arXiv subjects

Héctor Gil-Marín

Publications and source records attributed to Héctor Gil-Marín.

At least 55 records · Page 3Linked to original sources

arXiv2020

Blind Observers of the Sky

The concept of blind analysis, a key procedure to remove the human-based systematic error called confirmation bias, has long been an integral part of data analysis in many research areas. In cosmology, blind analysis is recently making its entrance, as the field progresses into a fully fledged high-precision science. The credibility, reliability and robustness of results from future sky-surveys will dramatically increase if the effect of confirmation bias is kept under control by using an appropriate blinding procedure. Here, we present a catalog-level blinding scheme for galaxy clustering data apt to be used in future spectroscopic galaxy surveys. We shift the individual galaxy positions along the line of sight based on 1) a geometric shift mimicking the Alcock-Paczynski effect and 2) a perturbative shift akin to redshift-space distortions. This procedure has several advantages. After combining the two steps above, it is almost impossible to accidentally unblind. The procedure induces a shift in cosmological parameters without changing the galaxies' angular positions, hence without interfering with the effects of angular systematics. Since the method is applied at catalog level, there is no need to adopt several blinding schemes tuned to different summary statistics, likelihood choices or types of analyses. By testing the method on mock catalogs and the BOSS DR12 catalog we demonstrate its performance in blinding galaxy clustering data for relevant cosmological parameters sensitive to the background expansion rate and the growth rate of structures.

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arXiv2020

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR16 luminous red galaxy and emission line galaxy samples: cosmic distance and structure growth measurements using multiple tracers in configuration space

We perform a multi-tracer analysis using the complete Sloan Digital Sky Survey IV (SDSS-IV) extended Baryon Oscillation Spectroscopic Survey (eBOSS) DR16 luminous red galaxy (LRG) and the DR16 emission line galaxy (ELG) samples in the configuration space, and successfully detect a cross correlation between the two samples, and find the growth rate to be $fσ_8=0.342 \pm 0.085$ ($\sim25$ per cent accuracy) from the cross sample alone. We perform a joint measurement of the baryonic acoustic oscillation (BAO) and redshift space distortion (RSD) parameters at a single effective redshift of $z_{\rm eff}= 0.77$, using the auto- and cross-correlation functions of the LRG and ELG samples, and find that the comoving angular diameter distance $D_M(z_{\rm eff})/r_d = 18.85\pm 0.38$, the Hubble distance $D_H(z_{\rm eff})/r_d = 19.64 \pm 0.57$, and $fσ_8(z_{\rm eff}) = 0.432 \pm 0.038$, which is consistent with a $Λ$CDM model at $68\%$ CL. Compared to the single-tracer analysis on the LRG sample, the Figure of Merit (FoM) of $α_{\perp}, α_{||}$ and $fσ_8$ is improved by a factor of $1.11$ in our multi-tracer analysis, and in particular, the statistical uncertainty of $fσ_8$ is reduced by $11.6 \%$.

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arXiv2020

The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Pairwise-Inverse-Probability and Angular Correction for Fibre Collisions in Clustering Measurements

The completed eBOSS catalogues contain redshifts of 344080 QSOs over 0.8<z<2.2 covering 4808 deg$^2$, 174816 LRGs over 0.6<z<1.0 covering 4242 deg$^2$ and 173736 ELGs over 0.6<z<1.1 covering 1170 deg$^2$ in order to constrain the expansion history of the Universe and the growth rate of structure through clustering measurements. Mechanical limitations of the fibre-fed spectrograph on the Sloan telescope prevent two fibres being placed closer than 62", the fibre-collision scale, in a single pass of the instrument on the sky. These `fibre collisions' strongly correlate with the intrinsic clustering of targets and can bias measurements of the two-point correlation function resulting in a systematic error on the inferred values of the cosmological parameters. We combine the new techniques of pairwise-inverse-probability weighting and the angular up-weighting to correct the clustering measurements for the effect of fibre collisions. Using mock catalogues we show that our corrections provide unbiased measurements, within data precision, of both the projected correlation function $w_p$ and the multipoles $ξ^l$ of the redshift-space correlation functions down to 0.1Mpc/h, regardless of the tracer type. We apply the corrections to the eBOSS DR16 catalogues. We find that, on scales greater than s~20Mpc/h for $ξ^l$, as used to make BAO and large-scale RSD measurements, approximate methods such as Nearest-Neighbour up-weighting are sufficiently accurate given the statistical errors of the data. Using the PIP method, for the first time for a spectroscopic program of the Sloan Digital Sky Survey we are able to successfully access the 1-halo term in the 3D clustering measurements down to ~0.1Mpc/h scales. Our results will therefore allow studies that use the small-scale clustering measurements to strengthen the constraints on both cosmological parameters and the halo-occupation distribution models.

