Function Of Cosmological Parameters Research Articles

A precise symbolic emulator of the linear matter power spectrum

Computing the matter power spectrum, $P(k)$, as a function of cosmological parameters can be prohibitively slow in cosmological analyses, hence emulating this calculation is desirable. Previous analytic approximations are insufficiently accurate for modern applications, so black-box, uninterpretable emulators are often used. We aim to construct an efficient, differentiable, interpretable, symbolic emulator for the redshift zero linear matter power spectrum which achieves sub-percent level accuracy. We also wish to obtain a simple analytic expression to convert $A_ s $ to $ given the other cosmological parameters. We utilise an efficient genetic programming based symbolic regression framework to explore the space of potential mathematical expressions which can approximate the power spectrum and $ We learn the ratio between an existing low-accuracy fitting function for $P(k)$ and that obtained by solving the Boltzmann equations and thus still incorporate the physics which motivated this earlier approximation. We obtain an analytic approximation to the linear power spectrum with a root mean squared fractional error of 0.2<!PCT!> between $k = 9 $ and across a wide range of cosmological parameters, and we provide physical interpretations for various terms in the expression. Our analytic approximation is 950 times faster to evaluate than and 36 times faster than the neural network based matter power spectrum emulator We also provide a simple analytic approximation for $ with a similar accuracy, with a root mean squared fractional error of just 0.1<!PCT!> when evaluated across the same range of cosmologies. This function is easily invertible to obtain s $ as a function of $ and the other cosmological parameters, if preferred. It is possible to obtain symbolic approximations to a seemingly complex function at a precision required for current and future cosmological analyses without resorting to deep-learning techniques, thus avoiding their black-box nature and large number of parameters. Our emulator will be usable long after the codes on which numerical approximations are built become outdated.

Syren-halofit: A fast, interpretable, high-precision formula for the Lambda CDM nonlinear matter power spectrum

Rapid and accurate evaluation of the nonlinear matter power spectrum, $P(k)$, as a function of cosmological parameters and redshift is of fundamental importance in cosmology. Analytic approximations provide an interpretable solution, yet current approximations are neither fast nor accurate relative to numerical emulators. We aim to accelerate symbolic approximations to $P(k)$ by removing the requirement to perform integrals, instead using short symbolic expressions to compute all variables of interest. We also wish to make such expressions more accurate by re-optimising the parameters of these models (using a larger number of cosmologies and focussing on cosmological parameters of more interest for present-day studies) and providing correction terms. We use symbolic regression to obtain simple analytic approximations to the nonlinear scale, $k_ the effective spectral index eff $, and the curvature, $C$, which are required for the model. We then re-optimise the coefficients of to fit a wide range of cosmologies and redshifts. We then again exploit symbolic regression to explore the space of analytic expressions to fit the residuals between $P(k)$ and the optimised predictions of Our results are designed to match the predictions of but we validate our methods against $N$-body simulations. We find symbolic expressions for $k_ eff $ and $C$ which have root mean squared fractional errors of 0.8<!PCT!>, 0.2<!PCT!> and 0.3<!PCT!>, respectively, for redshifts below 3 and a wide range of cosmologies. We provide re-optimised parameters, which reduce the root mean squared fractional error (compared to ) from 3<!PCT!> to below 2<!PCT!> for wavenumbers $k=9 $. We introduce (symbolic-regression-enhanced an extension to containing a short symbolic correction which improves this error to 1<!PCT!>. Our method is 2350 and 3170 times faster than current and implementations, respectively, and 2680 and 64 times faster than (which requires running and the emulator. We obtain comparable accuracy to and the emulator when tested on $N$-body simulations. Our work greatly increases the speed and accuracy of symbolic approximations to $P(k)$, making them significantly faster than their numerical counterparts without loss of accuracy.

