arXiv subjects

Daniel Eisenstein

Publications and source records attributed to Daniel Eisenstein.

At least 37 records · Page 2Linked to original sources

arXiv2022

The MillenniumTNG Project: Refining the one-halo model of red and blue galaxies at different redshifts

Luminous red galaxies (LRGs) and blue star-forming emission-line galaxies (ELGs) are key tracers of large-scale structure used by cosmological surveys. Theoretical predictions for such data are often done via simplistic models for the galaxy-halo connection. In this work, we use the large, high-fidelity hydrodynamical simulation of the MillenniumTNG project (MTNG) to inform a new phenomenological approach for obtaining an accurate and flexible galaxy-halo model on small scales. Our aim is to study LRGs and ELGs at two distinct epochs, $z = 1$ and $z = 0$, and recover their clustering down to very small scales, $r \sim 0.1 \ {\rm Mpc}/h$, i.e. the one-halo regime, while a companion paper extends this to a two-halo model for larger distances. The occupation statistics of ELGs in MTNG inform us that: (1) the satellite occupations exhibit a slightly super-Poisson distribution, contrary to commonly made assumptions, and (2) that haloes containing at least one ELG satellite are twice as likely to host a central ELG. We propose simple recipes for modeling these effects, each of which calls for the addition of a single free parameter to simpler halo occupation models. To construct a reliable satellite population model, we explore the LRG and ELG satellite radial and velocity distributions and compare them with those of subhalos and particles in the simulation. We find that ELGs are anisotropically distributed within halos, which together with our occupation results provides strong evidence for cooperative galaxy formation (manifesting itself as one-halo galaxy conformity); i.e.~galaxies with similar properties form in close proximity to each other. Our refined galaxy-halo model represents a useful improvement of commonly used analysis tools and thus can be of help to increase the constraining power of large-scale structure surveys.

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arXiv2022

The MillenniumTNG Project: An improved two-halo model for the galaxy-halo connection of red and blue galaxies

Approximate methods to populate dark matter halos with galaxies are of great utility to large galaxy surveys. However, the limitations of simple halo occupation models (HODs) preclude a full use of small-scale galaxy clustering data and call for more sophisticated models. We study two galaxy populations, luminous red galaxies (LRGs) and star-forming emission-line galaxies (ELGs), at two epochs, $z=1$ and $z=0$, in the large volume, high-resolution hydrodynamical simulation of the MillenniumTNG project. In a partner study we concentrated on the small-scale, one-halo regime down to $r\sim 0.1{\rm Mpc}/h$, while here we focus on modeling galaxy assembly bias in the two-halo regime, $r\gtrsim 1{\rm Mpc}/h$. Interestingly, the ELG signal exhibits scale dependence out to relatively large scales ($r\sim 20{\rm Mpc}/h$), implying that the linear bias approximation for this tracer is invalid on these scales, contrary to common assumptions. The 10-15\% discrepancy present in the standard halo model prescription is only reconciled when we augment our halo occupation model with a dependence on extrinsic halo properties ("shear" being the best-performing one) rather than intrinsic ones (e.g., concentration, peak mass). We argue that this fact constitutes evidence for two-halo galaxy conformity. Including tertiary assembly bias (i.e. a property beyond mass and "shear") is not an essential requirement for reconciling the galaxy assembly bias signal of LRGs, but the combination of external and internal properties is beneficial for recovering ELG the clustering. We find that centrals in low-mass haloes dominate the assembly bias signal of both populations. Finally, we explore the predictions of our model for higher-order statistics such as nearest-neighbor counts. The latter supplies additional information about galaxy assembly bias and can be used to break degeneracies between halo model parameters.