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arXiv2020

GEOMAX: beyond linear compression for 3pt galaxy clustering statistics

We present the GEOMAX algorithm and its Python implementation for a two-step compression of bispectrum measurements. The first step groups bispectra by the geometric properties of their arguments; the second step then maximises the Fisher information with respect to a chosen set of model parameters in each group. The algorithm only requires the derivatives of the data vector with respect to the parameters and a small number of mock data, producing an effective, non-linear compression. By applying GEOMAX to bispectrum monopole measurements from BOSS DR12 CMASS redshift-space galaxy clustering data, we reduce the $68\%$ credible intervals for the inferred parameters $\left(b_1,b_2,f,σ_8\right)$ by $\left(50.4\%,56.1\%,33.2\%,38.3\%\right)$ with respect to standard MCMC on the full data vector. We run the analysis and comparison between compression methods over one hundred galaxy mocks to test the statistical significance of the improvements. On average GEOMAX performs $\sim15\%$ better than geometrical or maximal linear compression alone and is consistent with being lossless. Given its flexibility, the GEOMAX approach has the potential to optimally exploit three-point statistics of various cosmological probes like weak lensing or line-intensity maps from current and future cosmological data-sets such as DESI, Euclid, PFS and SKA.

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arXiv2019

Beyond two-point statistics: using the minimum spanning tree as a tool for cosmology

Cosmological studies of large-scale structure have relied on two-point statistics, not fully exploiting the rich structure of the cosmic web. In this paper we show how to capture some of this cosmic web information by using the minimum spanning tree (MST), for the first time using it to estimate cosmological parameters in simulations. Discrete tracers of dark matter such as galaxies, $N$-body particles or haloes are used as nodes to construct a unique graph, the MST, that traces skeletal structure. We study the dependence of the MST on cosmological parameters using haloes from a suite of COLA simulations with a box size of $250\ h^{-1}{\rm Mpc}$, varying the amplitude of scalar fluctuations $\left(A_{\rm s}\right)$, matter density $\left(Ω_{\rm m}\right)$, and neutrino mass $\left(\sum m_ν\right)$. The power spectrum $P$ and bispectrum $B$ are measured for wavenumbers between $0.125$ and $0.5$ $h{\rm Mpc}^{-1}$, while a corresponding lower cut of $\sim12.6$ $h^{-1}{\rm Mpc}$ is applied to the MST. The constraints from the individual methods are fairly similar but when combined we see improved $1σ$ constraints of $\sim 17\%$ ($\sim 12\%$) on $Ω_{\rm m}$ and $\sim 12\%$ ($\sim 10\%$) on $A_{\rm s}$ with respect to $P$ ($P+B$) thus showing the MST is providing additional information. The MST can be applied to current and future spectroscopic surveys (BOSS, DESI, Euclid, PSF, WFIRST, and 4MOST) in 3D and photometric surveys (DES and LSST) in tomographic shells to constrain parameters and/or test systematics.

