arXiv subjects

Alex Laguë

Publications and source records attributed to Alex Laguë.

At least 19 recordsLinked to original sources

arXiv2026

Optimal and exact wide-angle power spectrum estimation

What is the optimal power spectrum estimator on ultra-large scales where the plane-parallel approximation breaks down? Conventional estimators, such as the Yamamoto estimator, are only optimal in the plane-parallel limit, while their associated window functions are typically approximated by truncating a slowly converging infinite series. We address two outstanding challenges in the analysis of wide-angle power spectra. First, we derive the optimal estimator for a broad class of clustering signals and show that it is equivalent to a previously proposed two-$\ell$ generalization of the Yamamoto estimator. Second, we show how to write the exact two-$\ell$ window function as a finite number of terms that can be efficiently evaluated using FFTs. Our results apply to a wide range of observables, including redshift-space distortions (RSDs) and large-scale radial-velocity reconstruction from the kinetic Sunyaev-Zel'dovich effect. Focusing on linear-theory RSDs, we validate the finite window-function representation numerically and show that the two-$\ell$ estimator can yield order-unity improvements in the signal-to-noise ratio of ultra-large-scale power spectrum measurements.

astro-ph.CO↗

arXiv2026

The Atacama Cosmology Telescope: Probing new signatures of ultralight axions with gravitational lensing

Ultralight axions (ULAs) are well-motivated dark matter particle candidates that arise in many extensions of the Standard Model of particle physics. ULAs with mass $m_\mathrm{a} \lesssim 10^{-27}$ eV have been strongly constrained by cosmic microwave background (CMB) observations in temperature and polarization. We fit recent measurements of gravitational lensing of the CMB from \textit{Planck}, the Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT-3G) using a state-of-the-art simulation-calibrated nonlinear clustering model for ULAs. We derive the strongest constraints on ULAs in the mass range $10^{-26}\;\mathrm{eV}\leq m_\mathrm{a}\leq 10^{-24.5}\;\mathrm{eV}$. ULAs of this mass have been shown to alleviate tensions between inferences of the matter clustering if they compose a few percent of the total dark matter content of the Universe. We conclude that ULAs with a mass of $10^{-26}$ eV make up less than 1.5\% of the dark matter and $10^{-25}$ eV axions make less than 9\% (both at 95\% confidence level). We identify a slight preference for non-zero axion density at $10^{-24.5}$ eV at $2.1σ$. We find that the preference for ULAs is largely driven by a few data points and that further investigation of non-linear ULA physics is needed to confirm or rule out this signal.

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arXiv2026

Cosmic voids as a probe of the nature of dark matter: simulations and galaxy survey forecasts

Voids are parts of the cosmic web least affected by non-linearities and baryonic feedback. We thus calculate the sensitivity of voids to the nature of dark matter (DM), using ultra-light axions as a concrete model and the ongoing Dark Energy Spectroscopic Instrument (DESI) and \textit{Euclid} galaxy surveys as observational settings. We simulate axion effects on voids using mass-peak patch simulations and find that: (i) axions suppress the formation of lower-mass halos leading to the merging of smaller (radius $< 25\,\mathrm{Mpc}/h$) voids into fewer larger (radius $> 25\,\mathrm{Mpc}/h$) voids; and (ii) voids in the presence of axions are emptier of halos, thereby suppressing the void-halo correlation function. These effects strengthen as axion particle mass $m_\mathrm{a}$ decreases. We forecast improvements in axion constraints from the void size function (VSF; the void number density as function of their radius). A \textit{Euclid}-like survey (effective volume of $73\,\mathrm{Gpc}^3$ with a prior on the other $Λ$CDM cosmological parameters from the Simons Observatory cosmic microwave background experiment) can limit the axion energy density (for $m_\mathrm{a} = 10^{-25}\,\mathrm{eV}$) to $< 4.6\%$ of the DM (at $95\%$ credibility), about two times stronger than current limits. Conversely, we show that a Universe with a dark sector consisting of axions at the $10\%$ level, as motivated by the string axiverse, can be recovered with $\sim 2 σ$ preference. A DESI-like survey achieves comparable results. Axion and $Λ$CDM parameters have different degeneracies given VSF and galaxy power spectrum data, indicating future combined analyses will be most powerful in disentangling the DM nature. We anticipate our results will extend to other (e.g., warm or interacting) DM models.

