Cosmological Parameter Estimation Research Articles

Suppressing cosmic variance with paired-and-fixed cosmological simulations: average properties and covariances of dark matter clustering statistics

ABSTRACT Making cosmological inferences from the observed galaxy clustering requires accurate predictions for the mean clustering statistics and their covariances. Those are affected by cosmic variance – the statistical noise due to the finite number of harmonics. The cosmic variance can be suppressed by fixing the amplitudes of the harmonics instead of drawing them from a Gaussian distribution predicted by the inflation models. Initial realizations also can be generated in pairs with 180○ flipped phases to further reduce the variance. Here, we compare the consequences of using paired-and-fixed versus Gaussian initial conditions on the average dark matter clustering and covariance matrices predicted from N-body simulations. As in previous studies, we find no measurable differences between paired-and-fixed and Gaussian simulations for the average density distribution function, power spectrum, and bispectrum. Yet, the covariances from paired-and-fixed simulations are suppressed in a complicated scale- and redshift-dependent way. The situation is particularly problematic on the scales of Baryon acoustic oscillations where the covariance matrix of the power spectrum is lower by only $\sim 20{{\ \rm per\ cent}}$ compared to the Gaussian realizations, implying that there is not much of a reduction of the cosmic variance. The non-trivial suppression, combined with the fact that paired-and-fixed covariances are noisier than from Gaussian simulations, suggests that there is no path towards obtaining accurate covariance matrices from paired-and-fixed simulations – result, that is theoretically expected and accepted in the field. Because the covariances are crucial for the observational estimates of galaxy clustering statistics and cosmological parameters, paired-and-fixed simulations, though useful for some applications, cannot be used for the production of mock galaxy catalogues.

Real-time cosmology with SKA

In this work, we investigate what role the redshift-drift data of the Square Kilometre Array (SKA) will play in the cosmological parameter estimation in the future. To test the constraint capability of the redshift-drift data of SKA-only, the Lambda CDM model is chosen as a reference model. We find that using the SKA1 mock data, the Lambda CDM model can be loosely constrained, while the model can be well constrained when the SKA2 mock data are used. When the mock data of SKA are combined with the data of the European Extremely Large Telescope (E-ELT), the constraints can be significantly improved, becoming almost as good as the data combination of the type Ia supernovae observation (SN), the cosmic microwave background observation (CMB), and the baryon acoustic oscillations observation (BAO). Furthermore, we explore the impact of the redshift-drift data of SKA on the basis of SN+CMB+BAO+E-ELT in the Lambda CDM model, the wCDM model, the CPL model, and the HDE model. We find that the redshift-drift measurement of SKA could help to significantly improve the constraints on dark energy and could break the degeneracy between the cosmological parameters. Therefore, we conclude that redshift-drift observation of SKA would provide a good improvement in the cosmological parameter estimation in the future and has the enormous potential to be one of the most competitive cosmological probes in constraining dark energy.

Baryonic effects for weak lensing. Part I. Power spectrum and covariance matrix

Baryonic feedback effects lead to a suppression of the weak lensing angular power spectrum on small scales. The poorly constrained shape and amplitude of this suppression is an important source of uncertainties for upcoming cosmological weak lensing surveys such as Euclid or LSST. In this first paper in a series of two, we use simulations to build a Euclid-like tomographic mock data-set for the cosmic shear power spectrum and the corresponding covariance matrix, which are both corrected for baryonic effects following the baryonification method of [1]. In addition, we develop an emulator to obtain fast predictions of the baryonic power suppression, allowing us to perform a likelihood inference analysis for a standard ΛCDM cosmology with both cosmological and astrophysical parameters. Our main findings are the following: (i) ignoring baryonic effects leads to a greater than 5σ bias on the cosmological parameters Ωm and σ8; (ii) restricting the analysis to the largest scales, that are mostly unaffected by baryons, makes the bias disappear, but results in a blow-up of the Ωm-σ8 contour area by more than a factor of 10; (iii) ignoring baryonic effects on the covariance matrix does not significantly affect cosmological parameter estimates; (iv) while the baryonic suppression is mildly cosmology dependent, this effect does not noticeably modify the posterior contours. Overall, we conclude that including baryonic uncertainties in terms of nuisance parameters results in unbiased and surprisingly tight constraints on cosmology.

