Blinded challenge for precision cosmology with large-scale structure: results from effective field theory for the redshift-space galaxy power spectrum
Takahiro Nishimichi, Guido D'Amico, Mikhail M. Ivanov, Leonardo Senatore, Marko Simonović, Masahiro Takada, Matias Zaldarriaga, Pierre Zhang
备注：
24 pages, 13 figures, version accepted for publication in PRD, post-unblinding analysis added in Appendices including a forecast for a DESI-like survey, participation in the challenge still welcome, mock data available at https://www2.yukawa.kyoto-u.ac.jp/~takahiro.nishimichi/data/PTchallenge/
An accurate theoretical template for the galaxy power spectrum is a key for the success of ongoing and future spectroscopic surveys. We examine to what extent the Effective Field Theory of Large Scale Structure is able to provide such a template and correctly estimate cosmological parameters. To that end, we initiate a blinded challenge to infer cosmological parameters from the redshift-space power spectrum of high-resolution mock catalogs mimicking the BOSS galaxy sample but covering a hundred times larger cumulative volume. This gigantic simulation volume allows us to separate systematic bias due to theoretical modeling from the statistical error due to sample variance. The challenge task was to measure three unknown input parameters used in the simulation: the Hubble constant, the matter density fraction, and the clustering amplitude. We present analyses done by two independent teams, who have fitted the mock simulation data generated by yet another independent group. This allows us to avoid any confirmation bias by analyzers and pin down possible tuning of the specific EFT implementations. Both independent teams have recovered the true values of the input parameters within sub-percent statistical errors corresponding to the total simulation volume.
Presently a ${>}3σ$ tension exists between values of the Hubble constant $H_0$ derived from analysis of fluctuations in the Cosmic Microwave Background by Planck, and local measurements of the expansion using calibrators of type Ia supernovae (SNe Ia). We perform a blinded reanalysis of Riess et al. 2011 to measure $H_0$ from low-redshift SNe Ia, calibrated by Cepheid variables and geometric distances including to NGC 4258. This paper is a demonstration of techniques to be applied to the Riess et at. 2016 data. Our end-to-end analysis starts from available CfA3 and LOSS photometry, providing a…
Pushing spectral siren cosmology into the third-generation era: a blinded mock data challenge
Università di Bologna（博洛尼亚大学）；INFN - Sezione di Bologna（意大利国家核物理研究所博洛尼分部）；INAF - Osservatorio di Astrofisica e Scienza dello Spazio di Bologna（意大利国家天体物理研究所博洛尼亚天文与空间科学观测站）；Aix-Marseille Université（艾克斯-马赛大学）；Université de Toulon（土伦大学）；CNRS, CPT（法国国家科学研究中心， cpt 中心）；INFN, Sezione di Roma（意大利国家核物理研究所罗马分部）；“Sapienza” Universitá di Roma（罗马大学）；CNRS/IN2P3, CPPM（法国国家科学研究中心/法国粒子与核物理研究所，马赛质子与核物理中心）
Blinded Mock Data Challenge: Is the Spectral Siren Technique Robust for Measuring the Hubble Constant?
Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology（高等能源物理研究所，巴塞罗那科学技术大学）；Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research（塔塔基础研究院天体物理学系）；Inter-University Centre for Astronomy and Astrophysics (IUCAA)（大学间天文学与天体物理学中心）；Instituto de Fisica, Universidad de Antioquia（安蒂奥基亚大学物理研究所）；Subatech, CNRS - Institut Mines-Telecom Atlantique - Université de Nantes（Subatech，法国国家科学研究中心-矿业电信大西洋学院-南特大学）；Université Paris-Saclay, CNRS/IN2P3, IJCLab（巴黎萨克雷大学，法国国家科学研究中心/粒子核物理国际研究所，IJCLab）；Instituto de Fisica Teorica, Universidad Autonoma de Madrid（马德里自治大学理论物理研究所）
Some million Type Ia supernovae (SN) will be discovered and monitored during upcoming wide area time domain surveys such as the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). For cosmological use, accurate redshifts are needed among other characteristics; however the vast majority of the SN will not have spectroscopic redshifts, even for their host galaxies, only photometric redshifts. We assess the redshift systematic control necessary for robust cosmology. Based on the photometric vs true redshift relation generated by machine learning applied to a simulation of 500,000 ga…
Recent papers have shown that a small systematic redshift shift ($Δz\sim 10^{-5}$) in measurements of type Ia supernovae can cause a significant bias ($\sim$1\%) in the recovery of cosmological parameters. Such a redshift shift could be caused, for example, by a gravitational redshift due to the density of our local environment. The sensitivity of supernova data to redshift shifts means supernovae make excellent probes of inhomogeneities. We therefore invert the analysis, and try to diagnose the nature of our local gravitational environment by fitting for $Δz$ as an extra free parameter alongs…
Following the success of type Ia supernovae in constraining cosmologies at lower redshift $(z\lesssim2)$, effort has been spent determining if a similarly useful standardisable candle can be found at higher redshift. {In this work we determine the largest possible magnitude discrepancy between a constant dark energy $Λ$CDM cosmology and a cosmology in which the equation of state $w(z)$ of dark energy is a function of redshift for high redshift standard candles $(z\gtrsim2)$}. We discuss a number of popular parametrisations of $w(z)$ with two free parameters, $w_z$CDM cosmologies, including the…
Motivated by recent suggestions that a number of observed galaxy clusters have masses which are too high for their given redshift to occur naturally in a standard model cosmology, we use Extreme Value Statistics to construct confidence regions in the mass-redshift plane for the most extreme objects expected in the universe. We show how such a diagram not only provides a way of potentially ruling out the concordance cosmology, but also allows us to differentiate between alternative models of enhanced structure formation. We compare our theoretical prediction with observations, placing currently…
With the remarkable increase in scale and precision provided by upcoming galaxy redshift surveys, systematic errors that were previously negligible may become significant. In this paper, we explore the potential impact of low-magnitude systematic redshift offsets on measurements of the Baryon Acoustic Oscillation (BAO) feature, and the cosmological constraints recovered from such measurements. Using 500 mock galaxy redshift surveys as our baseline sample, we inject a series of systematic redshift biases (ranging from +/-0.2% to +/-2%), and measure the resulting shift in the recovered isotropic…
The concentrations of dark matter haloes provide crucial information about their internal structure and how it depends on mass and redshift -- the so-called concentration-mass-redshift relation, denoted $c(M,z)$. We present here an extensive study of the cosmology-dependence of $c(M,z)$ that is based on a suite of 72 gravity-only, full N-body simulations in which the following cosmological parameters were varied: $σ_{8}$, $Ω_{\mathrm{M}}$, $Ω_{\mathrm{b}}$, $n_{\mathrm{s}}$, $h$, $M_ν$, $w_{0}$ and $w_{\mathrm{a}}$. We characterize the impact of these parameters on concentrations for different…
The 4MOST Cosmology Redshift Survey (CRS) will perform stringent cosmological tests via spectroscopic clustering measurements that will complement the best lensing, cosmic microwave background and other surveys in the southern hemisphere. The combination of carefully selected samples of bright galaxies, luminous red galaxies, emission-line galaxies and quasars, totalling about 8 million objects over the redshift range $z = 0.15$ to $3.5$, will allow definitive tests of gravitational physics. Many key science questions will be addressed by combining CRS spectra of these targets with data from c…
We investigate the impact of different observational effects affecting a precise and accurate measurement of the growth rate of fluctuations from the anisotropy of clustering in galaxy redshift surveys. We focus on redshift measurement errors, on the reconstruction of the underlying real-space clustering and on the apparent degeneracy existing with the geometrical distortions induced by the cosmology-dependent conversion of redshifts into distances. We use a suite of mock catalogues extracted from large N-body simulations, focusing on the analysis of intermediate, mildly non-linear scales and …