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arXiv2025

Inferring the Impacts of Baryonic Feedback from Kinetic Sunyaev-Zeldovich Cross-Correlations

The complex processes of baryonic feedback associated with galaxy evolution are still poorly understood, and their impact on the clustering of matter on small scales remains difficult to quantify. While many fitting functions and emulators exist to model the matter power spectrum, their input parameters are not directly observable. However, recent studies using hydrodynamical simulations have identified a promising correlation between the gas content of halos and changes to the matter power spectrum from feedback. Building on these findings, we create the first fully data-driven power spectrum emulator. We utilize the kinematic Sunyaev-Zeldovich (kSZ) effect, a secondary anisotropy in the cosmic microwave background, as a tracer of free electrons in and around halos. We train a neural network to learn the mapping between the suppression of the matter power spectrum and the shape of the kSZ power spectrum extracted with a radial velocity template. We train and validate our algorithm using the FLAMINGO suite of hydrodynamical simulations, which encompasses a wide range of feedback models. Our emulator can reconstruct the matter power spectrum at the sub-percent level for scales $k\leq 5\;h/$Mpc and $0.2\leq z \leq 1.25$ directly from the data. Our model is robust and retains percent-level accuracy even for feedback models and cosmological parameter values not seen during training (except in a few extreme cases drastically different from the fiducial model). Due to its robustness, our algorithm offers a new way to identify the sources of suppression in the matter power spectrum, breaking the degeneracies between baryonic feedback and new physics. Finally, we present a forecast for reconstruction of the matter power spectrum combining maps of the microwave background anisotropies from a Simons Observatory-like experiment and galaxy catalogs from the Dark Energy Spectroscopic Instrument.

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arXiv2025

The Atacama Cosmology Telescope: DR6 Maps

We present Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) maps of the Cosmic Microwave Background temperature and polarization anisotropy at arcminute resolution over three frequency bands centered on 98, 150 and 220 GHz. The maps are based on data collected with the AdvancedACT camera over the period 2017--2022 and cover 19,000 square degrees with a median combined depth of 10 uK arcmin. We describe the instrument, mapmaking and map properties and illustrate them with a number of figures and tables. The ACT DR6 maps and derived products are available on LAMBDA at https://lambda.gsfc.nasa.gov/product/act/actadv_prod_table.html. We also provide an interactive web atlas at https://phy-act1.princeton.edu/public/snaess/actpol/dr6/atlas and HiPS data sets in Aladin (e.g. https://alasky.cds.unistra.fr/ACT/DR4DR6/color_CMB).

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arXiv2025

Improved Halo Model Calibrations for Mixed Dark Matter Models of Ultralight Axions

We study the implications of relaxing the requirement for ultralight axions to account for all dark matter in the Universe by examining mixed dark matter (MDM) cosmologies with axion fractions $f \leq 0.3$ within the fuzzy dark matter (FDM) window $10^{-25}$ eV $\lesssim m \lesssim 10^{-23}$ eV. Our simulations, using a new MDM gravity solver implemented in AxiREPO, capture wave dynamics across various scales with high accuracy down to redshifts $z\approx 1$. We identify halos with Rockstar using the CDM component and find good agreement of inferred halo mass functions (HMFs) and concentration-mass relations with theoretical models across redshifts $z=1-10$. This justifies our halo finder approach a posteriori as well as the assumptions underlying the MDM halo model AxionHMcode. Using the inferred axion halo mass-cold halo mass relation $M_{\text{a}}(M_{\text{c}})$ and calibrating a generalised smoothing parameter $α$ to our MDM simulations, we present a new version of AxionHMcode. The code exhibits excellent agreement with simulations on scales $k< 20 \ h$ cMpc$^{-1}$ at redshifts $z=1-3.5$ for $f\leq 0.1$ around the fiducial axion mass $m = 10^{-24.5}$ eV $ = 3.16\times 10^{-25}$ eV, with maximum deviations remaining below 10%. For axion fractions $f\leq 0.3$, the model maintains accuracy with deviations under 20% at redshifts $z\approx 1$ and scales $k< 10 \ h$ cMpc$^{-1}$, though deviations can reach up to 30% for higher redshifts when $f=0.3$. Reducing the run-time for a single evaluation of AxionHMcode to below $1$ minute, these results highlight the potential of AxionHMcode to provide a robust framework for parameter sampling across MDM cosmologies in Bayesian constraint and forecast analyses.

