that drive the theoretical value of the cosmological parameter $N_{\rm eff}$, the effective number of neutrinos in the early universe, away from 3. Our chief focus is finite-temperature corrections to the equation of state of the QED plasma in the vicinity of neutrino decoupling at $T \sim 1$ MeV, where $T$ is the photon temperature. Working in the instantaneous decoupling approximation, we recover at ${\cal O}(e^2)$, where $e$ is the elementary electric charge, the well-established correction of $δN_{\rm eff}^{(2)} \simeq 0.010$ across a range of plausible neutrino decoupling temperatures, in contrast to an erroneous claim in the recent literature which found twice as large an effect. At ${\cal O}(e^3)$ we find a new and significant correction of $δN_{\rm eff}^{(3)} \simeq -0.001$ that has so far not been accounted for in any precision calculation of $N_{\rm eff}$, significant because this correction is potentially larger than the change in $N_{\rm eff}$ induced between including and excluding neutrino oscillations in the transport modelling. In addition to the QED equation of state, we make a first pass at quantifying finite-temperature QED corrections to the weak interaction rates that directly affect the neutrino decoupling process, and find that the ${\cal O}(e^2)$ thermal electron mass correction induces a change of $δN_{\rm eff}^{m_{\rm th}} \lesssim 10^{-4}$. A complete assessment of the various effects considered in this work on the final value of $N_{\rm eff}$ will necessitate an account of neutrino energy transport beyond the instantaneous decoupling approximation. However, relative to $N_{\rm eff} = 3.044$ obtained in the most recent such calculation, we expect the new effects found in this work to lower the number to $N_{\rm eff} = 3.043$.
Joe Zhiyu Chen, Isabel M. Oldengott, Giovanni Pierobon, Yvonne Y. Y. Wong
We consider invisible neutrino decay $ν_H \to ν_l + φ$ in the ultra-relativistic limit and compute the neutrino anisotropy loss rate relevant for the cosmic microwave background (CMB) anisotropies. Improving on our previous work which assumed massless $ν_l$ and $φ$, we reinstate in this work the daughter neutrino mass $m_{νl}$ in a manner consistent with the experimentally determined neutrino mass splittings. We find that a nonzero $m_{νl}$ introduces a new phase space factor in the loss rate $Γ_{\rm T}$ proportional to $(Δm_ν^2/m_{ν_H}^2)^2$ in the limit of a small squared mass gap between the parent and daughter neutrinos, i.e., $Γ_{\rm T} \sim (Δm_ν^2/m_{νH}^2)^2 (m_{νH}/E_ν)^5 (1/τ_0)$, where $τ_0$ is the $ν_H$ rest-frame lifetime. Using a general form of this result, we update the limit on $τ_0$ using the Planck 2018 CMB data. We find that for a parent neutrino of mass $m_{νH} \lesssim 0.1 {\rm eV}$, the new phase space factor weakens the constraint on its lifetime by up to a factor of 50 if $Δm_ν^2$ corresponds to the atmospheric mass gap and up to $10^{5}$ if the solar mass gap, in comparison with naive estimates that assume $m_{νl}=0$. The revised constraints are (i) $τ^0 \gtrsim (6 \to 10) \times 10^5~{\rm s}$ and $τ^0 \gtrsim (400 \to 500)~{\rm s}$ if only one neutrino decays to a daughter neutrino separated by, respectively, the atmospheric and the solar mass gap, and (ii) $τ^0 \gtrsim (2 \to 3) \times 10^7~{\rm s}$ in the case of two decay channels with one near-common atmospheric mass gap. In contrast to previous, naive limits which scale as $m_{νH}^5$, these mass spectrum-consistent $τ_0$ constraints are remarkably independent of the parent mass and open up a swath of parameter space within the projected reach of IceCube and other neutrino telescopes in the next two decades.
