Fisher Matrix Research Articles

Probing dark relativistic species and their interactions with dark matter through CMB and 21 cm surveys

We investigate the sensitivity of the 21 cm power spectrum from cosmic dawn and the epoch of reionization to models of free-streaming dark radiation (parameterized through N eff) and interacting dark radiation-dark matter models (DM-DR). The latter models have gained attention for their potential in addressing recent cosmological tensions and structure formation challenges.We perform a Fisher matrix analysis under different assumptions regarding the astrophysical modeling, and forecast the sensitivity of HERA observations, combined with CMB data from Planck and the Simons Observatory (SO), to N eff and DM-DR interaction modeled using the ETHOS framework assuming a constant scattering rate between the two components.Most importantly, we find that 21 cm observations can improve the sensitivity to the DM-DR interaction rate by up to four order of magnitude compared to Planck and SO. Conversely, in the limit of low interaction rate (which asymptotically matches N eff), CMB data dominates the constraining power, but the inclusion of HERA data can provide a ∼ 20% improvement in sensitivity over CMB data alone.Moreover, we find that HERA observations will be able to probe a region of the DM-DR interaction parameter space which is promising to explain the weak lensing amplitude `S 8' tension. Our results demonstrate the complementarity of 21 cm and CMB data in exploring dark sector interactions.

Invariance transformations in wave-optics lensing: Implications for gravitational-wave astrophysics and cosmology

Gravitational lensing offers unique opportunities to learn about the astrophysical origin of distant sources, the abundance of intervening objects acting as lenses, and gravity and cosmology in general. However, all this information can only be retrieved as long as one can disentangle each effect from the finite number of observables. In the geometric optics regime, typical of electromagnetic radiation, when the wavelength of the lensed signal is small compared to the size of the lens, there are invariance transformations that change the mass of the lens and the source-lens configuration but leave the observables unchanged. Neglecting this “mass-sheet degeneracy” can lead to biased lens parameters or unrealistic low uncertainties, which could then transfer to an incorrect cosmography study. This might be different for gravitational waves as their long wavelengths can be comparable to the lens size and lensing enters into the wave-optics limit. We explore the existence of invariance transformations in the wave-optics regime of gravitational-wave lensing, extending previous work and examining the implications for astrophysical and cosmological studies. We study these invariance transformations using three different methods of increasing level of complexity: template mismatch, Fisher Matrix, and Bayesian parameter estimation. We find that, for a sufficiently loud signal, the degeneracy is partially broken and the lens and cosmological parameters, e.g. H0, can be retrieved independently and unbiased. In current ground-based detectors, though, considering also population studies, a strong constraint on these parameters seems quite remote and the prevailing degeneracy implies a larger uncertainty in the lens model reconstruction. However, with better sensitivity of the third-generation ground-based detectors, a meaningful constraint on H0 is possible to obtain. Published by the American Physical Society 2024

The MeerKAT Pulsar Timing Array: Maps of the gravitational wave sky with the 4.5-yr data release

ABSTRACT In an accompanying publication, the MeerKAT Pulsar Timing Array (MPTA) Collaboration reports tentative evidence for the presence of a stochastic gravitational wave background, following observations of similar signals from the European and Indian Pulsar Timing Arrays, the North American Nanohertz Observatory for Gravitational Waves, the Parkes Pulsar Timing Array, and the Chinese Pulsar Timing Array. If such a gravitational wave background signal originates from a population of inspiraling supermassive black hole binaries, the signal may be anisotropically distributed in the sky. In this paper, we evaluate the anisotropy of the MPTA signal using a spherical harmonic decomposition. We discuss complications arising from the covariance between pulsar pairs and the regularization of the Fisher matrix. Applying our method to the $4.5 \hbox{-}\text{yr}$ data set, we obtain two forms of sky maps for the three most sensitive MPTA frequency bins between $7 \ {\rm and} \ 21 \, {\rm nHz}$. Our ‘clean maps’ estimate the distribution of gravitational wave strain power with minimal assumptions. Our radiometer maps answer the question: Is there a statistically significant point source? We find a noteworthy hotspot in the $7 \, \mathrm{nHz}$ clean map with a p-factor of $p=0.015$ (not including trial factors). Future observations are required to determine if this hotspot is of astrophysical origin.

