Planck CMB Research Articles

ΛCDM model against gravity-thermodynamics conjecture: observational constraints after DESI 2024

In the context of the gravity-thermodynamics conjecture based on the Tsallis entropy-area relation, we investigate the standard ΛCDM cosmology and examine some potential deviations from it. Utilizing recent updates from geometrical datasets, including the DESI BAO measurements (2024), Planck CMB anisotropy measurements (2018), and the Pantheon+ catalogue for SNIa (2022), we conduct a thorough analysis via the window of Tsallis cosmology. In the first step, our analysis reveals no significant deviation from the standard model when using DESI BAO data alone, Pantheon+ data alone, or a combination of both. In the next step, we incorporate all datasets by adding the CMB data to our analysis, indicating a potential deviation from the standard model within the framework of Tsallis cosmology. Imposing the Planck prior to the sound horizon at the baryon drag epoch, we observe support for the standard model and consistency between our constraints on the Hubble constant and the Planck value. Finally, we compare the Tsallis and ΛCDM cosmologies using the Akaike Information Criterion (AIC).

Measuring the matter fluctuations in the Local Universe with the ALFALFA catalogue

Abstract The standard model of cosmology describes the matter fluctuations through the matter power spectrum, where σ8 ≡ σ8, 0 ≡ σ8(z = 0), defined at the scale of 8 h−1 Mpc, acts as a normalisation parameter. Currently, the literature reports measurements of σ8 analysing different cosmic tracers, where some of these results were obtained assuming a fiducial cosmology. In this study we measure, in a model-independent approach, the matter fluctuations in the Local Universe using HI extragalactic sources mapped by the ALFALFA survey. Our analyses allow us to test the standard cosmological model under extreme conditions in the highly non-linear Local Universe, quantifying the amplitude of the matter fluctuations there. Our work directly measures σ8 using the 3-dimensional distances of the HI sources determined by the ALFALFA survey without assuming a fiducial cosmology, resulting in a robust model-independent measurement of σ8. Our methodology involves the construction of suitable mock catalogues to simulate the large scale structure features observed in the data, applying the 2-point correlation function, and making use of Markov Chain Monte Carlo methods to estimate the parameters. Analysing these data we measure σ8 = 0.78 ± 0.04 for h = 0.6727, σ8 = 0.80 ± 0.05 for h = 0.698, and σ8 = 0.83 ± 0.05 for h = 0.7304. Considering the data pairs (σ8, H0) from the Planck CMB and ACT CMB-lensing analyses, our measurement agrees with them within 1 σ confidence level. From a model-independent perspective, we find that the scale where the matter fluctuation is 1, is R = 7.2 ± 1.5 Mpc.

An analysis of parameter compression and Full-Modeling techniques with Velocileptors for DESI 2024 and beyond

In anticipation of forthcoming data releases of current and future spectroscopic surveys, we present the validation tests and analysis of systematic effects within velocileptors modeling pipeline when fitting mock data from the AbacusSummit N-body simulations. We compare the constraints obtained from parameter compression methods to the direct fitting (Full-Modeling) approaches of modeling the galaxy power spectra, and show that the ShapeFit extension to the traditional template method is consistent with the Full-Modeling method within the standard ΛCDM parameter space. We show the dependence on scale cuts when fitting the different redshift bins using the ShapeFit and Full-Modeling methods. We test the ability to jointly fit data from multiple redshift bins as well as joint analysis of the pre-reconstruction power spectrum with the post-reconstruction BAO correlation function signal. We further demonstrate the behavior of the model when opening up the parameter space beyond ΛCDM and also when combining likelihoods with external datasets, namely the Planck CMB priors. Finally, we describe different parametrization options for the galaxy bias, counterterm, and stochastic parameters, and employ the halo model in order to physically motivate suitable priors that are necessary to ensure the stability of the perturbation theory.