We present a method of calibrating the properties of photometric redshift bins as part of a larger Markov Chain Monte Carlo (MCMC) analysis for the inference of cosmological parameters. The redshift bins are characterised by their mean and variance, which are varied as free parameters and marginalised over when obtaining the cosmological parameters. We demonstrate that the likelihood function for cross-correlations in an angular power spectrum framework tightly constrains the properties of bins such that they may be well determined, reducing their influence on cosmological parameters and avoid…
Double source lensing, with two sources lensed by the same foreground galaxy, involves the distance between each source and the lens and hence is a probe of the universe away from the observer. The double source distance ratio also reduces sensitivity to the lens model and has good complementarity with standard distance probes. We show that using this technique at high redshifts $z>1$, to be enabled by data from the Euclid satellite and other surveys, can give insights on dark energy, both in terms of $w_0$-$w_a$ and redshift binned density. We find a dark energy figure of merit of 245 from co…
We investigate the expected cosmological constraints from a combination of weak lensing and large-scale galaxy clustering using realistic redshift distributions. Introducing a systematic bias in the weak lensing redshift distributions (of 0.05 in redshift) produces a $>2σ$ bias in the recovered matter power spectrum amplitude and dark energy equation of state, for preliminary Stage III surveys. We demonstrate that these cosmological errors can be largely removed by marginalising over unknown biases in the assumed weak lensing redshift distributions, if we assume high quality redshift informati…
We propose a new consistency test for the $Λ$CDM cosmology using baryonic acoustic oscillations (BAO) and redshift space distortion (RSD) measurements from galaxy redshift surveys. Specifically, we determine the peak position of $fσ_8(z)$ in redshift $z$ offered by a RSD measurement, and compare it to the one predicted by the BAO observables assuming a flat $Λ$CDM cosmology. We demonstrate this new test using the simulated data for the DESI galaxy survey, and argue that this test complements those using the background observables alone, and is less subject to systematics in the RSD analysis, c…
An observational program focused on the high redshift ($2<z<6$) Universe has the opportunity to dramatically improve over upcoming LSS and CMB surveys on measurements of both the standard cosmological model and its extensions. Using a Fisher matrix formalism that builds upon recent advances in Lagrangian perturbation theory, we forecast constraints for future spectroscopic and 21-cm surveys on the standard cosmological model, curvature, neutrino mass, relativistic species, primordial features, primordial non-Gaussianity, dynamical dark energy, and gravitational slip. We compare these constrain…
In addition to being a probe of Cosmic Dawn and Epoch of Reionization astrophysics, the 21cm line at $z>6$ is also a powerful way to constrain cosmology. Its power derives from several unique capabilities. First, the 21cm line is sensitive to energy injections into the intergalactic medium at high redshifts. It also increases the number of measurable modes compared to existing cosmological probes by orders of magnitude. Many of these modes are on smaller scales than are accessible via the CMB, and moreover have the advantage of being firmly in the linear regime (making them easy to model theor…
El Gordo (ACT-CL J0102-4915) is an extremely massive galaxy cluster ($M_{200} \approx 3 \times 10^{15}$ $M_{\odot}$) at redshift $z = 0.87 $ composed of two subclusters with mass ratio 3.6 merging at speed $V_{infall} \approx 2500$ km/s. Such a fast collision between individually rare massive clusters is unexpected in Lambda cold dark matter ($Λ$CDM) cosmology at such high $z$. However, this is required for non-cosmological hydrodynamical simulations of the merger to match its observed properties (Zhang et al. 2015). Here, we determine the probability of finding a similar object in a $Λ$CDM co…
Many schemes have been proposed to perform a model-independent constraint on cosmological dynamics, such as nonparametric dark energy equation of state (EoS) ω(z) or the deceleration parameter q(z). These methods usually contain derivative processes with respect to observational data with noise. However, it still remains remarkably uncertain when one estimates the numerical differentiation, especially the corresponding truncation errors. In this work, we introduce a global numerical differentiation method, first formulated by Reinsch(1967), which is smoothed by cubic spline functions. The opti…
Kinematic lensing with high-resolution spectroscopic surveys. A unique opportunity for transformative cosmology at high redshifts in the 2040s
Università degli Studi di Torino（都灵大学）；INFN – Istituto Nazionale di Fisica Nucleare, Sezione di Torino（意大利国家核物理研究所都灵分部）；INAF – Istituto Nazionale di Astrofisica, Osservatorio Astrofisico di Torino（意大利国家天体物理研究所都灵天文台）