The interacting double white dwarf population with LISA: Stochastic foreground and resolved sources

Aims. We investigate the impact of tidal torques and mass transfer on the population of double white dwarfs that will be observed with LISA. Methods. Our Galactic distribution of double white dwarfs is based on the combination of a cosmological simulation and a binary population synthesis model. We used a semi-analytical model to evolve double white dwarf binaries considering ten different hypotheses for the efficiency of tidal coupling and three hypotheses for the birth spins of white dwarfs. We then estimated the stochastic foreground and the population of resolvable binaries for LISA for these different combinations. Results. Our predicted double white dwarf binary distribution can differ substantially from the distribution expected if only gravitational waves (GWs) are considered. If white dwarfs spin slowly, then we predict an excess of systems around a few due to binaries that outspiral after the onset of mass transfer. This excess of systems leads to differences in the confusion noise, which are most pronounced for strong tidal coupling. In that case, we find a significantly higher number of resolvable binaries than in the GW-only scenario. If instead white dwarfs spin rapidly and tidal coupling is weak, then we find no excess around a few mHz, and the confusion noise due to double white dwarfs is very low. In that scenario, we also predict a subpopulation of outspiralling binaries below 0.1 mHz. Using the Fisher matrix approximation, we estimate the uncertainty on the GW-frequency derivative of resolvable systems. We find that, even for non-accreting systems, the mismodelling error due to neglecting effects other than GWs is larger than the statistical uncertainty, and thus this neglect would lead to biased estimates for mass and distance. Conclusions. Our results suggest that the population of double white dwarfs is likely to be different from what is expected in the standard picture, which highlights the need for flexible tools in LISA data analysis. Because our semi-analytical model hinges upon a simplistic approach to determining the stability of mass accretion, it will be important to deepen our comprehension of stability in mass-transferring double white dwarf binaries.

Systematic bias due to mismodeling precessing binary black hole ringdown

Accurate waveform modeling is crucial for parameter estimation in gravitational wave astronomy, impacting our understanding of source properties and the testing of general relativity. The precession of orbital and spin angular momenta in binary black hole (BBH) systems with misaligned spins presents a complex challenge for gravitational waveform modeling. Current precessing BBH waveform models employ a coprecessing frame, which precesses along with the binary. In this paper, we investigate a source of bias stemming from the mismodeling of ringdown frequency in the coprecessing frame. We find that this mismodeling of the coprecessing frame ringdown frequency introduces systematic biases in parameter estimation, for high-mass systems in particular, and in the inspiral-merger-ringdown (IMR)-consistency test of general relativity. Employing the waveform model henom, we conduct an IMR-consistency test using a Fisher matrix analysis across parameter space, as well as full injected signal parameter estimation studies. Our results show that this mismodeling particularly affects BBH systems with high-mass ratios, high-spin magnitudes, and highly inclined spins. These findings suggest inconsistencies for all waveform models which do not address this issue. Published by the American Physical Society 2024

Power spectrum multipoles and clustering wedges during the Epoch of Reionization

Abstract We study the viability of using power spectrum clustering wedges as summary statistics of 21 cm surveys during the Epoch of Reionization (EoR). For observations in a wide redshift range z ∼ 7 − 9 corresponding to a line-of-sight scale of ∼500 Mpc, the power spectrum is subject to anisotropic effects due to the evolution along the light-of-sight. Information on the physics of reionization can be extracted from the anisotropy using the power spectrum multipoles. Signals of the power spectrum monopole are highly correlated at scales smaller than the typical ionization bubble, which can be disentangled by including higher-order multipoles. By simulating observations of the low frequency part of the Square Kilometre Array (SKA) Observatory, we find that the sampling of the cylindrical wavenumber k-space is highly non-uniform due to the baseline distribution, i.e. the distribution of antenna pairs sampling different transverse k⊥ scales. Measurements in clustering wedges partition the cylindrical k-space into different radial k∥ scales, and can be used for isolating parts of k-space with relatively uniform sampling, allowing for more precise parameter inference. Using Fisher Matrix forecasts, we find that the reionization model can be inferred with per-cent level precision with ∼120 hrs of integration time using SKA-Low. Compared to model inference using only the power spectrum monopole above the foreground wedge, model inference using multipole power spectra in clustering wedges yields a factor of ∼3 improvement on the marginalised 1D parameter constraints.