Critical look at the cosmological neutrino mass bound

Cosmological neutrino mass bounds are becoming increasingly stringent. The latest limit within ΛCDM from Planck 2018+ACT lensing+DESI is ∑mν<0.072 eV at 95% CL, very close to the minimum possible sum of neutrino masses (∑mν>0.06 eV), hinting at vanishing or even “negative” cosmological neutrino masses. In this context, it is urgent to carefully evaluate the origin of these cosmological constraints. In this paper, we investigate the robustness of these results in three ways: (i) we check the role of potential anomalies in Planck CMB and DESI BAO data; (ii) we compare the results for frequentist and Bayesian techniques, as very close to physical boundaries subtleties in the derivation and interpretation of constraints can arise; (iii) we investigate how deviations from ΛCDM, potentially alleviating these anomalies, can alter the constraints. From a profile likelihood analysis, we derive constraints in agreement at the ∼10% level with Bayesian posteriors. We find that the weak preference for negative neutrino masses is mostly present for Planck 18 data, affected by the well-known “lensing anomaly.” It disappears when the new Planck 2020 HiLLiPoP is used, leading to significantly weaker constraints. Additionally, the pull toward negative masses in DESI data stems from the z=0.7 bin, which contains a BAO measurement in ∼3σ tension with Planck expectations. Without this bin, and in combination with HiLLiPoP, the bound relaxes to ∑mν<0.11 eV at 95% CL. The recent preference for dynamical dark energy alleviates this tension and further weakens the bound. As we are at the dawn of a neutrino mass discovery from cosmology, it will be very exciting to see if this trend is confirmed by future data. Published by the American Physical Society 2024

CombineHarvesterFlow: Joint Probe Analysis Made Easy with Normalizing Flows

We show how to efficiently sample the joint posterior of two non-covariant experiments with a large set of nuisance parameters. Specifically, we train an ensemble of normalizing flows to learn the posterior distribution of both experiments. Once trained, we can use the flows to reweight 𝒪(109) samples from both measurements to compute the joint posterior in seconds – saving up to 𝒪(1) ton of CO2 per Monte Carlo run. Using this new technique we find joint constraints between the Dark Energy Survey 3×2 point measurement, South Pole Telescope and Planck CMB lensing and a BOSS direct fit full shape analyses, for the first time. We find and S8=0.79−0.01+0.01. We release a public package called {} (https://github.com/pltaylor16/CombineHarvesterFlow) which performs these calculations.

DESI 2024: reconstructing dark energy using crossing statistics with DESI DR1 BAO data

We implement Crossing Statistics to reconstruct in a model-agnostic manner the expansion history of the universe and properties of dark energy, using DESI Data Release 1 (DR1) BAO data in combination with one of three different supernova compilations (PantheonPlus, Union3, and DES-SN5YR) and Planck CMB observations. Our results hint towards an evolving and emergent dark energy behaviour, with negligible presence of dark energy at z ≳ 1, at varying significance depending on data sets combined. In all these reconstructions, the cosmological constant lies outside the 95% confidence intervals for some redshift ranges. This dark energy behaviour, reconstructed using Crossing Statistics, is in agreement with results from the conventional w 0–w a dark energy equation of state parametrization reported in the DESI Key cosmology paper. Our results add an extensive class of model-agnostic reconstructions with acceptable fits to the data, including models where cosmic acceleration slows down at low redshifts. We also report constraints on H 0 r d from our model-agnostic analysis, independent of the pre-recombination physics.

Sound horizon independent constraints on early dark energy: the role of supernova data

We assess the consistency of cosmological models that alter the size of the sound horizon at last scattering to resolve the Hubble tension with data from ACT + Planck CMB lensing, Big Bang Nucleosynthesis, and supernova data from Pantheon or Pantheon+. We use early dark energy (EDE) as an example model but conclude that the results could apply to other similar models. We constrain ΛCDM and EDE with these data finding that while they can constrain ΛCDM very tightly, EDE opens up the parameter space significantly and allows H 0 > 72 km s-1Mpc-1. We combine these data with measurements from ACT + Planck TT650TEEE CMB primary anisotropy and galaxy baryon acoustic oscillations, and find that overall, EDE fits these data better than ΛCDM at ≈ 2σ. However, the fit to specifically the sound-horizon-independent measurements is worse for EDE than ΛCDM. We assess this increase in χ 2 coming from the sound-horizon-independent measurements and find that the best-fit model is still consistent with a random statistical fluctuation even with H 0 values around 72 km s-1Mpc-1. Finally, we find that supernova data play an important role in constraining EDE-like models with higher preferred values of Ω m , as preferred by Pantheon+, reducing the allowed parameter space for H 0 values greater than 70 km s-1Mpc-1.