The efficient selection of high-redshift emission galaxies is important for future large galaxy redshift surveys for cosmology. Here we describe the target selection methods for the FastSound project, a redshift survey for H alpha emitting galaxies at z=1.2-1.5 using Subaru/FMOS to measure the linear growth rate fσ8 via Redshift Space Distortion (RSD) and constrain the theory of gravity. To select ~400 target galaxies in the 0.2 deg^2 FMOS field-of-view from photometric data of CFHTLS-Wide (u*g'r'i'z'), we test several different methods based on color-color diagrams or photometric redshift est…
Redshift-space distortions in the clustering of galaxy clusters provide a novel probe to test the gravity theory on cosmological scales. The aim of this work is to derive new constraints on the linear growth rate of cosmic structures from the redshift-space two-point correlation function of galaxy clusters. We construct a large spectroscopic catalogue of optically-selected clusters from the Sloan Digital Sky Survey. The selected sample consists of $43,743$ clusters in the redshift range $0.1<z<0.42$, with masses estimated from weak-lensing calibrated scaling relations. We measure the transvers…
The large-scale matter distribution in the late-time Universe exhibits gravity-induced non-Gaussianity, and the bispectrum, three-point cumulant is expected to contain significant cosmological information. In particular, the measurement of the bispectrum helps to tighten the constraints on dark energy and modified gravity through the redshift-space distortions (RSD). In this paper, extending the work by Taruya, Nishimichi & Saito (2010, Phys.Rev.D 82, 063522), we present a perturbation theory (PT) based model of redshift-space matter bispectrum that can keep the non-perturbative damping effect…
Our group has developed a technique that makes use of the observed non-linear relation between the ultraviolet and the X-ray luminosity in quasars to provide an independent measurement of their distances, thus turning quasars into standardizable candles. This technique, at present, it is mostly based upon quasar samples with data from public catalogues both in the X-rays and in the optical/ultraviolet and extends the Hubble diagram of supernovae to a redshift range still poorly explored (z>2). From the X-ray perspective, we are now on the eve of a major change, as the upcoming mission eROSITA …
A new generation of cosmological experiments will spectroscopically detect the H$α$ line from ELGs at optical/near-infrared frequencies. Other emission lines will also be present, which may come from the same H$α$ sample or constitute a new galaxy sample altogether. Our goal is to assess the value, for cosmological investigation, of galaxies at $z\gtrsim2$ present in H$α$ galaxy surveys and identifiable by the highly redshifted ultra-violet and optical lines - namely the OII line and the OIII doublet in combination with the H$β$ line. We use state-of-the-art luminosity functions to estimate th…
The homogeneous, isotropic, and flat $Λ$CDM universe favored by observations of the cosmic microwave background can be described using only Euclidean geometry, locally correct Newtonian mechanics, and the basic postulates of special and general relativity. We present simple derivations of the most useful equations connecting astronomical observables (redshift, flux density, angular diameter, brightness, local space density,...) with the corresponding intrinsic properties of distant sources (lookback time, distance, spectral luminosity, linear size, specific intensity, source counts,...). We al…
Cosmological galaxy surveys aim at mapping the largest volumes to test models with techniques such as cluster abundance, cosmic shear correlations or baryon acoustic oscillations (BAO), which are designed to be independent of galaxy bias. Here we explore an alternative route to constrain cosmology: sampling more moderate volumes with the cross-correlation of photometric and spectroscopic surveys. We consider the angular galaxy-galaxy autocorrelation in narrow redshift bins and its combination with different probes of weak gravitational lensing (WL) and redshift space distortions (RSD). Includi…
The collapse barrier, $δ_{c}$, of the field clusters located in the low-density environment is deterministic rather than diffusive, unlike that of the wall counterparts located in the superclusters. Analyzing the data from the Mira-Titan simulations for eleven different cosmologies including the standard $Λ$CDM cosmology at various redshifts, we investigate the evolution of the deterministic collapse barrier of the field clusters and explore its dependence on the background cosmology. Regardless of the background cosmology, the deterministic $δ_{c}$ exhibits a universal behavior of having a hi…
A new method to constrain the cosmological equation of state is proposed by using combined samples of gamma-ray bursts (GRBs) and supernovae (SNeIa). The Chevallier-Polarski-Linder parameterization is adopted for the equation of state in order to find out a realistic approach to achieve the deceleration/acceleration transition phase of dark energy models. As results, we find that GRBs, calibrated by SNeIa, could be, at least, good distance indicators capable of discriminating cosmological models with respect to $Λ$CDM at high redshift. Besides, GRBs+SNeIa combined redshift-distance diagram put…