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arXiv2022

Accuracy of power spectra in dissipationless cosmological simulations

We exploit a suite of large \emph{N}-body simulations (up to N=$4096^3$) performed with \Abacus, of scale-free models with a range of spectral indices $n$, to better understand and quantify convergence of the matter power spectrum. Using self-similarity to identify converged regions, we show that the maximal wavenumber resolved at a given level of accuracy increases monotonically as a function of time. At the 1\% level it starts at early times from a fraction of $k_Λ$, the Nyquist wavenumber of the initial grid, and reaches at most, if the force softening is sufficiently small, $\sim 2-3 k_Λ$ at the very latest times we evolve to. At the $5\%$ level, accuracy extends up to wavenumbers of order $5k_Λ$ at late times. Expressed as a suitable function of the scale-factor, accuracy shows a very simple $n$-dependence, allowing a extrapolation to place conservative bounds on the accuracy of \emph{N}-body simulations of non-scale free models like LCDM. We note that deviations due to discretization in the converged range are not well modelled by shot noise, and subtracting it in fact degrades accuracy. Quantitatively our findings are broadly in line with the conservative assumptions about resolution adopted by recent studies using large cosmological simulations (e.g. Euclid Flagship) aiming to constrain the mildly non-linear regime. On the other hand, we remark that conclusions about small scale clustering (e.g. concerning the validity of stable clustering) obtained using PS data at wavenumbers larger than a few $k_Λ$ may need revision in light of our convergence analysis.

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arXiv2022

A fully Lagrangian, non-parametric bias model for dark-matter halos

We present a non-parametric Lagrangian biasing model and fit the ratio of the halo and mass densities at the field level using the mass-weighted halo field in the AbacusSummit simulations at $z=0.5$. Unlike the perturbative halo bias model widely used in interpreting the observed large-scale structure traced by galaxies, we find a non-negative halo-to-mass ratio that increases monotonically with the linear overdensity $δ_1$ in the initial Lagrangian space. The bias expansion, however, does not guarantee non-negativity of the halo counts, and may give rising halo number counts at negative overdensities. The shape of the halo-to-mass ratio is unlikely to be described by a polynomial of $δ_1$ and other quantities. Especially for massive halos with $6\times10^{12}\ h^{-1}\ M_\odot$, the halo-to-mass ratio starts soaring up at $δ_1>0$, substantially different from the predictions of the bias expansion. We show that for the halo masses we consider ($M>3\times10^{11}\ h^{-1}\ M_\odot$) a non-parametric halo-to-mass ratio as a function of $δ_1$ and its local derivative $\nabla^2δ_1$ can recover the halo power spectra to sub-percent level for wavenumbers $k=0.01-0.1\ h\ {\rm Mpc}^{-1}$ given a proper smoothing scale to filter the initial density field, even though we do not fit the power spectrum directly. However, there is mild dependence of the recovery of the halo power spectrum on the smoothing scale and other input parameters. At $k<0.01\ h\ {\rm Mpc}^{-1}$ and for massive halos with $M>6\times10^{12}\ h^{-1}\ M_\odot$, our non-parametric model leads to a few percent overestimation of the halo power spectrum, indicating the need for larger or multiple smoothing scales. The halo-to-mass ratios obtained qualitatively agree with intuitions from extended Press-Schechter theory. We compare our framework to the bias expansion and discuss possible extensions.

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arXiv2021

The DESI $N$-body Simulation Project I: Testing the Robustness of Simulations for the DESI Dark Time Survey

Analysis of large galaxy surveys requires confidence in the robustness of numerical simulation methods. The simulations are used to construct mock galaxy catalogs to validate data analysis pipelines and identify potential systematics. We compare three $N$-body simulation codes, ABACUS, GADGET, and SWIFT, to investigate the regimes in which their results agree. We run $N$-body simulations at three different mass resolutions, $6.25\times10^{8}$, $2.11\times10^{9}$, and $5.00\times10^{9}~h^{-1}$M$_{\odot}$, matching phases to reduce the noise within the comparisons. We find systematic errors in the halo clustering between different codes are smaller than the DESI statistical error for $s > 20\, h^{-1}$Mpc in the correlation function in redshift space. Through the resolution comparison we find that simulations run with a mass resolution of $2.1\times10^{9}~h^{-1}$M$_{\odot}$ are sufficiently converged for systematic effects in the halo clustering to be smaller than the DESI statistical error at scales larger than $20 \, h^{-1}$Mpc. These findings show that the simulations are robust for extracting cosmological information from large scales which is the key goal of the DESI survey. Comparing matter power spectra, we find the codes agree to within 1% for $k \leq 10~h$Mpc$^{-1}$. We also run a comparison of three initial condition generation codes and find good agreement. In addition, we include a quasi-$N$-body code, FastPM, since we plan use it for certain DESI analyses. The impact of the halo definition and galaxy-halo relation will be presented in a follow up study.