Forecast for cosmological parameter estimation with gravitational-wave standard siren observation from the Cosmic Explorer

The third-generation ground-based gravitational-wave (GW) detector, Cosmic Explorer (CE), is scheduled to start its observation in the 2030s. In this paper, we make a forecast for cosmological parameter estimation with gravitational-wave standard siren observation from the CE. We use the simulated GW standard siren data of CE to constrain the ΛCDM, wCDM and CPL models. We combine the simulated GW data with the current cosmological electromagnetic observations including the latest cosmic microwave background anisotropies data from Planck, the optical baryon acoustic oscillation measurements, and the type Ia supernovae observation (Pantheon compilation) to do the analysis. We find that the future standard siren observation from CE will improve the cosmological parameter estimation to a great extent, since the future GW standard siren data can well break the degeneracies generated by the optical observations between various cosmological parameters. We also find that the CE's constraining capability on the cosmological parameters is slightly better than that of the same-type GW detector, the Einstein Telescope. In addition, the synergy between the GW standard siren observation from CE and the 21 cm emission observation from SKA is also discussed.

Euclid preparation

Aims. Our aim is to quantify the impact of systematic effects on the inference of cosmological parameters from cosmic shear. Methods. We present an “end-to-end” approach that introduces sources of bias in a modelled weak lensing survey on a galaxy-by-galaxy level. We propagated residual biases through a pipeline from galaxy properties at one end to cosmic shear power spectra and cosmological parameter estimates at the other end. We did this to quantify how imperfect knowledge of the pipeline changes the maximum likelihood values of dark energy parameters. Results. We quantify the impact of an imperfect correction for charge transfer inefficiency and modelling uncertainties of the point spread function for Euclid, and find that the biases introduced can be corrected to acceptable levels.

Likelihood Methods for CMB Experiments

A great deal of experimental effort is currently being devoted to the precise measurements of the cosmic microwave background (CMB) sky in temperature and polarisation. Satellites, balloon-borne, and ground-based experiments scrutinize the CMB sky at multiple scales, and therefore enable to investigate not only the evolution of the early Universe, but also its late-time physics with unprecedented accuracy. The pipeline leading from time ordered data as collected by the instrument to the final product is highly structured. Moreover, it has also to provide accurate estimates of statistical and systematic uncertainties connected to the specific experiment. In this paper, we review likelihood approaches targeted to the analysis of the CMB signal at different scales, and to the estimation of key cosmological parameters. We consider methods that analyze the data in the spatial (i.e., pixel-based) or harmonic domain. We highlight the most relevant aspects of each approach and compare their performance.

Footprints of Doppler and aberration effects in cosmic microwave background experiments: statistical and cosmological implications

ABSTRACT In the frame of the Solar system, the Doppler and aberration effects cause distortions in the form of mode couplings in the cosmic microwave background (CMB) temperature and polarization power spectra and, hence, impose biases on the statistics derived by the moving observer. We explore several aspects of such biases and pay close attention to their effects on CMB polarization, which, previously, have not been examined in detail. A potentially important bias that we introduce here is boost variance—an additional term in cosmic variance, induced by the observer’s motion. Although this additional term is negligible for whole-sky experiments, in partial-sky experiments it can reach 10 per cent (temperature) to 20 per cent (polarization) of the standard cosmic variance (σ). Furthermore, we investigate the significance of motion-induced power and parity asymmetries in TT, EE, and TE as well as potential biases induced in cosmological parameter estimation performed with whole-sky TTTEEE. Using Planck-like simulations, we find that our local motion induces $\sim 1\!-\!2 {{\ \rm per\ cent}}$ hemispherical asymmetry in a wide range of angular scales in the CMB temperature and polarization power spectra; however, it does not imply any significant amount of parity asymmetry or shift in cosmological parameters. Finally, we examine the prospects of measuring the velocity of the Solar system w.r.t. the CMB with future experiments via the mode coupling induced by the Doppler and aberration effects. Using the CMB TT, EE, and TE power spectra up to ℓ = 4000, the Simons Observatory and CMB-S4 can make a dipole-independent measurement of our local velocity, respectively, at 8.5σ and 20σ.