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arXiv2025

Reconstructing the shape of the non-linear matter power spectrum using CMB lensing and cosmic shear

We reconstruct the non-linear matter power spectrum $P(k)$ using a joint analysis of gravitational lensing of the cosmic microwave background (CMB) and lensing of galaxies. This reconstruction is motivated by the $S_8$ tension between early-universe CMB predictions and late-time observables. We use CMB lensing data from the Atacama Cosmology Telescope DR6 and cosmic shear data from the Dark Energy Survey (DES) Y3 release to perform a gravity-only (i.e. no baryonic feedback) fit to $P(k)$ in bins of wave-number, within $\rm{ΛCDM}$. We find that with DES cosmic shear data alone, $P(k)$ departs from the early-universe CMB prediction on all scales. The joint fit with CMB lensing is consistent on large scales $k<0.2 \;{\rm Mpc}^{-1}$ but shows a $\sim 2 σ$ deviation from scale-independence when extending to $k = 10 \;h/\mathrm{Mpc}$. We compare our agnostic $P(k)$ reconstruction to baryonic feedback models and non-standard dark matter models: reasonable variations of both scenarios can recover the shape and amplitude of the suppression. We discuss the advances needed to disentangle these physical effects with a full mapping of $P(k,z)$.

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arXiv2024

Constraints on local primordial non-Gaussianity with 3d Velocity Reconstruction from the Kinetic Sunyaev-Zeldovich Effect

The cosmic velocity field is an unbiased probe of the total matter distribution but is challenging to measure directly at intermediate and high redshifts. The large-scale velocity field imprints a signal in the cosmic microwave background (CMB) through the kinetic Sunyaev-Zeldovich (kSZ) effect. We perform the first 3d reconstruction of the large-scale velocity field from the kSZ effect by applying a quadratic estimator to CMB temperature maps and the 3d positions of galaxies. We do so by combining CMB data from the fifth data release of the Atacama Cosmology Telescope (in combination with Planck) and a spectroscopic galaxy sample from the Sloan Digital Sky Survey. We then measure the galaxy-velocity cross-power spectrum and detect the presence of the kSZ signal at a signal-to-noise ratio of 7.2$σ$. Using this galaxy-velocity cross-correlation alone, we constrain the amplitude of local primordial non-Gaussianity finding $f_{\rm NL}=-90^{+210}_{-350}$. This pathfinder measurement sets the stage for joint galaxy-CMB kSZ constraints to significantly enhance the $f_{\rm NL}$ information obtained from galaxy surveys through sample variance cancellation.

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arXiv2024

The Atacama Cosmology Telescope: Large-scale velocity reconstruction with the kinematic Sunyaev--Zel'dovich effect and DESI LRGs

The kinematic Sunyaev--Zel'dovich (kSZ) effect induces a non-zero density-density-temperature bispectrum, which we can use to reconstruct the large-scale velocity field from a combination of cosmic microwave background (CMB) and galaxy density measurements, in a procedure known as ``kSZ velocity reconstruction''. This method has been forecast to constrain large-scale modes with future galaxy and CMB surveys, improving their measurement beyond what is possible with the galaxy surveys alone. Such measurements will enable tighter constraints on large-scale signals such as primordial non-Gaussianity, deviations from homogeneity, and modified gravity. In this work, we demonstrate a statistically significant measurement of kSZ velocity reconstruction for the first time, by applying quadratic estimators to the combination of the ACT DR6 CMB+kSZ map and the DESI LRG galaxies (with photometric redshifts) in order to reconstruct the velocity field. We do so using a formalism appropriate for the 2-dimensional projected galaxy fields that we use, which naturally incorporates the curved-sky effects important on the largest scales. We find evidence for the signal by cross-correlating with an external estimate of the velocity field from the spectroscopic BOSS survey and rejecting the null (no-kSZ) hypothesis at $3.8σ$. Our work presents a first step towards the use of this observable for cosmological analyses.