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arXiv2021

\textsc{CompaSO}: A new halo finder for competitive assignment to spherical overdensities

We describe a new method (\textsc{CompaSO}) for identifying groups of particles in cosmological $N$-body simulations. \textsc{CompaSO} builds upon existing spherical overdensity (SO) algorithms by taking into consideration the tidal radius around a smaller halo before competitively assigning halo membership to the particles. In this way, the \textsc{CompaSO} finder allows for more effective deblending of haloes in close proximity as well as the formation of new haloes on the outskirts of larger ones. This halo-finding algorithm is used in the \textsc{AbacusSummit} suite of $N$-body simulations, designed to meet the cosmological simulation requirements of the Dark Energy Spectroscopic Instrument (DESI) survey. \textsc{CompaSO} is developed as a highly efficient on-the-fly group finder, which is crucial for enabling good load-balancing between the GPU and CPU and the creation of high-resolution merger trees. In this paper, we describe the halo-finding procedure and its particular implementation in \Abacus{Abacus}, accompanying it with a qualitative analysis of the finder. {We test the robustness of the \textsc{CompaSO} catalogues before and after applying the cleaning method described in an accompanying paper and demonstrate its effectiveness by comparing it with other validation techniques.} We then visualise the haloes and their density profiles, finding that they are well fit by the NFW formalism. Finally, we compare other properties such as radius-mass relationships and two-point correlation functions with that of another widely used halo finder, \textsc{ROCKSTAR}.

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arXiv2021

The halo light cone catalogues of \Abacus{AbacusSummit}

We describe a method for generating halo catalogues on the light cone using the \Abacus{AbacusSummit} suite of $N$-body simulations. The main application of these catalogues is the construction of realistic mock galaxy catalogues and weak lensing maps on the sky. Our algorithm associates the haloes from a set of coarsely-spaced snapshots with their positions at the time of light-cone crossing by matching halo particles to on-the-fly light cone particles. It then records the halo and particle information into an easily accessible product, which we call the \Abacus{AbacusSummit} halo light cone catalogues. Our recommended use of this product is in the halo mass regime of $M_{\rm halo} > 2.1 \times 10^{11} \ M_\odot/h$ for the \texttt{base} resolution simulations, i.e. haloes containing at least 100 particles, where the interpolated halo properties are most reliable. To test the validity of the obtained catalogues, we perform various visual inspections and consistency checks. In particular, we construct galaxy mock catalogues of emission-line galaxies (ELGs) at $z \sim 1$ by adopting a modified version of the \Abacus{AbacusHOD} script, which builds on the standard halo occupation distribution (HOD) method by including various extensions. We find that the multipoles of the auto-correlation function are consistent with the predictions from the full-box snapshot, implicitly validating our algorithm. In addition, we compute and output CMB convergence maps and find that the auto- and cross-power spectrum agrees with the theoretical prediction at the subpercent level. Halo light cone catalogues for 25 \texttt{base} and 2 \texttt{huge} simulations at the fiducial cosmology is available at DOI:\href{https://www.doi.org/10.13139/OLCF/1825069}{10.13139/OLCF/1825069}

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arXiv2021

The high-redshift tail of stellar reionization in LCDM is beyond the reach of the low-$\ell$ CMB

The first generation (Pop-III) stars can ionize 1-10% of the universe by $z=15$, when the metal-enriched (Pop-II) stars may contribute negligibly to the ionization. This low ionization tail might leave detectable imprints on the large-scale CMB E-mode polarization. However, we show that physical models for reionization are unlikely to be sufficiently extended to detect any parameter beyond the total optical depth through reionization. This result is driven in part by the total optical depth inferred by Planck, indicating a reionization midpoint around $z=8$, which in combination with the requirement that reionization completes by $z\approx 5.5$ limits the amplitude of an extended tail. To demonstrate this, we perform semi-analytic calculations of reionization including Pop-III star formation in minihalos with Lyman-Werner feedback. We find that standard Pop-III models need to produce very extended reionization at $z>15$ to be distinguishable at 2-$σ$ from Pop-II-only models, assuming a cosmic variance-limited measurement of the low-$\ell$ EE power spectrum. However, we show that unless there is (1) a late-time quenching mechanism such as from strong X-ray feedback or (2) some other extreme Pop-III scenario, structure formation makes it quite challenging to produce high enough Thomson scattering optical depth from $z>15$, $τ(z>15)$, and still be consistent with other observational constraints on reionization.