Positivity in the Sky: Constraining dark energy and modified gravity from the UV

Positivity bounds - the consequences of requiring a unitary, causal, local UV completion - place strong restrictions on theories of dark energy and/or modified gravity. We derive and investigate such bounds for Horndeski scalar-tensor theories and for the first time pair these bounds with a cosmological parameter estimation analysis, using CMB, redshift space distortion, matter power spectrum and BAO measurements from the Planck, SDSS/BOSS and 6dF surveys. Using positivity bounds as theoretical priors, we show that their inclusion in the parameter estimation significantly improves the constraints on dark energy/modified gravity parameters. Considering as an example a specific class of models, which are particularly well-suited to illustrate the constraining power of positivity bounds, we find that these bounds eliminate over 60% of the previously allowed parameter space. We also discuss how combining positivity requirements with additional theoretical priors has the potential to further tighten these constraints: for instance also requiring a subluminal speed of gravitational waves eliminates all but 1% of the previously allowed parameter space.

Baryon Physics and Tight Coupling Approximation in Boltzmann Codes

We provide two derivations of the baryonic equations that can be straightforwardly implemented in existing Einstein–Boltzmann solvers. One of the derivations begins with an action principle, while the other exploits the conservation of the stress-energy tensor. While our result is manifestly covariant and satisfies the Bianchi identities, we point out that this is not the case for the implementation of the seminal work by Ma and Bertschinger and in the existing Boltzmann codes. We also study the tight coupling approximation up to the second order without choosing any gauge using the covariant full baryon equations. We implement the improved baryon equations in a Boltzmann code and investigate the change in the estimate of cosmological parameters by performing an MCMC analysis. With the covariantly correct baryon equations of motion, we find 1 % deviation for the best fit values of the cosmological parameters that should be taken into account. While in this paper, we study the Λ CDM model only, our baryon equations can be easily implemented in other models and various modified gravity theories.

Ensemble Average of Three-dimensional Minkowski Tensors of a Gaussian Random Field in Redshift Space

Abstract We present the ensemble expectation values for the translation-invariant, rank-2 Minkowski tensors in three dimensions, for a linearly redshift-space-distorted Gaussian random field. The Minkowski tensors , are sensitive to global anisotropic signals present within a field, and by extracting these statistics from the low-redshift matter density one can place constraints on the redshift-space distortion parameter β = f/b. We begin by reviewing the calculation of the ensemble expectation values , for isotropic, Gaussian random fields, then consider how these results are modified by the presence of a linearly anisotropic signal. Under the assumption that all fields remain Gaussian, we calculate the anisotropic correction due to redshift-space distortion in a coordinate system aligned with the line of sight, finding inequality between the diagonal elements of , . The ratio of diagonal elements of these matrices provides a set of statistics that are sensitive only to the redshift-space distortion parameter β. We estimate the Fisher information that can be extracted from the Minkowski tensors, and find is more sensitive to β than , and a measurement of accurate to ∼1% can yield a constraint on β. Finally, we discuss the difference between using the matrix elements of the Minkowski tensors directly against measuring the eigenvalues. For the purposes of cosmological parameter estimation we advocate the use of the matrix elements, to avoid spurious anisotropic signals that can be generated by the eigenvalue decomposition.