astro-ph.CO↗

arXiv2024

Constraints on Dark Matter-Dark Energy Scattering from ACT DR6 CMB Lensing

The predicted present-day amplitude of matter fluctuations based on cosmic microwave background (CMB) anisotropy data has sometimes been found discrepant with more direct measurements of late-time structure. This has motivated many extensions to the standard cosmological model, including kinetic interactions between dark matter and dark energy that introduce a drag force slowing the growth of structure at late times. Exploring this scenario, we develop a model for quasi-linear scales in the matter power spectrum by calculating the critical overdensity in the presence of this interaction and a varying dark energy equation of state. We explicitly avoid modeling or interpretation of data on non-linear scales in this model (such as use of $Λ$CDM-calibrated priors), which would require numerical simulations. We find that the presence of the drag force hinders halo formation, thus increasing the deviation from $Λ$CDM in the mildly non-linear regime. We use CMB lensing observations from the sixth data release of the Atacama Cosmology Telescope up to $L=1250$ (in combination with Planck, Sloan Digital Sky Survey, and 6dFGS data) to derive the strongest constraints to date on the amplitude of the drag term, finding the dimensionless interaction strength $Γ_\mathrm{DMDE}/(H_0ρ_\mathrm{c})<0.831\; (2.81)$ at the 68\% (95\%) confidence level. The inclusion of non-linear corrections improves our constraints by about 35\% compared to linear theory. Our results do not exclude the best-fit values of $Γ_\mathrm{DMDE}$ found in previous studies using information from galaxy weak lensing, though we find no statistical preference for the dark matter-dark energy kinetic interactions over $Λ$CDM. We implement our model in a publicly available fork of the Boltzmann code CLASS at https://github.com/fmccarthy/Class_DMDE.

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arXiv2023

Cosmological simulations of mixed ultralight dark matter

The era of precision cosmology allows us to test the composition of the dark matter. Mixed ultralight or fuzzy dark matter (FDM) is a cosmological model with dark matter composed of a combination of particles of mass $m\leq 10^{-20}\;\mathrm{eV}$, with an astrophysical de Broglie wavelength, and particles with a negligible wavelength sharing the properties of cold dark matter (CDM). In this work, we simulate cosmological volumes with a dark matter wave function for the ultralight component coupled gravitationally to CDM particles. We investigate the impact of a mixture of CDM and FDM in various proportions $(0\%,\;1\%,\;10\%,\;50\%,\;100\%)$ and for ultralight particle masses ranging over five orders of magnitude $(2.5\times 10^{-25}\;\mathrm{eV}-2.5\times 10^{-21}\;\mathrm{eV})$. To track the evolution of density perturbations in the non-linear regime, we adapt the simulation code AxioNyx to solve the CDM dynamics coupled to a FDM wave function obeying the Schrödinger-Poisson equations. We obtain the non-linear power spectrum and study the impact of the wave effects on the growth of structure on different scales. We confirm that the steady-state solution of the Schrödinger-Poisson system holds at the center of halos in the presence of a CDM component when it composes $50\%$ or less of the dark matter but find no stable density core when the FDM accounts for $10\%$ or less of the dark matter. We implement a modified friends-of-friends halo finder and find good agreement between the observed halo abundance and the predictions from the adapted halo model axionHMCode.

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arXiv2023

Ultra-light axions and the $S_8$ tension: joint constraints from the cosmic microwave background and galaxy clustering