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arXiv2021

Tests of Acoustic Scale Shifts in Halo-based Mock Galaxy Catalogues

We utilise mock catalogues from high-accuracy cosmological $N$-body simulations to quantify shifts in the recovery of the acoustic scale that could potentially result from galaxy clustering bias. The relationship between galaxies and dark matter halos presents a complicated source of systematic errors in modern redshift surveys, particularly when aiming to make cosmological measurements to sub-percent precision. Apart from a scalar, linear bias parameter accounting for the density contrast ratio between matter tracers and the true matter distribution, other types of galaxy bias, such as assembly and velocity biases, may also significantly alter clustering signals from small to large scales. We create mocks based on generalised halo occupation populations of 36 periodic boxes from the \abacuscosmos release with. In a total volume of $48 \, h^{-3} \mathrm{Gpc}^3$, we test various biased models along with an unbiased base case. Two reconstruction methods are applied to galaxy samples and the apparent acoustic scale is derived by fitting the two-point correlation function multipoles. With respect to the baseline, we find a $0.3\%$ shift in the line-of-sight acoustic scale for one variation in the satellite galaxy population, and we find an $0.7\%$ shift for an extreme level of velocity bias of the central galaxies. All other bias models are consistent with zero shift at the $0.2\%$ level after reconstruction. We note that the bias models explored are relatively large variations, producing sizeable and likely distinguishable changes in small-scale clustering, the modelling of which would further calibrate the BAO standard ruler.

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arXiv2021

Galaxy assembly bias and large-scale distribution: a comparison between IllustrisTNG and a semi-analytic model

In this work, we compare large scale structure observables for stellar mass selected samples at $z=0$, as predicted by two galaxy models, the hydrodynamical simulation IllustrisTNG and the Santa-Cruz semi-analytic model (SC-SAM). Although both models have been independently calibrated to match observations, rather than each other, we find good agreement between the two models for two-point clustering and galaxy assembly bias signatures. The models also show a qualitatively similar response of occupancy and clustering to secondary halo paramaters other than mass, such as formation history and concentration, although with some quantitative differences. Thus, our results demonstrate that the galaxy-halo relationships in SC-SAM and TNG are quite similar to first order. However, we also find areas in which the models differ. For example, we note a strong correlation between halo gas content and environment in TNG, which is lacking in the SC-SAM, as well as differences in the occupancy predictions for low-mass haloes. Moreover, we show that higher-order statistics, such as cumulants of the density field, help to accurately describe the galaxy distribution and discriminate between models that show degenerate behavior for two-point statistics. Our results suggest that SAMs are a promising cost-effective and intuitive method for generating mock catalogues for next generation cosmological surveys.

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arXiv2021

Quantifying resolution in cosmological N-body simulations using self-similarity

We demonstrate that testing for self-similarity in scale-free simulations provides an excellent tool to quantify the resolution at small scales of cosmological N-body simulations. Analysing two-point correlation functions measured in simulations using ABACUS, we show how observed deviations from self-similarity reveal the range of time and distance scales in which convergence is obtained. While the well-converged scales show accuracy below 1 percent, our results show that, with a small force softening length, the spatial resolution is essentially determined by the mass resolution. At later times the lower cut-off scale on convergence evolves in comoving units as $a^{-1/2}$ ($a$ being the scale factor), consistent with a hypothesis that it is set by two-body collisionality. A corollary of our results is that N-body simulations, particularly at high red-shift, contain a significant spatial range in which clustering appears converged with respect to the time-stepping and force softening but has not actually converged to the physical continuum result. The method developed can be applied to determine the resolution of any clustering statistic and extended to infer resolution limits for non-scale-free simulations.

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arXiv2020

On the accuracy of common moment-based radiative transfer methods for simulating reionization

Cosmological simulations of reionization often treat radiative transfer by solving for the monopole and dipoles of the intensity field and by making ansatz for the quadrupole moments to close the system of equations. We investigate the accuracy of the most common closure methods, i.e. Eddington tensor choices. We argue that these algorithms are most likely to err after reionization and study quasi-analytic test problems mimicking these situations: large-scale post-reionization ionizing background fluctuations and radiative transfer in a predominantly ionized medium with discrete absorbers. We show that OTVET and M1 over-ionize self-shielding absorbers when fixing the background photoionization rate, leading to 30-40% higher emissivity to balance the increased recombination. This over-ionization results in a simulation run with these algorithms having a factor of ~2 lower average metagalactic photoionization rate relative to truth given an ionizing emissivity. Furthermore, these algorithms are unlikely to reproduce ionizing background fluctuations on scales below the photon mean path: OTVET tends to overpredict the fluctuations there when the simulation box is smaller than twice the mean free path and underpredict otherwise, while M1 drastically underpredicts these fluctuations. As a result, these numerical methods are likely not sufficiently accurate to interpret the Ly$α$ forest opacity fluctuations observed after reionzation. We show that a high number of angular directions need to be followed to capture the post-reionization ionizing background fluctuations accurately with ray-tracing codes. Lastly, we argue that the strong dependence of the post-reionization ionizing background on the value of the reduced speed of light found in many simulations signals that the ionizing photon mean free path is several times larger in such simulations than the observationally measured value.