Markus R. Mosbech, Celine Boehm, Yvonne Y. Y. Wong
Similarly to warm dark matter which features a cut-off in the matter power spectrum due to free-streaming, many interacting dark matter models predict a suppression of the matter power spectrum on small length scales through collisional damping. Forecasts for 21cm line intensity mapping have shown that an instrument like the SKA will be able to probe a suppression of power in warm dark matter scenarios in a statistically significant way. Here we investigate the implications of these findings on interacting dark matter scenarios, particularly dark matter-neutrino interactions, which we use as an example. Using a suite of cosmological $N$-body simulations, we demonstrate that interacting scenarios show a suppression of the non-linear power spectrum similar to warm dark matter models. This implies that 21cm line intensity mapping will be able to set the strongest limits yet on dark matter-neutrino scattering, improving the constraints by two orders of magnitude over current Lyman-$α$ bounds, and by four orders of magnitude over cosmic microwave background and baryon acoustic oscillations limits. However, to distinguish between warm dark matter and interacting scenarios, our simulations show that percent-level precision measurements of the matter power spectrum at redshifts $z\gtrsim15$ are necessary, as the key features of interacting scenarios are washed out by non-linear evolution at later times.
Benedikt Eggemeier, Ciaran A. J. O'Hare, Giovanni Pierobon, Javier Redondo, Yvonne Y. Y. Wong
In the scenario in which QCD axion dark matter is produced after inflation, the Universe is populated by large inhomogeneities on very small scales. Eventually, these fluctuations will collapse gravitationally to form dense axion miniclusters that trap up to $\sim$75% of the dark matter within asteroid-mass clumps. Axion miniclusters are physically tiny however, so haloscope experiments searching for axions directly on Earth are much more likely to be probing ``minivoids'' -- the space in between miniclusters. This scenario seems like it ought to spell doom for haloscopes, but while these minivoids might be underdense, they are not totally devoid of axions. Using Schrödinger-Poisson and N-body simulations to evolve from realistic initial field configurations, we quantify the extent to which the local ambient dark matter density is suppressed in the post-inflationary scenario. We find that a typical experimental measurement will sample an axion density that is only around 10% of the expected galactic dark matter density. Our results also have implications for experimental campaigns lasting longer than a few years, as well as broadband haloscopes that have sensitivity to transient signatures. We show that for a $\mathcal{O}$(year)-long integration times, the measured dark matter density should be expected to vary by 20--30%.
Jacob Brandbyge, Steen Hannestad, Troels Haugboelle, Yvonne Y. Y. Wong
Apr 23, 2010·astro-ph.CO·PDF We use N-body simulations to find the effect of neutrino masses on halo properties, and investigate how the density profiles of both the neutrino and the dark matter components change as a function of the neutrino mass. We compare our neutrino density profiles with results from the N-one-body method and find good agreement. We also show and explain why the Tremaine-Gunn bound for the neutrinos is not saturated. Finally we study how the halo mass function changes as a function of the neutrino mass and compare our results with the Sheth-Tormen semi-analytic formulae. Our results are important for surveys which aim at probing cosmological parameters using clusters, as well as future experiments aiming at measuring the cosmic neutrino background directly.
Joe Zhiyu Chen, Markus R. Mosbech, Amol Upadhye, Yvonne Y. Y. Wong
Oct 28, 2022·astro-ph.CO·PDF Simulation of the cosmic clustering of massive neutrinos is a daunting task, due both to their large velocity dispersion and to their weak clustering power becoming swamped by Poisson shot noise. We present a new approach, the multi-fluid hybrid-neutrino simulation, which partitions the neutrino population into multiple flows, each of which is characterised by its initial momentum and treated as a separate fluid. These fluid flows respond initially linearly to nonlinear perturbations in the cold matter, but slowest flows are later converted to a particle realisation should their clustering power exceed some threshold. After outlining the multi-fluid description of neutrinos, we study the conversion of the individual flows into particles, in order to quantify transient errors, as well as to determine a set of criteria for particle conversion. Assembling our results into a total neutrino power spectrum, we demonstrate that our multi-fluid hybrid-neutrino simulation is convergent to $<3\%$ if conversion happens at $z=19$ and agrees with more expensive simulations in the literature for neutrino fractions as high as $Ω_νh^2 = 0.005$. Moreover, our hybrid-neutrino approach retains fine-grained information about the neutrinos' momentum distribution. However, the momentum resolution is currently limited by free-streaming transients excited by missing information in the neutrino particle initialisation procedure, which restricts the particle conversion to z $\gtrsim 19$ if percent-level resolution is desired.