Even in a universe that is homogeneous on large scales, local density fluctuations can imprint a systematic signature on the cosmological inferences we make from distant sources. One example is the effect of a local under-density on supernova cosmology. Also known as a Hubble-bubble, it has been suggested that a large enough under-density could account for the supernova magnitude- redshift relation without the need for dark energy or acceleration. Although the size and depth of under-density required for such an extreme result is extremely unlikely to be a random fluctuation in an on-average h…
The non-linear relation between X-ray and UV luminosity in quasars can be used to estimate their distance. Recently, we have shown that despite the large dispersion of the relation, a Hubble Diagram made of large samples of quasars can provide unique constraints on cosmology at high redshift. Furthermore, the dispersion of the relation is heavily affected by measurement errors: until now we have used serendipitous X-ray observations, but dedicated observations would significantly increase the precision of the distance estimates. We discuss the future role of XMM in this new field, showing (1) …
Weak gravitational lensing is becoming a mature technique for constraining cosmological parameters, and future surveys will be able to constrain the dark energy equation of state $w$. When analyzing galaxy surveys, redshift information has proven to be a valuable addition to angular shear correlations. We forecast parameter constraints on the triplet $(Ω_m,w,σ_8)$ for an LSST-like photometric galaxy survey, using tomography of the shear-shear power spectrum, convergence peak counts and higher convergence moments. We find that redshift tomography with the power spectrum reduces the area of the …
The success of future large scale weak lensing surveys will critically depend on the accurate estimation of photometric redshifts of very large samples of galaxies. This in turn depends on both the quality of the photometric data and the photo-z estimators. In a previous study, (Bordoloi et al. 2010) we focussed primarily on the impact of photometric quality on photo-z estimates and on the development of novel techniques to construct the N(z) of tomographic bins at the high level of precision required for precision cosmology, as well as the correction of issues such as imprecise corrections fo…
Based on a set of cosmological N-body simulations we analyze properties of the dark matter haloes (DM) in a galaxy mass range ($10^{11} - 10^{13} h^{-1}M_{\odot}$) in modified $\lcdm$ cosmology with additional dynamically screened scalar interactions in DM sector. Our simulations show that scalar interactions support picture of the Island Universe. Rapid structure formation processes are shifted into higher redshifts resulting in a much smaller accretion and merging rates for galactic haloes at low redshifts. Finally, we present how this "fifth" force affects halo properties, like density prof…
A Fully Photometric Approach to Type Ia Supernova Cosmology in the LSST Era: Host Galaxy Redshifts and Supernova Classification
National Center for Supercomputing Applications（国家超级计算应用中心）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of Chicago（芝加哥大学）；Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；Massachusetts Institute of Technology（麻省理工学院）；Center for Astrophysics | Harvard & Smithsonian（天体物理中心|哈佛与史密森尼学会）；The Inter-University Centre for Astronomy and Astrophysics (IUCAA)（大学间天文学和天体物理学中心）
Modeling Redshift Uncertainties in Roman Weak Lensing Cosmology
Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）；Duke University（杜克大学）；University of Arizona（亚利桑那大学）；Stony Brook University（石溪大学）；University of Chicago（芝加哥大学）；University of Pittsburgh（匹兹堡大学）
A goal of forthcoming imaging surveys is to use weak gravitational lensing shear measurements to constrain dark energy. We quantify the importance of uncalibrated photometric redshift outliers to the dark energy goals of forthcoming imaging surveys in a manner that does not assume any particular photometric redshift technique or template. In so doing, we provide an approximate blueprint for computing the influence of specific outlier populations on dark energy constraints. We find that outliers whose photo-z distributions are tightly localized about a significantly biased redshift must be cont…
Perturbations from inflation evolve into large scale structure of the late universe, and encode abundant cosmic structure formation physics. We allow freedom in the primordial power spectrum, rather than assuming a power law scale dependence, to study its impact on cosmological parameter determination. Combining various generations of cosmic microwave background (CMB) data and galaxy redshift survey data, we investigate the constraints on reconstruction of the primordial curvature perturbation power spectrum and the late time cosmology, especially the sum of neutrino masses. We quantify how ea…