A neural network emulator for the Lyman-α forest 1D flux power spectrum

ABSTRACT The Lyman-α forest offers a unique avenue for studying the distribution of matter in the high redshift universe and extracting precise constraints on the nature of dark matter, neutrino masses, and other ΛCDM extensions. However, interpreting this observable requires accurate modelling of the thermal and ionization state of the intergalactic medium, and therefore resorting to computationally expensive hydrodynamical simulations. In this work, we build a neural network that serves as a surrogate model for rapid predictions of the one-dimensional Lyman-α flux power spectrum (P1D), thereby making Bayesian inference feasible for this observable. Our emulation technique is based on modelling P1D as a function of the slope and amplitude of the linear matter power spectrum rather than as a function of cosmological parameters. We show that our emulator achieves sub-percent precision across the full range of scales (k∥ = 0.1 – $4\, \mathrm{Mpc}^{-1}$) and redshifts (z = 2 – 4.5) considered, and also for three ΛCDM extensions not included in the training set: massive neutrinos, running of the spectral index, and curvature. Furthermore, we show that it performs at the 1 per cent level for ionization and thermal histories not present in the training set and performs at the percent level when emulating down to $k_{\parallel }=8\, \mathrm{Mpc}^{-1}$. These results affirm the efficacy of our emulation strategy in providing accurate predictions even for cosmologies and reionization histories that were not explicitly incorporated during the training phase, and we expect it to play a critical role in the cosmological analysis of the DESI survey.

The bacco simulation project: bacco hybrid Lagrangian bias expansion model in redshift space

ABSTRACT We present an emulator that accurately predicts the power spectrum of galaxies in redshift space as a function of cosmological parameters. Our emulator is based on a second-order Lagrangian bias expansion that is displaced to Eulerian space using cosmological N-body simulations. Redshift space distortions are then imprinted using the non-linear velocity field of simulated particles and haloes. We build the emulator using a forward neural network trained with the simulations of the BACCO project, which covers an eight-dimensional parameter space including massive neutrinos and dynamical dark energy. We show that our emulator provides unbiased cosmological constraints from the monopole, quadrupole, and hexadecapole of a mock galaxy catalogue that mimics the BOSS-CMASS sample down to non-linear scales ($k\sim 0.6{h\, {\rm Mpc}^{-1}}$). This work opens up the possibility of robustly extracting cosmological information from small scales using observations of the large-scale structure of the universe.

Constraining cosmology with weak lensing voids

Abstract Upcoming surveys such as lsst and euclid will significantly improve the power of weak lensing as a cosmological probe. To maximise the information that can be extracted from these surveys, it is important to explore novel statistics that complement standard weak lensing statistics such as the shear-shear correlation function and peak counts. In this work, we use a recently proposed weak lensing observable — weak lensing voids — to make parameter constraint forecasts for an $\rm \small {LSST}$-like survey. We use the cosmo-SLICS wCDM simulation suite to measure void statistics as a function of cosmological parameters. The simulation data is used to train a Gaussian process regression emulator that we use to generate likelihood contours and provide parameter constraints from mock observations. We find that the void abundance is more constraining than the tangential shear profiles, though the combination of the two gives additional constraining power. We forecast that without tomographic decomposition, these void statistics can constrain the matter fluctuation amplitude, S8 within 0.3 per cent (68 per cent confidence interval), while offering 1.5, 1.5 and 2.7 per cent precision on the matter density parameter, Ωm, the reduced Hubble constant, h, and the dark energy equation of state parameter, w0, respectively. These results are tighter than the constraints from the shear-shear correlation function with the same observational specifications for Ωm, S8 and w0. The constraints from the WL voids also have complementary parameter degeneracy directions to the shear 2PCF for all combinations of parameters that include h, making weak lensing void statistics a promising cosmological probe.