Joe Zhiyu Chen, Amol Upadhye, Yvonne Y. Y. Wong
Oct 28, 2022·astro-ph.CO·PDF Velocity dispersion of the massive neutrinos presents a daunting challenge for non-linear cosmological perturbation theory. We consider the neutrino population as a collection of non-linear fluids, each with uniform initial momentum, through an extension of the Time Renormalization Group perturbation theory. Employing recently-developed Fast Fourier Transform techniques, we accelerate our non-linear perturbation theory by more than two orders of magnitude, making it quick enough for practical use. After verifying that the neutrino mode-coupling integrals and power spectra converge, we show that our perturbation theory agrees with N-body neutrino simulations to within 10% for neutrino fractions $Ω_{ν,0} h^2 \leq 0.005$ up to wave numbers of k = 1 h/Mpc, an accuracy consistent with 2.5% errors in the neutrino mass determination. Non-linear growth represents a >10% correction to the neutrino power spectrum even for density fractions as low as $Ω_{ν,0} h^2 = 0.001$, demonstrating the limits of linear theory for accurate neutrino power spectrum predictions. Our code FlowsForTheMasses is avaliable online at github.com/upadhye/FlowsForTheMasses .
Amol Upadhye, Juliana Kwan, Ian G. McCarthy, Jaime Salcido, Kelly R. Moran, Earl Lawrence, Yvonne Y. Y. Wong
Nov 19, 2023·astro-ph.CO·PDF Cosmology is poised to measure the neutrino mass sum $M_ν$ and has identified several smaller-scale observables sensitive to neutrinos, necessitating accurate predictions of neutrino clustering over a wide range of length scales. The FlowsForTheMasses non-linear perturbation theory for the massive neutrino power spectrum, $Δ^2_ν(k)$, agrees with its companion N-body simulation at the $10\%-15\%$ level for $k \leq 1~h/$Mpc. Building upon the Mira-Titan IV emulator for the cold matter, we use FlowsForTheMasses to construct an emulator for $Δ^2_ν(k)$ covering a large range of cosmological parameters and neutrino fractions $Ω_{ν,0} h^2 \leq 0.01$, which corresponds to $M_ν\leq 0.93$~eV. Consistent with FlowsForTheMasses at the $3.5\%$ level, it returns a power spectrum in milliseconds. Ranking the neutrinos by initial momenta, we also emulate the power spectra of momentum deciles, providing information about their perturbed distribution function. Comparing a $M_ν=0.15$~eV model to a wide range of N-body simulation methods, we find agreement to $3\%$ for $k \leq 3 k_\mathrm{FS} = 0.17~h/$Mpc and to $19\%$ for $k \leq 0.4~h/$Mpc. We find that the enhancement factor, the ratio of $Δ^2_ν(k)$ to its linear-response equivalent, is most strongly correlated with $Ω_{ν,0} h^2$, and also with the clustering amplitude $σ_8$. Furthermore, non-linearities enhance the free-streaming-limit scaling $\partial \log(Δ^2_ν/ Δ^2_{\rm m}) / \partial \log(M_ν)$ beyond its linear value of 4, increasing the $M_ν$-sensitivity of the small-scale neutrino density.