We search for ultra-light axions as dark matter (DM) and dark energy particle candidates, for axion masses $10^{-32}\,\mathrm{eV} \leq m_\mathrm{a} \leq 10^{-24}\,\mathrm{eV}$, by a joint analysis of cosmic microwave background (CMB) and galaxy clustering data -- and consider if axions can resolve the tension in inferred values of the matter clustering parameter $S_8$. We give legacy constraints from Planck 2018 CMB data, improving 2015 limits on the axion density $Ω_\mathrm{a} h^2$ by up to a factor of three; CMB data from the Atacama Cosmology Telescope and the South Pole Telescope marginally weaken Planck bounds at $m_\mathrm{a} = 10^{-25}\,\mathrm{eV}$, owing to lower (and theoretically-consistent) gravitational lensing signals. We jointly infer, from Planck CMB and full-shape galaxy power spectrum and bispectrum data from the Baryon Oscillation Spectroscopic Survey (BOSS), that axions are, today, $< 10\%$ of the DM for $m_\mathrm{a} \leq 10^{-26}\,\mathrm{eV}$ and $< 1\%$ for $10^{-30}\,\mathrm{eV} \leq m_\mathrm{a} \leq 10^{-28}\,\mathrm{eV}$. BOSS data strengthen limits, in particular at higher $m_\mathrm{a}$ by probing high-wavenumber modes ($k < 0.4 h\,\mathrm{Mpc}^{-1}$). BOSS alone finds a preference for axions at $2.7 σ$, for $m_\mathrm{a} = 10^{-26}\,\mathrm{eV}$, but Planck disfavours this result. Nonetheless, axions in a window $10^{-28}\,\mathrm{eV} \leq m_\mathrm{a} \leq 10^{-25}\,\mathrm{eV}$ can improve consistency between CMB and galaxy clustering data, e.g., reducing the $S_8$ discrepancy from $2.7 σ$ to $1.6 σ$, since these axions suppress structure growth at the $8 h^{-1}\,\mathrm{Mpc}$ scales to which $S_8$ is sensitive. We expect improved constraints with upcoming high-resolution CMB and galaxy lensing and future galaxy clustering data, where we will further assess if axions can restore cosmic concordance.

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arXiv2023

Improved Mixed Dark Matter Halo Model for Ultralight Axions

We present a complete halo model for mixed dark matter composed of cold dark matter (CDM) and ultralight axion-like particles (ULAs). Our model treats ULAs as a biased tracer of CDM, in analogy to treatments of massive neutrinos and neutral hydrogen. The model accounts for clustering of ULAs around CDM host halos, and fully models the cross correlations of both components. The model inputs include the ULA Jeans scale, and soliton density profile. Our model can be used to predict the matter power spectrum, $P(k)$, on non-linear scales for sub-populations of ULAs across the mass range $10^{-33}\text{ eV}\leq m\leq 10^{-21}\text{ eV}$, and can be calibrated against future mixed DM simulations to improve its accuracy. The mixed DM halo model also allows us to assess the importance of various approximations.

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arXiv2022

Fuzzy Dark Matter and the Dark Energy Survey Year 1 Data

Gravitational weak lensing by dark matter halos leads to a measurable imprint in the shear correlation function of galaxies. Fuzzy dark matter (FDM), composed of ultralight axion-like particles of mass $m\sim 10^{-22}\text{ eV}$, suppresses the matter power spectrum and shear correlation with respect to standard cold dark matter. We model the effect of FDM on cosmic shear using the optimised halo model \textsc{HMCode}, accounting for additional suppression of the mass function and halo concentration in FDM as observed in $N$-body simulations. We combine Dark Energy Survey year 1 (DES-Y1) data with the \emph{Planck} cosmic microwave background anisotropies to search for shear correlation suppression caused by FDM. We find no evidence of suppression compared to the preferred cold DM model, and thus set a new lower limit to the FDM particle mass. Using a log-flat prior and marginalising over uncertainties related to the non-linear model of FDM, we find a new, independent 95\% C.L. lower limit $\log_{10}m>-23$ combining \emph{Planck} and DES-Y1 shear, an improvement of almost two orders of magnitude on the mass bound relative to CMB-only constraints. Our analysis is largely independent of baryonic modelling, and of previous limits to FDM covering this mass range. Our analysis highlights the most important aspects of the FDM non-linear model for future investigation. The limit to FDM from weak lensing could be improved by up to three orders of magnitude with $\mathcal{O}(0.1)$ arcmin cosmic shear angular resolution, if FDM and baryonic feedback can be simultaneously modelled to high precision in the halo model.