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arXiv2019

The Cosmological Analysis of the SDSS/BOSS data from the Effective Field Theory of Large-Scale Structure

The Effective Field Theory of Large-Scale Structure (EFTofLSS) is a formalism that allows us to predict the clustering of Cosmological Large-Scale Structure in the mildly non-linear regime in an accurate and reliable way. After validating our technique against several sets of numerical simulations, we perform the analysis for the cosmological parameters of the DR12 BOSS data. We assume $Λ$CDM, a fixed value of the baryon/dark-matter ratio, $Ω_b/Ω_c$, and of the tilt of the primordial power spectrum, $n_s$, and no significant input from numerical simulations. By using the one-loop power spectrum multipoles, we measure the primordial amplitude of the power spectrum, $A_s$, the abundance of matter, $Ω_m$, and the Hubble parameter, $H_0$, to about $13\%$, $3.2\%$ and $3.2\%$ respectively, obtaining $\ln(10^{10}As)=2.72\pm 0.13$, $Ω_m=0.309\pm 0.010$, $H_0=68.5\pm 2.2$ km/(s Mpc) at 68\% confidence level. If we then add a CMB prior on the sound horizon, the error bar on $H_0$ is reduced to $1.6\%$. These results are a substantial qualitative and quantitative improvement with respect to former analyses, and suggest that the EFTofLSS is a powerful instrument to extract cosmological information from Large-Scale Structure.

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arXiv2019

Redshift-weighted constraints on primordial non-Gaussianity from the clustering of the eBOSS DR14 quasars in Fourier space

We present constraints on local primordial non-Gaussianity (PNG), parametrized through $f^{\rm loc}_{\rm NL}$, using the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 14 quasar sample. We measure and analyze the anisotropic clustering of the quasars in Fourier space, testing for the scale-dependent bias introduced by primordial non-Gaussianity on large scales. We derive and employ a power spectrum estimator using optimal weights that account for the redshift evolution of the PNG signal. We find constraints of $-51<f^{\rm loc}_{\rm NL}<21$ at 95% confidence level. These are amont the tightest constraints from Large Scale Structure (LSS) data. Our redshift weighting improves the error bar by 15% in comparison to the unweighted case. If quasars have lower response to PNG, the constraint degrades to $-81<f^{\rm loc}_{\rm NL}<26$, with a 40% improvement over the standard approach. We forecast that the full eBOSS dataset could reach $σ_{f^{\rm loc}_{\rm NL}}\simeq 5\text{-}8$ using optimal methods and full range of scales.

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arXiv2019

Enhancing BOSS bispectrum cosmological constraints with maximal compression

We apply two compression methods to the galaxy power spectrum monopole/quadrupole and bispectrum monopole measurements from the BOSS DR12 CMASS sample. Both methods reduce the dimension of the original data-vector to the number of cosmological parameters considered, using the Karhunen-Loève algorithm with an analytic covariance model. In the first case, we infer the posterior through MCMC sampling from the likelihood of the compressed data-vector (MC-KL). The second, faster option, works by first Gaussianising and then orthogonalising the parameter space before the compression; in this option (G-PCA) we only need to run a low-resolution preliminary MCMC sample for the Gaussianization to compute our posterior. Both compression methods accurately reproduce the posterior distributions obtained by standard MCMC sampling on the CMASS dataset for a $k$-space range of $0.03-0.12\,h/\mathrm{Mpc}$. The compression enables us to increase the number of bispectrum measurements by a factor of $\sim 23$ over the standard binning (from 116 to 2734 triangles used), which is otherwise limited by the number of mock catalogues available. This reduces the $68\%$ credible intervals for the parameters $\left(b_1,b_2,f,σ_8\right)$ by $\left(-24.8\%,-52.8\%,-26.4\%,-21\%\right)$, respectively. The best-fit values we obtain are $(b_1=2.31\pm0.17,b_2=0.77\pm0.19,$ $f(z_{\mathrm{CMASS}})=0.67\pm0.06,σ_8(z_{\mathrm{CMASS}})=0.51\pm0.03)$. Using these methods for future redshift surveys like DESI, Euclid and PFS will drastically reduce the number of simulations needed to compute accurate covariance matrices and will facilitate tighter constraints on cosmological parameters.