Optimal estimation of parameters for scalar field in an expanding spacetime exhibiting Lorentz invariance violation

We address the optimal estimation of quantum parameters, in the framework of local quantum estimation theory, for a massive scalar quantum field in the expanding Robertson–Walker universe exhibiting Lorentz invariance violation (LIV). We find that, in the estimation of cosmological parameters, the ultimate bounds to the precision of the Lorentz-invariant massive scalar field can be improved due to the effects of LIV under some appropriate conditions. We also show that, in the Lorentz-invariant massive scalar field and massless scalar field due to LIV backgrounds, the optimal precision can be achieved by choosing the particles with some suitable LIV, cosmological and field parameters. Moreover, in the estimation of LIV parameter during the spacetime expansion, we prove that the appropriate momentum mode of field particles and larger cosmological parameters can provide us a better precision.

Improving cosmological parameter estimation with the future 21 cm observation from SKA

Future observations of 21 cm emission from neutral hydrogen survey will become a promising approach to probe the large scale structure of the Universe. In this paper, we investigate the impacts of Square Kilometre Array (SKA) 21 cm observation on the estimation of cosmological parameters. We use the simulated data of the baryonic acoustic oscillation (BAO) measurements based on the future SKA experiment with the intensity mapping (IM) technique to do the analysis. For the current observations, we use the latest cosmic microwave background (CMB) observation from Planck, the optical BAO measurements, and the Type Ia supernovae (SN) observation (Pantheon compilation). We find that the SKA mock data could break the degeneracy between the matter density and the Hubble constant, further improving the cosmological constraints to a great extent. We also find that the constraint on the equation of state parameters of dark energy could be significantly improved by including the SKA mock data into the cosmological global fit.

Developing a unified pipeline for large-scale structure data analysis with angular power spectra – I. The importance of redshift-space distortions for galaxy number counts

ABSTRACT We develop a cosmological parameter estimation code for (tomographic) angular power spectra analyses of galaxy number counts, for which we include, for the first time, redshift-space distortions (RSDs) in the Limber approximation. This allows for a speed-up in computation time, and we emphasize that only angular scales where the Limber approximation is valid are included in our analysis. Our main result shows that a correct modelling of RSD is crucial not to bias cosmological parameter estimation. This happens not only for spectroscopy-detected galaxies, but even in the case of galaxy surveys with photometric redshift estimates. Moreover, a correct implementation of RSD is especially valuable in alleviating the degeneracy between the amplitude of the underlying matter power spectrum and the galaxy bias. We argue that our findings are particularly relevant for present and planned observational campaigns, such as the Euclid satellite or the Square Kilometre Array, which aim at studying the cosmic large-scale structure and trace its growth over a wide range of redshifts and scales.

Cosmological parameter estimation with future gravitational wave standard siren observation from the Einstein Telescope

In this work, we use the simulated gravitational wave (GW) standard siren data from the future observation of the Einstein Telescope (ET) to constrain various dark energy cosmological models, including the ΛCDM, wCDM, CPL, αDE, GCG, and NGCG models. We also use the current mainstream cosmological electromagnetic observations, i.e., the cosmic microwave background anisotropies data, the baryon acoustic oscillations data, and the type Ia supernovae data, to constrain these models. We find that the GW standard siren data could tremendously improve the constraints on the cosmological parameters for all these dark energy models. For all the cases, the GW standard siren data can be used to break the parameter degeneracies generated by the current cosmological electromagnetic observational data. Therefore, it is expected that the future GW standard siren observation from the ET would play a crucial role in the cosmological parameter estimation in the future. The conclusion of this work is quite solid because it is based on the analysis for various dark energy models.