The BACCO simulation project: exploiting the full power of large-scale structure for cosmology

ABSTRACT We present the BACCO project, a simulation framework specially designed to provide highly-accurate predictions for the distribution of mass, galaxies, and gas as a function of cosmological parameters. In this paper, we describe our main suite of gravity-only simulations ($L\sim 2\,$ Gpc and 43203 particles) and present various validation tests. Using a cosmology-rescaling technique, we predict the non-linear mass power spectrum over the redshift range 0 < z < 1.5 and over scales $10^{-2} \lt k/(\, h\, {\rm Mpc}^{-1}) \lt 5$ for 800 points in an eight-dimensional cosmological parameter space. For an efficient interpolation of the results, we build an emulator and compare its predictions against several widely-used methods. Over the whole range of scales considered, we expect our predictions to be accurate at the $2{{\ \rm per\ cent}}$ level for parameters in the minimal Lambda cold dark matter model and to $3{{\ \rm per\ cent}}$ when extended to dynamical dark energy and massive neutrinos. We make our emulator publicly available under http://www.dipc.org/bacco

Variations of cosmic large-scale structure covariance matrices across parameter space

The likelihood function for cosmological parameters, given by e.g. weak lensing shear measurements, depends on contributions to the covariance induced by the nonlinear evolution of the cosmic web. As nonlinear clustering to date has only been described by numerical $N$-body simulations in a reliable and sufficiently precise way, the necessary computational costs for estimating those covariances at different points in parameter space are tremendous. In this work we describe the change of the matter covariance and of the weak lensing covariance matrix as a function of cosmological parameters by constructing a suitable basis, where we model the contribution to the covariance from nonlinear structure formation using Eulerian perturbation theory at third order. We show that our formalism is capable of dealing with large matrices and reproduces expected degeneracies and scaling with cosmological parameters in a reliable way. Comparing our analytical results to numerical simulations we find that the method describes the variation of the covariance matrix found in the SUNGLASS weak lensing simulation pipeline within the errors at one-loop and tree-level for the spectrum and the trispectrum, respectively, for multipoles up to $\ell\leq 1300$. We show that it is possible to optimize the sampling of parameter space where numerical simulations should be carried out by minimising interpolation errors and propose a corresponding method to distribute points in parameter space in an economical way.

Cosmology constraints from shear peak statistics in Dark Energy Survey Science Verification data

Shear peak statistics has gained a lot of attention recently as a practical alternative to the two point statistics for constraining cosmological parameters. We perform a shear peak statistics analysis of the Dark Energy Survey (DES) Science Verification (SV) data, using weak gravitational lensing measurements from a 139 deg$^2$ field. We measure the abundance of peaks identified in aperture mass maps, as a function of their signal-to-noise ratio, in the signal-to-noise range $0<\mathcal S / \mathcal N<4$. To predict the peak counts as a function of cosmological parameters we use a suite of $N$-body simulations spanning 158 models with varying $\Omega_{\rm m}$ and $\sigma_8$, fixing $w = -1$, $\Omega_{\rm b} = 0.04$, $h = 0.7$ and $n_s=1$, to which we have applied the DES SV mask and redshift distribution. In our fiducial analysis we measure $\sigma_{8}(\Omega_{\rm m}/0.3)^{0.6}=0.77 \pm 0.07$, after marginalising over the shear multiplicative bias and the error on the mean redshift of the galaxy sample. We introduce models of intrinsic alignments, blending, and source contamination by cluster members. These models indicate that peaks with $\mathcal S / \mathcal N>4$ would require significant corrections, which is why we do not include them in our analysis. We compare our results to the cosmological constraints from the two point analysis on the SV field and find them to be in good agreement in both the central value and its uncertainty. We discuss prospects for future peak statistics analysis with upcoming DES data.

Galaxy formation as a cosmological tool – I. The galaxy merger history as a measure of cosmological parameters