Jan Hamann, Steen Hannestad, Alessandro Melchiorri, Yvonne Y. Y. Wong
Apr 11, 2008·astro-ph·PDF We explore and compare the performances of two nonlinear correction and scale-dependent biasing models for the extraction of cosmological information from galaxy power spectrum data, especially in the context of beyond-LCDM cosmologies. The first model is the well known Q model, first applied in the analysis of 2dFGRS data. The second, the P model, is inspired by the halo model, in which nonlinear evolution and scale-dependent biasing are encapsulated in a single non-Poisson shot noise term. We find that while both models perform equally well in providing adequate correction for a range of galaxy clustering data in standard LCDM cosmology and in extensions with massive neutrinos, the Q model can give unphysical results in cosmologies containing a subdominant free-streaming dark matter whose temperature depends on the particle mass, e.g., relic thermal axions, unless a suitable prior is imposed on the correction parameter. This last case also exposes the danger of analytic marginalisation, a technique sometimes used in the marginalisation of nuisance parameters. In contrast, the P model suffers no undesirable effects, and is the recommended nonlinear correction model also because of its physical transparency.
Jan Hamann, Steen Hannestad, Georg G. Raffelt, Irene Tamborra, Yvonne Y. Y. Wong
Precision cosmology and big-bang nucleosynthesis mildly favor extra radiation in the universe beyond photons and ordinary neutrinos, lending support to the existence of low-mass sterile neutrinos. We use the WMAP 7-year data, small-scale CMB observations from ACBAR, BICEP and QuAD, the SDSS 7th data release, and measurement of the Hubble parameter from HST observations to derive credible regions for the assumed common mass scale m_s and effective number N_s of thermally excited sterile neutrino states. Our results are compatible with the existence of one or perhaps two sterile neutrinos, as suggested by LSND and MiniBooNE, if m_s is in the sub-eV range.
Maria Archidiacono, Tobias Basse, Jan Hamann, Steen Hannestad, Georg Raffelt, Yvonne Y. Y. Wong
Feb 11, 2015·astro-ph.CO·PDF We study the potential of a future, large-volume photometric survey to constrain the axion mass $m_a$ in the hot dark matter limit. Future surveys such as Euclid will have significantly more constraining power than current observations for hot dark matter. Nonetheless, the lowest accessible axion masses are limited by the fact that axions lighter than $\sim 0.15$ eV decouple before the QCD epoch, assumed here to occur at a temperature $T_{\rm QCD} \sim 170$ MeV; this leaves an axion population of such low density that its late-time cosmological impact is negligible. For larger axion masses, $m_a \gtrsim 0.15$ eV, where axions remain in equilibrium until after the QCD phase transition, we find that a Euclid-like survey combined with Planck CMB data can detect $m_a$ at very high significance. Our conclusions are robust against assumptions about prior knowledge of the neutrino mass. Given that the proposed IAXO solar axion search is sensitive to $m_a\lesssim 0.2$ eV, the axion mass range probed by cosmology is nicely complementary.
Florian Führer, Yvonne Y. Y. Wong
We develop a higher-order perturbation theory for large-scale structure formation involving a free-streaming hot or warm dark matter species. We focus on the case of mixed cold dark matter and massive neutrinos, although our approach is applicable also to a single warm dark matter species. In order to capture the suppressed growth of neutrino density perturbations on small scales, we account for the full momentum dependence of the phase space distribution using the Vlaslov equation, and derive from it a formal closed-form nonlinear equation for the neutrino density. Using a systematic perturbative expansion of this equation we compute high-order corrections to the neutrino density contrast without the explicit need to track the perturbed neutrino momentum distribution. We calculate the leading-order total matter bispectrum for several neutrino masses. Using our result as a benchmark, we test the accuracy of the fluid approximation and a linear approximation used in perturbative and N-body analyses, as well as a new hybrid approach that combines the exact linear evolution with the nonlinear structure of the fluid equations. Aiming at $\lesssim1%$ accuracy, we find that the total matter bispectrum with a low neutrino mass m=0.046 eV can be reproduced by all but the fluid approximation, while for larger neutrino masses m=0.46-0.93 eV only the hybrid approach has the desired accuracy on a large range of scales. This result serves as a cautionary note that approximate nonlinear models of neutrino clustering that reproduce the gross features of some observables may not suffice for precision calculations, nor are they guaranteed to apply to other observables. All of the approximation schemes fail to reproduce the bispectrum of the neutrino density perturbations at better than 20% accuracy across all scales, indicating that an exact treatment of nonlinear neutrino perturbations is necessary.