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arXiv2021

Constraining Ultralight Axions with Galaxy Surveys

Ultralight axions and other bosons are dark matter candidates present in many high energy physics theories beyond the Standard Model. In particular, the string axiverse postulates the existence of up to $\mathcal{O}(100)$ light scalar bosons constituting the dark sector. Considering a mixture of axions and cold dark matter, we obtain upper bounds for the axion relic density $Ω_a h^2 < 0.004$ for axions of mass $10^{-31}\;\mathrm{eV}\leq m_a \leq 10^{-26}\;\mathrm{eV}$ at 95% confidence. We also improve existing constraints by a factor of over 4.5 and 2.1 for axion masses of $10^{-25}$ eV and $10^{-32}$ eV, respectively. We use the Fourier-space galaxy clustering statistics from the Baryon Oscillation Spectroscopic Survey (BOSS) and demonstrate how galaxy surveys break important degeneracies in the axion parameter space compared to the cosmic microwave background (CMB). We test the validity of the effective field theory of large-scale structure approach to mixed ultralight axion dark matter by making our own mock galaxy catalogs and find an anisotropic ultralight axion signature in the galaxy quadrupole. We also observe an enhancement of the linear galaxy bias from 1.8 to 2.4 when allowing for 5% of the dark matter to be composed of a $10^{-28}$ eV axion in our simulations. Finally, we develop an augmented interpolation scheme allowing a fast computation of the axion contribution to the linear matter power spectrum leading to a 70% reduction of the computational cost for the full Monte Carlo Markov chains analysis.

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arXiv2020

Intensity Mapping as a Probe of Axion Dark Matter

Intensity mapping (IM) of spectral lines has the potential to revolutionize cosmology by increasing the total number of observed modes by several orders of magnitude compared to the cosmic microwave background (CMB) anisotropies. In this paper, we consider IM of neutral hydrogen (HI) in the redshift range $0 \lesssim z \lesssim 3$ employing a halo model approach where HI is assumed to follow the distribution of dark matter (DM) halos. If a portion of the DM is composed of ultralight axions then the abundance of halos is changed compared to cold dark matter below the axion Jeans mass. With fixed total HI density, $Ω_{\rm HI}$, assumed to reside entirely in halos, this effect introduces a scale-independent increase in the HI power spectrum on scales above the axion Jeans scale, which our model predicts consistent with N-body simulations. Lighter axions introduce a scale-dependent feature even on linear scales due to its suppression of the matter power spectrum near the Jeans scale. We use the Fisher matrix formalism to forecast the ability of future HI surveys to constrain the axion fraction of DM and marginalize over astrophysical and model uncertainties. We find that a HIRAX-like survey is a very reliable IM survey configuration, being affected minimally by uncertainties due to non-linear scales, while the SKA1MID configuration is the most constraining as it is sensitive to non-linear scales. Including non-linear scales and combining a SKA1MID-like IM survey with the Simons Observatory CMB, the benchmark "fuzzy DM" model with $m_a = 10^{-22}\text{ eV}$ can be constrained at the 10% level. For lighter ULAs this limit improves below 1%, and allows the possibility to test the connection between axion models and the grand unification scale across a wide range of masses.

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arXiv2020

Evolving Ultralight Scalars into Non-Linearity with Lagrangian Perturbation Theory

Many models of high energy physics suggest that the cosmological dark sector consists of not just one, but a spectrum of ultralight scalar particles with logarithmically distributed masses. To study the potential signatures of low concentrations of ultralight axion (also known as fuzzy) dark matter, we modify Lagrangian perturbation theory (LPT) by distinguishing between trajectories of different dark matter species. We further adapt LPT to include the effects of a quantum pressure, which is necessary to generate correct initial conditions for ultralight axion simulations. Based on LPT, our modified scheme is extremely efficient on large scales and it can be extended to an arbitrary number of particle species at very little computational cost. This allows for computation of self-consistent initial conditions in mixed dark matter models. Additionally, we find that shell-crossing is delayed for ultralight particles and that the deformation tensor extracted from LPT can be used to identify the range of redshifts and scales for which the Madelung formalism of fuzzy dark matter is a reliable approximation.

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arXiv2019

Prospects and Limitations for Constraining Light Relics with Primordial Abundance Measurements

The light relic density affects the thermal and expansion history of the early Universe leaving a number of observable imprints. We focus on the primordial abundances of light elements produced during the process of Big Bang nucleosynthesis which are influenced by the light relic density. Primordial abundances can be used to infer the density of light relics and thereby serve as a probe of physics beyond the Standard Model. We calculate the observational uncertainty on primordial light element abundances and associated quantities that would be required in order for these measurements to achieve sensitivity to the light relic density comparable to that anticipated from upcoming cosmic microwave background surveys. We identify the nuclear reaction rates that need to be better measured to maximize the utility of future observations. We show that improved measurements of the primordial helium-4 abundance can improve constraints on light relics, while more precise measurements of the primordial deuterium abundance are unlikely to be competitive with cosmic microwave background measurements of the light relic density.

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