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arXiv2019

Geometrical compression: a new method to enhance the BOSS galaxy bispectrum monopole constraints

We present a novel method to compress galaxy clustering three-point statistics and apply it to redshift space galaxy bispectrum monopole measurements from BOSS DR12 CMASS data considering a $k$-space range of $0.03-0.12\,h/\mathrm{Mpc}$. The method consists in binning together bispectra evaluated at sets of wave-numbers forming closed triangles with similar geometrical properties: the area, the cosine of the largest angle and the ratio between the cosines of the remaining two angles. This enables us to increase the number of bispectrum measurements for example by a factor of $23$ over the standard binning (from 116 to 2734 triangles used), which is otherwise limited by the number of mock catalogues available to estimate the covariance matrix needed to derive parameter constraints. The $68\%$ credible intervals for the inferred parameters $\left(b_1,b_2,f,σ_8\right)$ are thus reduced by $\left(-39\%,-49\%,-29\%,-22\%\right)$, respectively. We find very good agreement with the posteriors recently obtained by alternative maximal compression methods. This new method does not require the a-priori computation of the data-vector covariance matrix and has the potential to be directly applicable to other three-point statistics (e.g. glaxy clustering, weak gravitational lensing, 21 cm emission line) measured from future surveys such as DESI, Euclid, PFS and SKA.

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arXiv2018

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights

We develop a new method, which is based on the optimal redshift weighting scheme, to extract the maximal tomographic information of baryonic acoustic oscillations (BAO) and redshift space distortions (RSD) from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 14 quasar (DR14Q) survey. We validate our method using the EZ mocks, and apply our pipeline to the eBOSS DR14Q sample in the redshift range of $0.8<z<2.2$. We report a joint measurement of $fσ_8$ and two-dimensional BAO parameters $D_{\rm A}$ and $H$ at four effective redshifts of $z_{\rm eff}=0.98, 1.23, 1.52$ and $1.94$, and provide the full data covariance matrix. Using our measurement combined with BOSS DR12, MGS and 6dFGS BAO measurements, we find that the existence of dark energy is supported by observations at a $7.4σ$ significance level. Combining our measurement with BOSS DR12 and Planck observations, we constrain the gravitational growth index to be $γ=0.580\pm0.082$, which is fully consistent with the prediction of general relativity. This paper is part of a set that analyses the eBOSS DR14 quasar sample.

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arXiv2018

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: anisotropic clustering analysis in configuration-space

We explore the cosmological implications of anisotropic clustering measurements of the quasar sample from Data Release 14 of the Sloan Digital Sky Survey IV Extended Baryon Oscillation Spectroscopic Survey (eBOSS) in configuration space. The $\sim 147,000$ quasar sample observed by eBOSS offers a direct tracer of the density field and bridges the gap of previous BAO measurements between redshift $0.8<z<2.2$. By analysing the two-point correlation function characterized by clustering wedges $ξ_{\rm w_i}(s)$ and multipoles $ξ_{\ell}(s)$, we measure the angular diameter distance, Hubble parameter and cosmic structure growth rate. We define a systematic error budget for our measurements based on the analysis of $N$-body simulations and mock catalogues. Based on the DR14 large scale structure quasar sample at the effective redshift $z_{\rm eff}=1.52$, we find the growth rate of cosmic structure $fσ_8(z_{\rm eff})=0.396\pm 0.079$, and the geometric parameters $D_{\rm V}(z)/r_{\rm d}=26.47\pm 1.23$, and $F_{\rm AP}(z)=2.53\pm 0.22$, where the uncertainties include both statistical and systematic errors. These values are in excellent agreement with the best-fitting standard ${\rm ΛCDM}$ model to the latest cosmic microwave background data from Planck.

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arXiv2018

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: Anisotropic Baryon Acoustic Oscillations measurements in Fourier-space with optimal redshift weights

We present a measurement of the anisotropic and isotropic Baryon Acoustic Oscillations (BAO) from the extended Baryon Oscillation Spectroscopic Survey Data Release 14 quasar sample with optimal redshift weights. Applying the redshift weights improves the constraint on the BAO dilation parameter $α(z_{\rm eff})$ by 17\%. We reconstruct the evolution history of the BAO distance indicators in the redshift range of $0.8<z<2.2$. This paper is part of a set that analyses the eBOSS DR14 quasar sample.