Effect of redshift bin mismatch on the cross correlation between the DESI Legacy Imaging Survey and the Planck CMB lensing potential

Aims. We study the importance of precise modelling of the photometric redshift error distributions when estimating parameters from cross-correlation measurements. We present a working example of the scattering matrix formalism to correct for the effects of galaxies ending in wrong redshift bins due to their photometric redshift errors. Methods. We measured the angular galaxy auto-power spectrum and cross-power spectrum in four tomographic bins with the redshift intervals z = [0.0, 0.3, 0.45, 0.6, 0.8] from the cross-correlation of the Planck cosmic microwave background lensing potential and the photometric galaxy catalogue from the Dark Energy Spectroscopic Instrument Legacy Imaging Survey Data Release 8. We estimated the galaxy linear bias and the amplitude of cross correlation using maximum likelihood estimation to put constraints on the σ8 parameter. Results. We show that the modified Lorentzian function used to fit the photometric redshift error distribution performs well only near the peaks of the distribution. We adopt a sum of Gaussians model to capture the broad tails of the error distribution. Our sum of Gaussians model yields values of the cross-correlation amplitude that are ∼2–5 σ smaller than those expected based on the Λ cold dark matter (ΛCDM) model. We compute the σ8 parameter after correcting for the redshift bin mismatch of objects following the scattering matrix approach. The σ8 parameter becomes consistent with ΛCDM model in the last tomographic bin but shows a tension of ∼1–3 σ in other redshift bins.

Cosmological constraints on curved quintessence

Dynamical dark energy has gained renewed interest due to recent theoretical and observational developments. In the present paper, we focus on a string-motivated dark energy set-up, and perform a detailed cosmological analysis of exponential quintessence with potential V = V 0 e λϕ -, allowing for non-zero spatial curvature. We first gain some physical intuition into the full evolution of such a scenario by analysing the corresponding dynamical system. Then, we test the model using a combination of Planck CMB data, DESI BAO data, as well as recent supernovae datasets. For the model parameter λ, we obtain a preference for nonzero values: λ = 0.48+0.28 -0.21, 0.68+0.31 -0.20, 0.77+0.18 -0.15 at 68% C.L. when combining CMB+DESI with Pantheon+, Union3 and DES-Y5 supernovae datasets respectively. We find no significant hint for spatial curvature. We discuss the implications of current cosmological results for the exponential quintessence model, and more generally for dark energy in string theory.

Constraining holographic dark energy and analyzing cosmological tensions

We investigate cosmological constraints on the holographic dark energy (HDE) using the state-of-the-art cosmological datasets: Planck CMB angular power spectra and weak lensing power spectra, Atacama Cosmology Telescope (ACT) temperature power spectra, baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) measurements from six-degree-field galaxy survey and Sloan Digital Sky Survey (DR12 & DR16) and the Cepheids-Supernovae measurement from SH0ES team (R22). We also examine the HDE model and ΛCDM with and without Neff (effective number of relativistic species) being treated as a free parameter. We find that the HDE model can relieve the tensions of H0 and S8 to certain degrees. With “Planck+ACT+BAO+RSD” datasets, the constraints are H0=69.70±1.39km s−1Mpc−1 and S8=0.823±0.011 in HDE model, which brings down the Hubble tension down to 1.92σ confidence level (C.L.) and the S8 tension to (1−2)σ C.L. By adding the R22 data, their values are improved as H0=71.86±0.93km s−1Mpc−1 and S8=0.813±0.010, which further brings the Hubble tension down to 0.85σ C.L. and relieves the S8 tension. We also quantify the goodness-of-fit of different models with Akaike information criterion (AIC) and Bayesian information criterion (BIC), and find that the HDE agrees with the observational data better than the ΛCDM and other extended models (treating Neff as free for fitting).

Large-scale motions and growth rate from forward-modelling Tully–Fisher peculiar velocities