Steen Hannestad, Huitzu Tu, Yvonne Y. Y. Wong
Surveys of weak gravitational lensing of distant galaxies will be one of the key cosmological probes in the future. We study the ability of such surveys to constrain neutrino masses and the equation of state parameter of the dark energy, focussing on how tomographic information can improve the sensitivity to these parameters. We also provide a detailed discussion of systematic effects pertinent to weak lensing surveys, and the possible degradation of sensitivity to cosmological parameters due to these effects. For future probes such as the Large Synoptic Survey Telescope survey, we find that, when combined with cosmic microwave background data from the Planck satellite, a sensitivity to neutrino masses of sigma(sum m_nu) < 0.05 eV can be reached. This results is robust against variations in the running of the scalar spectral index, the time-dependence of dark energy equation of state, and/or the number of relativistic degrees of freedom.
Meera Deshpande, Jan Hamann, Dipan Sengupta, Martin White, Anthony G. Williams, Yvonne Y. Y. Wong
SuperWIMPs are extremely weakly interacting massive particles that inherit their relic abundance from late decays of frozen-out parent particles. Within supersymmetric models, gravitinos and axinos represent two of the most well-motivated superWIMPs. In this paper we revisit constraints on these scenarios from a variety of cosmological observations that probe their production mechanisms as well as the superWIMP kinematic properties in the early Universe. We consider in particular observables of Big Bang Nucleosynthesis and the Cosmic Microwave Background (spectral distortion and anisotropies), which limit the fractional energy injection from the late decays, as well as warm and mixed dark matter constraints derived from the Lyman-$α$ forest and other small-scale structure observables. We discuss complementary constraints from collider experiments, and argue that cosmological considerations rule out a significant part of the gravitino and the axino superWIMP parameter space.
Chiara Arina, Jan Hamann, Roberto Trotta, Yvonne Y Y Wong
We investigate the question of whether the recent modulation signal claimed by CoGeNT is best explained by the dark matter (DM) hypothesis from a Bayesian model comparison perspective. We consider five phenomenological explanations for the data: no modulation signal, modulation due to DM, modulation due to DM compatible with the total CoGeNT rate, and a signal coming from other physics with a free phase but annual period, or with a free phase and a free period. In each scenario, we assign to the free parameters physically motivated priors. We find that while the DM models are weakly preferred to the no modulation model, but when compared to models where the modulation is due to other physics, the DM hypothesis is favoured with odds ranging from 185:1 to 560:1. This result is robust even when astrophysical uncertainties are taken into account and the impact of priors assessed. Interestingly, the odds for the DM model in which the modulation signal is compatible with the total rate against a DM model in which this prior is not implemented is only 5:8, in spite of the former's prediction of a modulation amplitude in the energy range 0.9 to 3.0 keVee that is significantly smaller than the value observed by CoGeNT. Classical hypothesis testing also rules out the null hypothesis of no modulation at the 1.6 sigma to 2.3 sigma level, depending on the details of the alternative. Lastly, we investigate whether anisotropic velocity distributions can help to mitigate the tension between the CoGeNT total and modulated rates, and find encouraging results.