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arXiv2018

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: Measuring the anisotropic Baryon Acoustic Oscillations with redshift weights

We present an anisotropic analysis of Baryon Acoustic Oscillation (BAO) signal from the SDSS-IV extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 14 (DR14) quasar sample. The sample consists of 147,000 quasars distributed over a redshift range of $0.8 < z < 2.2$. We apply the redshift weights technique to the clustering of quasars in this sample and achieve a 4.6 per cent measurement of the angular distance measurement $D_M$ at $z = 2.2$ and Hubble parameter $H$ at $z=0.8$. We parameterize the distance-redshift relation, relative to a fiducial model, as a quadratic expansion. The coefficients of this expansion are used to reconstruct the distance-redshift relation and obtain distance and Hubble parameter measurements at all redshifts within the redshift range of the sample. Reporting the result at two characteristic redshifts, we determine $D_M(z=1) = 3405\pm305 \ (r_{\rm d} / r_{\rm d, fid}) \ {\rm Mpc}$, $H(z=1) = 120.7\pm 7.3 \ (r_{\rm d,fid} / r_{\rm d}) \ {\rm km} \ {\rm s}^{-1}{\rm Mpc}^{-1}$ and $D_M(z=2) = 5325\pm249 \ (r_{\rm d} / r_{\rm d, fid}) \ {\rm Mpc}$, $H(z=2) = 189.9\pm 32.9 \ (r_{\rm d,fid} / r_{\rm d}) \ {\rm km} \ {\rm s}^{-1}{\rm Mpc}^{-1}$. These measurements are highly correlated. We assess the outlook of BAO analysis from the final quasar sample by testing the method on a set of mocks that mimic the noise level in the final sample. We demonstrate on these mocks that redshift weighting shrinks the measurement error by over 25 per cent on average. We conclude redshift weighting can bring us closer to the cosmological goal of the final quasar sample.

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arXiv2018

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: structure growth rate measurement from the anisotropic quasar power spectrum in the redshift range $0.8<z<2.2$

We analyse the clustering of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 14 quasar sample (DR14Q). We measure the redshift space distortions using the power spectrum monopole, quadrupole and hexadecapole inferred from 148,659 quasars between redshifts 0.8 and 2.2 covering a total sky footprint of 2112.9 deg$^2$. We constrain the logarithmic growth of structure times the amplitude of dark matter density fluctuations, $fσ_8$, and the Alcock-Paczynski dilation scales which allow constraints to be placed on the angular diameter distance $D_A(z)$ and the Hubble $H(z)$ parameter. At the effective redshift of $z_{\rm eff}=1.52$, $fσ_8(z_{\rm eff})=0.420\pm0.076$, $H(z_{\rm eff})=[162\pm 12]\, (r_s^{\rm fid}/r_s)\,{\rm km\, s}^{-1}{\rm Mpc}^{-1}$, and $D_A(z_{\rm eff})=[1.85\pm 0.11]\times10^3\,(r_s/r_s^{\rm fid})\,{\rm Mpc}$, where $r_s$ is the comoving sound horizon at the baryon drag epoch and the superscript `fid' stands for its fiducial value. The errors take into account the full error budget, including systematics and statistical contributions. These results are in full agreement with the current $Λ$-Cold Dark Matter ($Λ$CDM) cosmological model inferred from Planck measurements. Finally, we compare our measurements with other eBOSS companion papers and find excellent agreement, demonstrating the consistency and complementarity of the different methods used for analysing the data.

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arXiv2017

The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: tomographic BAO analysis of DR12 combined sample in configuration space

We perform a tomographic baryon acoustic oscillations analysis using the two-point galaxy correlation function measured from the combined sample of BOSS DR12, which covers the redshift range of $0.2<z<0.75$. Splitting the sample into multiple overlapping redshift slices to extract the redshift information of galaxy clustering, we obtain a measurement of $D_A(z)/r_d$ and $H(z)r_d$ at nine effective redshifts with the full covariance matrix calibrated using MultiDark-Patchy mock catalogues. Using the reconstructed galaxy catalogues, we obtain the precision of $1.3\%-2.2\%$ for $D_A(z)/r_d$ and $2.1\%-6.0\%$ for $H(z)r_d$. To quantify the gain from the tomographic information, we compare the constraints on the cosmological parameters using our 9-bin BAO measurements, the consensus 3-bin BAO and RSD measurements at three effective redshifts in \citet{Alam2016}, and the non-tomographic (1-bin) BAO measurement at a single effective redshift. Comparing the 9-bin with 1-bin constraint result, it can improve the dark energy Figure of Merit by a factor of 1.24 for the Chevallier-Polarski-Linder parametrisation for equation of state parameter $w_{\rm DE}$. The errors of $w_0$ and $w_a$ from 9-bin constraints are slightly improved when compared to the 3-bin constraint result.