The Hubble constant determined through an inverse distance ladder including quasar time delays and Type Ia supernovae

Context.The precise determination of the present-day expansion rate of the Universe, expressed through the Hubble constantH0, is one of the most pressing challenges in modern cosmology. Assuming flat ΛCDM,H0inference at high redshift using cosmic microwave background data fromPlanckdisagrees at the 4.4σlevel with measurements based on the local distance ladder made up of parallaxes, Cepheids, and Type Ia supernovae (SNe Ia), often referred to as Hubble tension. Independent cosmological-model-insensitive ways to inferH0are of critical importance.Aims.We apply an inverse distance ladder approach, combining strong-lensing time-delay distance measurements with SN Ia data. By themselves, SNe Ia are merely good indicators of relative distance, but by anchoring them to strong gravitational lenses we can obtain anH0measurement that is relatively insensitive to other cosmological parameters.Methods.A cosmological parameter estimate was performed for different cosmological background models, both for strong-lensing data alone and for the combined lensing + SNe Ia data sets.Results.The cosmological-model dependence of strong-lensingH0measurements is significantly mitigated through the inverse distance ladder. In combination with SN Ia data, the inferredH0consistently lies around 73–74 km s−1Mpc−1, regardless of the assumed cosmological background model. Our results agree closely with those from the local distance ladder, but there is a > 2σtension withPlanckresults, and a ∼1.5σdiscrepancy with results from an inverse distance ladder includingPlanck, baryon acoustic oscillations, and SNe Ia. Future strong-lensing distance measurements will reduce the uncertainties inH0from our inverse distance ladder.

DeepCMB: Lensing reconstruction of the cosmic microwave background with deep neural networks

Next-generation cosmic microwave background (CMB) experiments will have lower noise and therefore increased sensitivity, enabling improved constraints on fundamental physics parameters such as the sum of neutrino masses and the tensor-to-scalar ratio r. Achieving competitive constraints on these parameters requires high signal-to-noise extraction of the projected gravitational potential from the CMB maps. Standard methods for reconstructing the lensing potential employ the quadratic estimator (QE). However, the QE performs suboptimally at the low noise levels expected in upcoming experiments. Other methods, like maximum likelihood estimators (MLE), are under active development. In this work, we demonstrate reconstruction of the CMB lensing potential with deep convolutional neural networks (CNN) - ie, a ResUNet. The network is trained and tested on simulated data, and otherwise has no physical parametrization related to the physical processes of the CMB and gravitational lensing. We show that, over a wide range of angular scales, ResUNets recover the input gravitational potential with a higher signal-to-noise ratio than the QE method, reaching levels comparable to analytic approximations of MLE methods. We demonstrate that the network outputs quantifiably different lensing maps when given input CMB maps generated with different cosmologies. We also show we can use the reconstructed lensing map for cosmological parameter estimation. This application of CNN provides a few innovations at the intersection of cosmology and machine learning. First, while training and regressing on images, we predict a continuous-variable field rather than discrete classes. Second, we are able to establish uncertainty measures for the network output that are analogous to standard methods. We expect this approach to excel in capturing hard-to-model non-Gaussian astrophysical foreground and noise contributions.

Effect of lensing magnification on type Ia supernova cosmology

ABSTRACT Effect of gravitational magnification on the measurement of distance modulus of type Ia supernovae is presented. We investigate a correlation between magnification and Hubble residual to explore how the magnification affects the estimation of cosmological parameters. We estimate magnification of type Ia supernovae in two distinct methods: one is based on convergence mass reconstruction under the weak lensing limit and the other is based on the direct measurement from galaxies distribution. Both magnification measurements are measured from Subaru Hyper Suprime-Cam survey catalogue. For both measurements, we find no significant correlation between Hubble residual and magnification. Furthermore, we correct for the apparent supernovae fluxes obtained by Supernova Legacy Survey 3-yr sample using direct measurement of the magnification. We find $\Omega _{\rm m0}= 0.282 ^{+0.109} _{-0.086}$ and $w = -1.132 ^{+0.571}_{-0.340}$ for supernovae samples corrected for lensing magnification when we use photometric redshift catalogue of Mizuki, while $\Omega _{\rm m0}= 0.267 ^{+0.114} _{-0.088}$ and $w = -1.074 ^{+0.504} _{-0.312}$ for DEmP photo-z catalogue. Therefore, we conclude that the effect of magnification on the supernova cosmology is negligibly small for the current surveys; however, it has to be considered for the future supernova survey like LSST.