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arXiv2020

Extensions to models of the galaxy-halo connection

We explore two widely used empirical models for the galaxy-halo connection, subhalo abundance matching (SHAM) and the halo occupation distribution (HOD) and compare their predictions with the hydrodynamical simulation IllustrisTNG (TNG) for a range of statistics that quantify the galaxy distribution at $n_{\rm gal}\approx1.3\times10^{-3}\,[{\rm Mpc}/h]^{-3}$. We observe that in their most straightforward implementations, both models fail to reproduce the two-point clustering measured in TNG. We find that SHAM models constructed using the relaxation velocity, $V_{\rm relax}$, and the peak velocity, $V_{\rm peak}$, perform best, and match the clustering reasonably well, although neither model captures adequately the one-halo clustering. Splitting the total sample into sub-populations, we discover that SHAM overpredicts the clustering of high-mass, blue, star-forming, and late-forming galaxies and uderpredicts that of low-mass, red, quiescent, and early-forming galaxies. We also study various baryonic effects, finding that subhalos in the dark-mater-only simulation have consistently higher values of their SHAM-proxy properties than their full-physics counterparts. We then consider a two-dimensional implementation of the HOD model augmented with a secondary parameter (environment, velocity anisotropy, $σ^2R_{\rm halfmass}$, and total potential) and tuned so as to match the two-point clustering of the IllustrisTNG galaxies on large scales. We analyze these galaxy populations adopting alternative statistical tools such as galaxy-galaxy lensing, void-galaxy cross-correlations and cumulants of the smoothed density field, finding that the hydrodynamical galaxy distribution disfavors $σ^2 R_{\rm halfmass}$ and the total potential as secondary parameters, while the environment and velocity anisotropy samples are consistent with full-physics across all statistical probes examined.

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arXiv2020

Limitations to the "basic'' HOD model and beyond

We make use of the IllustrisTNG cosmological, hydrodynamical simulations to test fundamental assumptions of the mass-based Halo Occupation Distribution (HOD) approach to modelling the galaxy-halo connection. By comparing the clustering of galaxies measured in the 300 Mpc TNG box (TNG300) with that predicted by the standard (``basic'') HOD model, we find that, on average, the ``basic'' HOD model underpredicts the real-space correlation function in the TNG300 box by $\sim$ 15\% on scales of $1 \ {\rm Mpc}/h < r < 20 \ {\rm Mpc}/h$, which is well beyond the target precision demanded of next-generation galaxy redshift surveys. We perform several tests to establish the robustness of our findings to systematic effects, including the effect of finite box size and the choice of halo finder. In our exploration of ``secondary'' parameters with which to augment the ``basic'' HOD, we find that the local environment of the halo, the velocity dispersion anisotropy, $β$, and the product of the half-mass radius and the velocity dispersion, $σ^2 R_{\rm halfmass}$, are the three most effective measures of assembly bias that help reconcile the ``basic'' HOD-predicted clustering with that in TNG300. In addition, we test other halo properties such as halo spin, formation epoch and halo concentration. We also find that at fixed halo mass, galaxies in one type of environment cluster differently from galaxies in another. We demonstrate that a more complete model of the galaxy-halo connection can be constructed if we combine both mass and local environment information about the halo.

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arXiv2019

The Dark Energy Spectroscopic Instrument (DESI)

We present the status of the Dark Energy Spectroscopic Instrument (DESI) and its plans and opportunities for the coming decade. DESI construction and its initial five years of operations are an approved experiment of the US Department of Energy and is summarized here as context for the Astro2020 panel. Beyond 2025, DESI will require new funding to continue operations. We expect that DESI will remain one of the world's best facilities for wide-field spectroscopy throughout the decade. More about the DESI instrument and survey can be found at https://www.desi.lbl.gov.