ABSTRACT Peculiar velocities are an important probe of the mass distribution in the Universe and the growth rate of structure, directly measuring the effects of gravity on the largest scales and providing a test for theories of gravity. Comparing peculiar velocities predicted from the density field mapped by a galaxy redshift survey with peculiar velocities measured using a distance estimator such as the Tully–Fisher relation yields the growth factor for large-scale structure. We present a method for forward modelling a sample of galaxy magnitudes and velocity widths that simultaneously determines the parameters of the Tully–Fisher relation and the peculiar velocity field. We apply this to the Cosmicflows-4 Tully–Fisher data set, using the peculiar velocities predicted from the 2M++ redshift survey. After validating the method on mock surveys, we measure the product of the growth rate and mass fluctuation amplitude to be fσ8 = 0.35 ± 0.03 at an effective redshift of z = 0.017. This is consistent at 3σ with the Planck CMB prediction, even though the uncertainty does not fully account for all sources of sample variance. We find the residual bulk flow from gravitational influences outside the 2M++ survey volume to be |V| = 227 ± 11 km s−1, (l, b) = (303°, −1°) in Galactic polar coordinates and the CMB frame. Using simulations, we show that applying our methodology to the large new sample of Tully–Fisher peculiar velocities expected from the WALLABY H I survey of the southern sky can improve the constraints on the growth rate by a factor of 2–3.

Deblurring the early Universe: reconstruction of primordial power spectrum from Planck CMB using image analysis techniques

While the simplest inflationary models predict the primordial perturbations to be near scale-invariant, the primordial power spectrum (PPS) can exhibit oscillatory features in many physically well-motivated models. We search for hints of such features via free-form reconstructions of the PPS based on Planck 2018 CMB temperature and polarization anisotropies. In order to robustly invert the oscillatory integrals and handle noisy unbinned data, we draw inspiration from image analysis techniques. In previous works, the Richardson-Lucy deconvolution algorithm for deblurring images has been modified for reconstructing PPS from the CMB temperature angular power spectrum. We extensively develop the methodology by including CMB polarization and introducing two new regularization techniques, also inspired by image analysis and adapted for our cosmological context. Regularization is essential for improving the fit to the temperature and polarization channels (TT, TE and EE) simultaneously without sacrificing one for another. The reconstructions we obtain are consistent with previous findings from temperature-only analyses. We evaluate the statistical significance of the oscillatory features in our reconstructions using mock data and find the observations to be consistent with having a featureless PPS. The machinery developed here will be a complimentary tool in the search for features with upcoming CMB surveys. Our methodology also shows competitive performance in image deconvolution tasks, which have various applications from microscopy to medical imaging.

Constraining primordial non-Gaussianity from DESI quasar targets and Planck CMB lensing

We detect the cross-correlation between 2.7 million DESI quasar targets across 14,700 deg2 (180 quasars deg-2) and Planck 2018 CMB lensing at ∼30σ. We use the cross-correlation on very large scales to constrain local primordial non-Gaussianity via the scale dependence of quasar bias. The DESI quasar targets lie at an effective redshift of 1.51 and are separated into four imaging regions of varying depth and image quality. We select quasar targets from Legacy Survey DR9 imaging, apply additional flux and photometric redshift cuts to improve the purity and reduce the fraction of unclassified redshifts, and use early DESI spectroscopy of 194,000 quasar targets to determine their redshift distribution and stellar contamination fraction (2.6%). Due to significant excess large-scale power in the quasar autocorrelation, we apply weights to mitigate contamination from imaging systematics such as depth, extinction, and stellar density. We use realistic contaminated mocks to determine the greatest number of systematic modes that we can fit, before we are biased by overfitting and spuriously remove real power. We find that linear regression with one to seven imaging templates removed per region accurately recovers the input cross-power, f NL and linear bias. As in previous analyses, our f NL constraint depends on the linear primordial non-Gaussianity bias parameter, bϕ = 2(b - p)δc assuming universality of the halo mass function. We measure f NL = -26+45 -40 with p = 1.6 (f NL = -18+29 -27 with p = 1.0), and find that this result is robust under several systematics tests. Future spectroscopic quasar cross-correlations with Planck lensing can tighten the f NL constraints by a factor of 2 if they can remove the excess power on large scales in the quasar auto power spectrum.

Emergent Unparticles Dark Energy can restore cosmological concordance

Addressing the discrepancy between the late and early time measurements of the Hubble parameter, H 0, and the so-called S 8 parameter has been a challenge in precision cosmology. Several models are present to address these tensions, but very few of them can do so simultaneously. In the past, we have suggested Banks-Zaks/Unparticles as an emergent Dark Energy model, and claimed that it can ameliorate the Hubble tension. In this work, we test this claim, and perform a likelihood analysis of the model and its parameters given current data, and compare it to ΛCDM. The model offers a possible resolution of Hubble tension and softens the Large Scale Structure (LSS) tension without employing a scalar field or modifying the gravitational sector. Our analysis shows a higher value of H 0 ∼ 70 – 73 km/sec/Mpc and a slightly lower value of S 8 for certain combinations of data sets. Consideration of Planck CMB data combined with the Pantheon sample and SH0ES priors lowers the H 0 and S 8 tension to 0.96σ and 0.94σ respectively with best-fit Δχ 2 ≈ -11 restoring cosmological concordance. Significant improvement in the likelihood persists for other combinations of data sets as well. Evidence for the model is given by inferring one of its parameters to be x 0 ≃ -4.46.The improvement in the fit is driven by the inclusion of the SH0ES prior. In its absence most of the improvement is due to larger error bars in the Emergent Unparticles Dark Energy model.