Jan Hamann, Steen Hannestad, Yvonne Y. Y. Wong
We perform a detailed forecast on how well a Euclid-like photometric galaxy and cosmic shear survey will be able to constrain the absolute neutrino mass scale. Adopting conservative assumptions about the survey specifications and assuming complete ignorance of the galaxy bias, we estimate that the minimum mass sum of sum m_nu ~ 0.06 eV in the normal hierarchy can be detected at 1.5 sigma to 2.5 sigma significance, depending on the model complexity, using a combination of galaxy and cosmic shear power spectrum measurements in conjunction with CMB temperature and polarisation observations from Planck. With better knowledge of the galaxy bias, the significance of the detection could potentially reach 5.4 sigma. Interestingly, neither Planck+shear nor Planck+galaxy alone can achieve this level of sensitivity; it is the combined effect of galaxy and cosmic shear power spectrum measurements that breaks the persistent degeneracies between the neutrino mass, the physical matter density, and the Hubble parameter. Notwithstanding this remarkable sensitivity to sum m_nu, Euclid-like shear and galaxy data will not be sensitive to the exact mass spectrum of the neutrino sector; no significant bias (< 1 sigma) in the parameter estimation is induced by fitting inaccurate models of the neutrino mass splittings to the mock data, nor does the goodness-of-fit of these models suffer any significant degradation relative to the true one (Delta chi_eff ^2< 1).
Tobias Basse, Ole Eggers Bjaelde, Steen Hannestad, Yvonne Y. Y. Wong
Future cluster surveys will observe galaxy clusters numbering in the hundred thousands. We consider this work how these surveys can be used to constrain dark energy parameters: in particular, the equation of state parameter w and the non-adiabatic sound speed c_s^2. We demonstrate that, in combination with Cosmic Microwave Background (CMB) observations from Planck, cluster surveys such as that in the ESA Euclid project will be able to determine a time-independent w with subpercent precision. Likewise, if the dark energy sound horizon falls within the length scales probed by the cluster survey, then c_s^2 can be pinned down to within an order of magnitude. In the course of this work, we also investigate the process of dark energy virialisation in the presence of an arbitrary sound speed. We find that dark energy clustering and virialisation can lead to dark energy contributing to the total cluster mass at approximately the 0.1% level at maximum.
Tobias Basse, Ole Eggers Bjaelde, Jan Hamann, Steen Hannestad, Yvonne Y. Y. Wong
We perform a detailed forecast on how well a {\sc Euclid}-like survey will be able to constrain dark energy and neutrino parameters from a combination of its cosmic shear power spectrum, galaxy power spectrum, and cluster mass function measurements. We find that the combination of these three probes vastly improves the survey's potential to measure the time evolution of dark energy. In terms of a dark energy figure-of-merit defined as $(σ(w_{\mathrm p}) σ(w_a))^{-1}$, we find a value of 690 for {\sc Euclid}-like data combined with {\sc Planck}-like measurements of the cosmic microwave background (CMB) anisotropies in a 10-dimensional cosmological parameter space, assuming a $Λ$CDM fiducial cosmology. For the more commonly used 7-parameter model, we find a figure-of-merit of 1900 for the same data combination. We consider also the survey's potential to measure dark energy perturbations in models wherein the dark energy is parameterised as a fluid with a nonstandard non-adiabatic sound speed, and find that in an \emph{optimistic} scenario in which $w_0$ deviates by as much as is currently observationally allowed from $-1$, models with $\hat{c}_\mathrm{s}^2 = 10^{-6}$ and $\hat{c}_\mathrm{s}^2 = 1$ can be distinguished at more than $2σ$ significance. We emphasise that constraints on the dark energy sound speed from cluster measurements are strongly dependent on the modelling of the cluster mass function; significantly weaker sensitivities ensue if we modify our model to include fewer features of nonlinear dark energy clustering. Finally, we find that the sum of neutrino masses can be measured with a $1 σ$ precision of 0.015~eV, (abridged)
Yvonne Y. Y. Wong
I give an overview of the effects of neutrino masses in cosmology, focussing on the role they play in the evolution of cosmological perturbations. I discuss how recent observations of the cosmic microwave background anisotropies and the large-scale matter distribution can probe neutrino masses with greater precision than current laboratory experiments. I describe several new techniques that will be used to probe cosmology in the future, as well as recent advances in the computation of the nonlinear matter power spectrum and related observables.