As galaxy formation and evolution over long cosmic time-scales depends to a large degree on the structure of the universe, the assembly history of galaxies is potentially a powerful approach for learning about the universe itself. In this paper we examine the merger history of dark matter halos based on the Extended Press-Schechter formalism as a function of cosmological parameters, redshift and halo mass. We calculate how major halo mergers are influenced by changes in the cosmological values of $\Omega_{\rm m}$, $\Omega_{\Lambda}$, $\sigma_{8}$, the dark matter particle temperature (warm vs. cold dark matter), and the value of a constant and evolving equation of state parameter $w(z)$. We find that the merger fraction at a given halo mass varies by up to a factor of three for halos forming under the assumption of Cold Dark Matter, within different underling cosmological parameters. We find that the current measurements of the merger history, as measured through observed galaxy pairs as well as through structure, are in agreement with the concordance cosmology with the current best fit giving $1 - \Omega_{\rm m} = \Omega_{\rm \Lambda} = 0.84^{+0.16}_{-0.17}$. To obtain a more accurate constraint competitive with recently measured cosmological parameters from Planck and WMAP requires a measured merger accuracy of $\delta f_{\rm m} \sim 0.01$, implying surveys with an accurately measured merger history over 2 - 20 deg$^{2}$, which will be feasible with the next generation of imaging and spectroscopic surveys such as Euclid and LSST.

Cluster Ellipticities as a Cosmological Probe

We investigate the dependence of the ellipticities of clusters of galaxies on cosmological parameters using large-scale cosmological simulations. We determine cluster ellipticities out to redshift unity for λCDM models with different mean densities Ωm and amplitudes of mass fluctuation σ8,0. The mean ellipticity increases monotonically with redshift for all models. Larger values of σ8,0, i.e., earlier cluster formation times, produce lower ellipticities. The dependence of ellipticity on Ωm is relatively weak in the range 0.2 ≤ Ωm ≤ 0.5 for high-mass clusters. The mean ellipticity (z) decreases linearly with the amplitude of mass fluctuations at the cluster redshift z, nearly independent of Ωm; on average, older clusters are more relaxed and are thus less elliptical. The distribution of ellipticities about the mean is approximated by a Gaussian, allowing a simple characterization of the evolution of ellipticity with redshift as a function of cosmological parameters. At z = 0, the mean ellipticity of high-mass clusters is approximated by (z = 0) = 0.245 - 0.070σ8,0 + 0.020Ωm,0. This relation opens up the possibility that, when compared with future observations of large cluster samples, the mean cluster ellipticity and its evolution could be used as a new, independent tool to constrain cosmological parameters, especially the amplitude of mass fluctuations, σ8,0.

Evolution of the dark matter distribution with three-dimensional weak lensing

We present a direct detection of the growth of large-scale structure, using weak gravitational lensing and photometric redshift data from the {COMBO-17} survey. We use deep R-band imaging of two 0.5 ?? 0.5 deg2 fields, affording shear estimates for over 52000 galaxies; we combine these with photometric redshift estimates from our 17-band survey, in order to obtain a {3D} shear field. We find theoretical models for evolving matter power spectra and correlation functions, and fit the corresponding shear correlation functions to the data as a function of redshift. We detect the evolution of the power at the 4.7?? level given reasonable priors, and measure the rate of evolution for 0 {\textless} z {\textless} 1. We also fit correlation functions to our {3D} data as a function of cosmological parameters ??8 and ????. We find joint constraints on ???? and ??8, demonstrating an improvement in accuracy by {\textasciitilde}=40 per cent over that available from {2D} weak lensing for the same area.

Cosmic microwave background constraints on the epoch of reionization

ABSTRA C T We use a compilation of cosmic microwave anisotropy data to constrain the epoch of reionization in the Universe, as a function of cosmological parameters. We consider spatially flat cosmologies, varying the matter density V0 (the flatness being restored by a cosmological constant), the Hubble parameter h and the spectral index n of the primordial power spectrum. Our results are quoted both in terms of the maximum permitted optical depth to the last-scattering surface, and in terms of the highest allowed reionization redshift assuming instantaneous reionization. For critical-density models, significantly tilted power spectra are excluded as they cannot fit the current data for any amount of reionization, and even scale-invariant models must have an optical depth to last scattering of below 0.3. For the currently favoured low-density model with V0a 0:3 and a cosmological constant, the earliest reionization permitted to occur is at around redshift 35, which roughly coincides with the highest estimate in the literature. We provide general fitting functions for the maximum permitted optical depth, as a function of cosmological parameters. We do not consider the inclusion of tensor perturbations, but if present they would strengthen the upper limits that we quote.