The cluster mass function and the σ8 tension

ABSTRACT We use a large set of halo mass function (HMF) models in order to investigate their ability to represent the observational cluster mass function (CMF), derived from the $\tt {GalWCat19}$ cluster catalogue, within the Lambda cold dark matter (ΛCDM) cosmology. We apply the χ2 minimization procedure to constrain the free parameters of the models, namely Ωm and σ8. We find that all HMF models fit well the observational CMF, while the Bocquet et al. model provides the best fit, with the lowest χ2 value. Utilizing the index of inconsistency (IOI) measure, we further test the possible inconsistency of the models with respect to a variety of Planck 2018 ΛCDM cosmologies, resulting from the combination of different probes (CMB–BAO or CMB–DES). We find that the HMF models that fitted well the observed CMF provide consistent cosmological parameters with those of the Planck CMB analysis, except for the Press and Schechter, Yahagi et al., and Despali et al. models that return large IOI values. The inverse $\chi _{\rm min}^2$-weighted average values of Ωm and σ8, overall 23 theoretical HMF models are ${\bar{\Omega }_{m,0}}=0.313\pm 0.022$ and ${\bar{\sigma }_8}=0.798\pm 0.040$, which are clearly consistent with the results of Planck–CMB, providing S8 = σ8(Ωm/0.3)1/2 = 0.815 ± 0.05. Within the ΛCDM paradigm and independently of the selected HMF model in the analysis, we find that the current CMF shows no σ8 tension with the corresponding Planck–CMB results.

S 8 increases with effective redshift in ΛCDM cosmology

ABSTRACT Hubble constant H0 and weighted amplitude of matter fluctuations S8 determinations are biased to higher and lower values, respectively, in the late universe with respect to early universe values inferred by the Planck collaboration within flat ΛCDM cosmology. If these anomalies are physical, that is, not due to systematics, they naively suggest that H0 decreases and S8 increases with effective redshift. Here, subjecting matter density today Ωm to a prior, corresponding to a combination of Planck CMB and BAO data, we perform a consistency test of the Planck-ΛCDM cosmology and show that S8 determinations from fσ8 (z) constraints increase with effective redshift. Due to the redshift evolution, a ∼3σ tension in the S8 parameter with Planck at lower redshifts remarkably becomes consistent with Planck within 1σ at high redshifts. This provides corroborating support for an S8 discrepancy that is physical in origin. We further confirm that the flat ΛCDM model is preferred over a theoretically ad hoc model with a jump in S8 at a given redshift. In the absence of the CMB+BAO Ωm prior, we find that >3σ tensions with Planck in low-redshift data are ameliorated by shifts in the parameters in high-redshift data. Results here and elsewhere suggest that the ΛCDM cosmological parameters are redshift dependent. Fitting parameters that evolve with redshift is a recognizable hallmark of model breakdown.

Do the early galaxies observed by JWST disagree with Planck's CMB polarization measurements?