Unbiased Cosmological Parameter Estimation from Emission-line Surveys with Interlopers

Abstract The galaxy catalogs generated from low-resolution emission-line surveys often contain both foreground and background interlopers due to line misidentification, which can bias the cosmological parameter estimation. In this paper, we present a method for correcting the interloper bias by using the joint analysis of auto- and cross-power spectra of the main and the interloper samples. In particular, we can measure the interloper fractions from the cross-correlation between the interlopers and survey galaxies, because the true cross-correlation must be negligibly small. The estimated interloper fractions, in turn, remove the interloper bias in the cosmological parameter estimation. For example, in the Hobby–Eberly Telescope Dark Energy Experiment low-redshift (z < 0.5) [O ii] λ3727Å emitters contaminate high-redshift (1.9 < z < 3.5) Lyα line emitters. We demonstrate that the joint-analysis method yields a high signal-to-noise ratio measurement of the interloper fractions while only marginally increasing the uncertainties in the cosmological parameters relative to the case without interlopers. We also show that the same is true for the high-latitude spectroscopic survey of the Wide-field Infrared Survey Telescope mission where contamination occurs between the Balmer-α line emitters at lower redshifts (1.1 < z < 1.9) and oxygen ([O iii] λ5007Å) line emitters at higher redshifts (1.7 < z < 2.8).

Accurately computing weak lensing convergence

ABSTRACT Weak lensing will play an important role in future cosmological surveys, including e.g. Euclid and SKA. Sufficiently accurate theoretical predictions are important for correctly interpreting these surveys and hence for extracting correct cosmological parameter estimations. We quantify for the first time in a relativistic setting how many post-Born and lens–lens coupling corrections are required for sub-per cent accuracy of the theoretical weak lensing convergence for $z$ ≤ 2 (the primary weak lensing range for Euclid and SKA). We do this by ray tracing through a fully relativistic exact solution of the Einstein field equations, which consists of randomly packed mass-compensated underdensities of realistic amplitudes. We find that including lens–lens coupling terms and post-Born corrections up to second and third order respectively is sufficient for sub-per cent accuracy of the convergence along $94{{\ \rm per\ cent}}$ of the studied light rays. We also find that a significant percentage of the studied rays have post-Born corrections of size over $10{{\ \rm per\ cent}}$ of the usual gravitational convergence, κ(1), and several rays even have post-Born corrections several times the size of κ(1) at $z$ = 2.

The effect on cosmological parameter estimation of a parameter dependent covariance matrix

Cosmological large-scale structure analyses based on two-point correlation functions often assume a Gaussian likelihood function with a fixed covariance matrix. We study the impact on cosmological parameter estimation of ignoring the parameter dependence of this covariance matrix, focusing on the particular case of joint weak-lensing and galaxy clustering analyses. Using a Fisher matrix formalism (calibrated against exact likelihood evaluation in particular simple cases), we quantify the effect of using a parameter dependent covariance matrix on both the bias and variance of the parameters. We confirm that the approximation of a parameter-independent covariance matrix is exceptionally good in all realistic scenarios. The information content in the covariance matrix (in comparison with the two point functions themselves) does not change with the fractional sky coverage. Therefore the increase in information due to the parameter dependent covariance matrix becomes negligible as the number of modes increases. Even for surveys covering less than 1% of the sky, this effect only causes a bias of up to of order 10% of the statistical uncertainties, with a misestimation of the parameter uncertainties at the same level or lower. The effect will only be smaller with future large-area surveys. Thus for most analyses the effect of a parameter-dependent covariance matrix can be ignored both in terms of the accuracy and precision of the recovered cosmological constraints.