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arXiv2016

The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: tomographic BAO analysis of DR12 combined sample in Fourier space

We perform a tomographic baryon acoustic oscillations (BAO) analysis using the monopole, quadrupole and hexadecapole of the redshift-space galaxy power spectrum measured from the pre-reconstructed combined galaxy sample of the completed Sloan Digital Sky Survey (SDSS-III) Baryon Oscillation Spectroscopic Survey (BOSS) Data Release (DR)12 covering the redshift range of $0.20<z<0.75$. By allowing for overlap between neighbouring redshift slices, we successfully obtained the isotropic and anisotropic BAO distance measurements within nine redshift slices to a precision of $1.5\%-3.4\%$ for $D_V/r_d$, $1.8\% -4.2\%$ for $D_A/r_d$ and $3.7\% - 7.5\%$ for $H \ r_d$, depending on effective redshifts. We provide our BAO measurement of $D_A/r_d$ and $H \ r_d$ with the full covariance matrix, which can be used for cosmological implications. Our measurements are consistent with those presented in \citet{Acacia}, in which the BAO distances are measured at three effective redshifts. We constrain dark energy parameters using our measurements, and find an improvement of the Figure-of-Merit of dark energy in general due to the temporal BAO information resolved. This paper is part of a set that analyses the final galaxy clustering dataset from BOSS.

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arXiv2016

The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Cosmological implications of the Fourier space wedges of the final sample

We extract cosmological information from the anisotropic power spectrum measurements from the recently completed Baryon Oscillation Spectroscopic Survey (BOSS), extending the concept of clustering wedges to Fourier space. Making use of new FFT-based estimators, we measure the power spectrum clustering wedges of the BOSS sample by filtering out the information of Legendre multipoles l > 4. Our modelling of these measurements is based on novel approaches to describe non-linear evolution, bias, and redshift-space distortions, which we test using synthetic catalogues based on large-volume N-body simulations. We are able to include smaller scales than in previous analyses, resulting in tighter cosmological constraints. Using three overlapping redshift bins, we measure the angular diameter distance, the Hubble parameter, and the cosmic growth rate, and explore the cosmological implications of our full shape clustering measurements in combination with CMB and SN Ia data. Assuming a ΛCDM cosmology, we constrain the matter density to Ω_m = 0.311 -0.010 +0.009 and the Hubble parameter to H_0 = 67.6 -0.6 +0.7 km s^-1 Mpc^-1, at a confidence level (CL) of 68 per cent. We also allow for non-standard dark energy models and modifications of the growth rate, finding good agreement with the ΛCDM paradigm. For example, we constrain the equation-of-state parameter to w = -1.019 -0.039 +0.048. This paper is part of a set that analyses the final galaxy clustering dataset from BOSS. The measurements and likelihoods presented here are combined with others in Alam et al. 2016 to produce the final cosmological constraints from BOSS.

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arXiv2016

Optimal Redshift Weighting For Redshift Space Distortions

The low statistical errors on cosmological parameters promised by future galaxy surveys will only be realised with the development of new, fast, analysis methods that reduce potential systematic problems to low levels. We present an efficient method for measuring the evolution of the growth of structure using Redshift Space Distortions (RSD), that removes the need to make measurements in redshift shells. We provide sets of galaxy-weights that cover a wide range in redshift, but are optimised to provide differential information about cosmological evolution. These are derived to optimally measure the coefficients of a parameterisation of the redshift-dependent matter density, which provides a framework to measure deviations from the concordance $Λ$CDM cosmology, allowing for deviations in both geometric and/or growth. We test the robustness of the weights by comparing with alternative schemes and investigate the impact of galaxy bias. We extend the results to measure the combined anisotropic Baryon Acoustic Oscillation (BAO) and RSD signals.

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