We present a method to measure the growth of structure and the background geometry of the Universe -- with no a priori assumption about the underlying cosmological model. Using Canada-France-Hawaii Lensing Survey (CFHTLenS) shear data we simultaneously reconstruct the lensing amplitude, the linear intrinsic alignment amplitude, the redshift evolving matter power spectrum, P(k,z), and the co-moving distance, r(z). We find that lensing predominately constrains a single global power spectrum amplitude and several co-moving distance bins. Our approach can localise precise scales and redshifts wher…
The splashback radius $R_{\rm sp}$, the apocentric radius of particles on their first orbit after falling into a dark matter halo, has recently been suggested as a physically motivated halo boundary that separates accreting from orbiting material. Using the SPARTA code presented in Paper I, we analyze the orbits of billions of particles in cosmological simulations of structure formation and measure $R_{\rm sp}$ for a large sample of halos that span a mass range from dwarf galaxy to massive cluster halos, reach redshift 8, and include WMAP, Planck, and self-similar cosmologies. We analyze the d…
Galaxy clusters observed through the thermal Sunyaev-Zeldovich (tSZ) effect are a recent cosmological probe. The precision on the cosmological constraints is affected mainly by the current knowledge of cluster physics, which enters the analysis through the scaling relations. Here we aim to study one of the most important sources of systematic uncertainties, the mass bias, $b$. We have analysed the effects of a mass-redshift dependence, adopting a power-law parametrisation. We applied this parametrisation to the combination of tSZ number counts and power spectrum, finding a hint of redshift dep…
Supernova cosmology without spectra will be an important component of future surveys such as LSST. This lack of supernova spectra results in uncertainty in the redshifts which, if ignored, leads to significantly biased estimates of cosmological parameters. Here we present a hierarchical Bayesian formalism -- zBEAMS -- that addresses this problem by marginalising over the unknown or uncertain supernova redshifts to produce unbiased cosmological estimates that are competitive with supernova data with spectroscopically confirmed redshifts. zBEAMS provides a unified treatment of both photometric r…
Systematic errors in the galaxy redshift distribution $n(z)$ can propagate to systematic errors in the derived cosmology. We characterize how the degenerate effects in tomographic bin widths and galaxy bias impart systematic errors on cosmology inference using observational data from the Deep Lens Survey. For this we use a combination of galaxy clustering and galaxy-galaxy lensing. We present two end-to-end analyses from the catalogue level to parameter estimation. We produce an initial cosmological inference using fiducial tomographic redshift bins derived from photometric redshifts, then com…
The Dark Ages, probed by the redshifted 21-cm signal, is the ideal epoch for a new rigorous test of the standard LCDM cosmological model. Divergences from that model would indicate new physics, such as dark matter decay (heating) or baryonic cooling beyond that expected from adiabatic expansion of the Universe. In the early Universe, most of the baryonic matter was in the form of neutral hydrogen (HI), detectable via its ground state's spin-flip transition. A measurement of the redshifted 21-cm spectrum maps the history of the HI gas through the Dark Ages and Cosmic Dawn and up to the Epoch of…
We report the first results of a programme aimed at studying the properties of high redshift galaxies with on-going massive and dominant episodes of star formation (HII galaxies). We use the $L(\mathrm{H}β) - σ$ distance estimator based on the correlation between the ionized gas velocity dispersions and Balmer emission line luminosities of HII galaxies and Giant HII regions to trace the expansion of the Universe up to $z \sim 2.33$. This approach provides an independent constraint on the equation of state of dark energy and its possible evolution with look-back time. Here we present high-dispe…
Cosmology and Source Redshift Constraints from Galaxy Clustering and Tomographic Weak Lensing with HSC Y3 and SDSS using the Point-Mass Correction Model
Motivated by the dawn of precision cosmology and the wealth of forthcoming high precision and volume galaxy surveys, in this paper we study the effects of inhomogeneities on light propagation in a flat ΛCDM background. To this end we use exact solutions of Einstein's equations (Meures & Bruni 2011) where, starting from small fluctuations, inhomogeneities arise from a standard growing mode and become non-linear. While the matter distribution in these models is necessarily idealised, there is still enough freedom to assume an arbitrary initial density profile along the line of sight. We can ther…
Accurate and efficient methods to evaluate cosmological distances are an important tool in modern precision cosmology. In a flat $Λ$CDM cosmology, the luminosity distance can be expressed in terms of elliptic integrals. We derive an alternative and simple expression for the luminosity distance in a flat $Λ$CDM based on hypergeometric functions. Using a timing experiment we compare the computation time for the numerical evaluation of the various exact formulae, as well as for two approximate fitting formulae available in the literature. We find that our novel expression is the most efficient ex…