The recent observations from the James Webb Space Telescope have led to a surprising discovery of a significant density of massive galaxies with masses of M ≥ 1010.5 M ⊙ at redshifts of approximately z ∼ 10. This corresponds to a stellar mass density of roughly ρ * ∼ 106 M ⊙ Mpc-3. Despite making conservative assumptions regarding galaxy formation, this finding may not be compatible with the standard ΛCDM cosmology that is favored by observations of CMB Anisotropies from the Planck satellite. In this paper, we confirm the substantial discrepancy with Planck's results within the ΛCDM framework. Assuming a value of ϵ = 0.2 for the efficiency of converting baryons into stars, we indeed find that the ΛCDM model is excluded at more than 99.7 % confidence level (C.L.). An even more significant exclusion is found for ϵ ∼ 0.1, while a better agreement, but still in tension at more than 95 %, is obtained for ϵ = 0.32.This tension, as already discussed in the literature, could arise either from systematics in the JWST measurements or from new physics. Here, as a last-ditch effort, we point out that disregarding the large angular scale polarization obtained by Planck, which allows for significantly larger values of the matter clustering parameter σ 8, could lead to better agreement between Planck and JWST within the ΛCDM framework. Assuming ΛCDM and no systematics in the current JWST results, this implies either an unknown systematic error in current large angular scale CMB polarization measurements or an unidentified physical mechanism that could lower the expected amount of CMB polarization produced during the epoch of reionization. Interestingly, the model compatible with Planck temperature-only data and JWST observation also favors a higher Hubble constant H 0 = 69.0±1.1 km/s/Mpc at 68% C.L., in better agreement with observations based on SN-Ia luminosity distances.

Isolating the linear signal when making redshift space distortion measurements

ABSTRACT Constraints on the linear growth rate, fσ8, using small-scale redshift space distortion measurements have a significant statistical advantage over those made on large scales. However, these measurements need to carefully disentangle the linear and non-linear information when interpreting redshift space distortions in terms of fσ8. It is particularly important to do this given that some previous measurements found a significant deviation from the expectation based on the Lambda cold dark matter (ΛCDM) model constrained by Planck cosmic microwave background data. We construct a new emulator-based model for small-scale galaxy clustering with scaling parameters for both the linear and non-linear velocities of galaxies, allowing us to isolate the linear growth rate. We train the emulator using simulations from the AbacusCosmos suite, and apply it to data from the extended Baryon Oscillation Spectroscopic Survey luminous red galaxy sample. We obtain a value of fσ8(z = 0.737) = 0.368 ± 0.041, in 2.3σ tension with the Planck 2018 ΛCDM expectation, and find less dependence on the minimum measurement scale than previous analyses.

Exploring mirror twin Higgs cosmology with present and future weak lensing surveys

We explore the potential of precision cosmological data to study non-minimal dark sectors by updating the cosmological constraint on the mirror twin Higgs model (MTH). The MTH model addresses the Higgs little hierarchy problem by introducing dark sector particles. In this work, we perform a Bayesian global analysis that includes the latest cosmic shear measurement from the DES three-year survey and the Planck CMB and BAO data. In the early Universe, the mirror baryon and mirror radiation behave as dark matter and dark radiation, and their presence modifies the Universe's expansion history. Additionally, the scattering between mirror baryon and photon generates the dark acoustic oscillation process, suppressing the matter power spectrum from the cosmic shear measurement. We demonstrate how current data constrain these corrections to the ΛCDM cosmology and find that for a viable solution to the little hierarchy problem, the proportion of MTH dark matter cannot exceed about 30% of the total dark matter density, unless the temperature of twin photon is less than 30% of that of the standard model photon. While the MTH model is presently not a superior solution to the observed H 0 tension compared to the ΛCDM+ΔN eff model, we demonstrate that it has the potential to alleviate both the H 0 and S 8 tensions, especially if the S 8 tension persists in the future and approaches the result reported by the Planck SZ (2013) analysis. In this case, the MTH model can relax the tensions while satisfying the DES power spectrum constraint up to k ≲ 10 hMpc-1. If the MTH model is indeed accountable for the S 8 and H 0 tensions, we show that the future China Space Station Telescope (CSST) can determine the twin baryon abundance with a 10% level precision.

On the impact of the galaxy window function on cosmological parameter estimation

ABSTRACT One important source of systematics in galaxy redshift surveys comes from the estimation of the galaxy window function. Up until now, the impact of the uncertainty in estimating the galaxy window function on parameter inference has not been properly studied. In this paper, we show that the uncertainty and the bias in estimating the galaxy window function will be salient for ongoing and next-generation galaxy surveys using a simulation-based approach. With a specific case study of cross-correlating emission-line galaxies from the DESI Legacy Imaging Surveys and the Planck cosmic microwave background lensing map, we show that neural network-based regression approaches to modelling the window function are superior in comparison to linear regression-based models. We additionally show that the definition of the galaxy overdensity estimator can impact the overall signal-to-noise of observed power spectra. Finally, we show that the additive biases coming from the window functions can significantly bias the modes of the inferred parameters and also degrade their precision. Thus, a careful understanding of the window functions will be essential to conduct cosmological experiments.