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arXiv2019

Cosmology with Stacked Cluster Weak Lensing and Cluster-Galaxy Cross-Correlations

Cluster weak lensing is a sensitive probe of cosmology, particularly the amplitude of matter clustering $σ_8$ and matter density parameter $Ω_m$. The main nuisance parameter in a cluster weak lensing cosmological analysis is the scatter between the true halo mass and the relevant cluster observable, denoted $σ_{\ln Mc}$. We show that combining the cluster weak lensing observable $ΔΣ$ with the projected cluster-galaxy cross-correlation function $w_{p,cg}$ and galaxy auto-correlation function $w_{p,gg}$ can break the degeneracy between $σ_8$ and $σ_{\ln Mc}$ to achieve tight, percent-level constraints on $σ_8$. Using a grid of cosmological N-body simulations, we compute derivatives of $ΔΣ$, $w_{p,cg}$, and $w_{p,gg}$ with respect to $σ_8$, $Ω_m$, $σ_{\ln Mc}$ and halo occupation distribution (HOD) parameters describing the galaxy population. We also compute covariance matrices motivated by the properties of the Dark Energy Suvery (DES) cluster and weak lensing survey and the BOSS CMASS galaxy redshift survey. For our fiducial scenario combining $ΔΣ$, $w_{p,cg}$, and $w_{p,gg}$ measured over $0.3-30.0 \; h^{-1} \; \mathrm{Mpc}$, for clusters at $z=0.35-0.55$ above a mass threshold $M_c\approx 2\times 10^{14} \; h^{-1} \; \mathrm{M_{\odot}}$, we forecast a $1.4\%$ constraint on $σ_8$ while marginalizing over $σ_{\ln Mc}$ and all HOD parameters. Reducing the mass threshold to $1\times 10^{14} \; h^{-1} \; \mathrm{M_{\odot}}$ and adding a $z=0.15-0.35$ redshift bin sharpens this constraint to $0.8\%$. The small scale $(r_p < 3.0 \; h^{-1} \; \mathrm{Mpc})$ ``mass function'' and large scale $(r_p > 3.0 \; h^{-1} \; \mathrm{Mpc})$ ``halo-mass cross-correlation'' regimes of $ΔΣ$ have comparable constraining power, allowing internal consistency tests from such an analysis.

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arXiv2019

Dark Energy and Modified Gravity

Despite two decades of tremendous experimental and theoretical progress, the riddle of the accelerated expansion of the Universe remains to be solved. On the experimental side, our understanding of the possibilities and limitations of the major dark energy probes has evolved; here we summarize the major probes and their crucial challenges. On the theoretical side, the taxonomy of explanations for the accelerated expansion rate is better understood, providing clear guidance to the relevant observables. We argue that: i) improving statistical precision and systematic control by taking more data, supporting research efforts to address crucial challenges for each probe, using complementary methods, and relying on cross-correlations is well motivated; ii) blinding of analyses is difficult but ever more important; iii) studies of dark energy and modified gravity are related; and iv) it is crucial that R&D for a vibrant dark energy program in the 2030s be started now by supporting studies and technical R&D that will allow embryonic proposals to mature. Understanding dark energy, arguably the biggest unsolved mystery in both fundamental particle physics and cosmology, will remain one of the focal points of cosmology in the forthcoming decade.

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arXiv2019

Inflation and Dark Energy from spectroscopy at $z > 2$

The expansion of the Universe is understood to have accelerated during two epochs: in its very first moments during a period of Inflation and much more recently, at $z < 1$, when Dark Energy is hypothesized to drive cosmic acceleration. The undiscovered mechanisms behind these two epochs represent some of the most important open problems in fundamental physics. The large cosmological volume at $2 < z < 5$, together with the ability to efficiently target high-$z$ galaxies with known techniques, enables large gains in the study of Inflation and Dark Energy. A future spectroscopic survey can test the Gaussianity of the initial conditions up to a factor of ~50 better than our current bounds, crossing the crucial theoretical threshold of $σ(f_{NL}^{\rm local})$ of order unity that separates single field and multi-field models. Simultaneously, it can measure the fraction of Dark Energy at the percent level up to $z = 5$, thus serving as an unprecedented test of the standard model and opening up a tremendous discovery space.

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