Euclid preparation

Context. Deviations from Gaussianity in the distribution of the fields probed by large-scale structure surveys generate additional terms in the data covariance matrix, increasing the uncertainties in the measurement of the cosmological parameters. Super-sample covariance (SSC) is among the largest of these non-Gaussian contributions, with the potential to significantly degrade constraints on some of the parameters of the cosmological model under study – especially for weak-lensing cosmic shear. Aims. We compute and validate the impact of SSC on the forecast uncertainties on the cosmological parameters for the Euclid photo-metric survey, and investigate how its impact depends on the specific details of the forecast. Methods. We followed the recipes outlined by the Euclid Collaboration (EC) to produce 1σ constraints through a Fisher matrix analysis, considering the Gaussian covariance alone and adding the SSC term, which is computed through the public code PySSC. The constraints are produced both by using Euclid’s photometric probes in isolation and by combining them in the ‘3×2pt’ analysis. Results. We meet EC requirements on the forecasts validation, with an agreement at the 10% level between the mean results of the two pipelines considered, and find the SSC impact to be non-negligible - halving the figure of merit (FoM) of the dark energy parameters (w0, wa) in the 3×2pt case and substantially increasing the uncertainties on Ωm,0,w0, w0, and σ8 for the weak-lensing probe. We find photometric galaxy clustering to be less affected as a consequence of the lower probe response. The relative impact of SSC, while highly dependent on the number and type of nuisance parameters varied in the analysis, does not show significant changes under variations of the redshift binning scheme. Finally, we explore how the use of prior information on the shear and galaxy bias changes the impact of SSC. We find that improving shear bias priors has no significant influence, while galaxy bias must be calibrated to a subpercent level in order to increase the FoM by the large amount needed to achieve the value when SSC is not included.

Cosmology with shear ratios: a joint study of weak lensing and spectroscopic redshift datasets

The ratio of the average tangential shear signal of different weak lensing source populations around the same lens galaxies, also known as a shear ratio, provides an important test of lensing systematics and a potential source of cosmological information. In this paper we measure shear ratios of three current weak lensing surveys –KiDS, DES, and HSC– using overlapping data from the Baryon Oscillation Spectroscopic Survey. We apply a Bayesian method to reduce bias in shear ratio measurement, and assess the degree to which shear ratio information improves the determination of important astrophysical parameters describing the source redshift distributions and intrinsic galaxy alignments, as well as cosmological parameters, in comparison with cosmic shear and full 3x2-pt correlations (cosmic shear, galaxy-galaxy lensing, and galaxy clustering). We consider both Fisher matrix forecasts, as well as full likelihood analyses of the data. We find that the addition of shear ratio information to cosmic shear allows the mean redshifts of the source samples and intrinsic alignment parameters to be determined significantly more accurately. Although the additional constraining power enabled by the shear ratio is less than that obtained by introducing an accurate prior in the mean source redshift using photometric redshift calibration, the shear ratio allows for a useful cross-check. The inclusion of shear ratio data consistently benefits the determination of cosmological parameters such as S_8, for which we obtain improvements up to 34%. However these improvements are less significant when shear ratio is combined with the full 3x2-pt correlations. We conclude that shear ratio tests will remain a useful source of cosmological information and cross-checks for lensing systematics, whose application will be further enhanced by upcoming datasets such as the Dark Energy Spectroscopic Instrument.

Cosmological forecasts from the combination of Stage-IV photometric galaxy surveys and the magnification from forthcoming GW observatories

In this work we have investigated the synergy between Stage-IV galaxy surveys and future GW observatories for constraining the underlying cosmological model of the Universe, focussing on photometric galaxy clustering, cosmic shear and GW magnification as cosmological probes. We have implemented a Fisher matrix approach for the evaluation of the full 6×2pt statistics composed by the angular power spectra of the single probes together with their combination. For our analysis, we have in particular considered dynamical dark energy and massive neutrino scenarios. We have found that the improvement to galaxy survey performance is below 1%, in the case of ℓ GW max=100 and a luminosity distance error of σ dL /dL =10%. However, when extending the analysis to ℓ GW max=1000, we find that the GW magnification improves the galaxy survey performance on all the cosmological parameters, reducing their errors by 3%-5%, when σ dL /dL =10%, and by 10%-18% when σ dL /dL =1%, especially for Mν , w 0 and wa . However, here our analysis is unavoidably optimistic: a much more detailed and realistic approach will be needed, especially by including systematic effects. But we can conclude that, in the case of future gravitational wave observatories, the inclusion of the gravitational wave magnification can improve Stage-IV galaxy surveys performance on constraining the underlying cosmological model of the Universe.

Natural Gradient Variational Bayes Without Fisher Matrix Analytic Calculation and Its Inversion

This article introduces a method for efficiently approximating the inverse of the Fisher information matrix, a crucial step in achieving effective variational Bayes inference. A notable aspect of our approach is the avoidance of analytically computing the Fisher information matrix and its explicit inversion. Instead, we introduce an iterative procedure for generating a sequence of matrices that converge to the inverse of Fisher information. The natural gradient variational Bayes algorithm without analytic expression of the Fisher matrix and its inversion is provably convergent and achieves a convergence rate of order O ( log s / s ) , with s the number of iterations. We also obtain a central limit theorem for the iterates. Implementation of our method does not require storage of large matrices, and achieves a linear complexity in the number of variational parameters. Our algorithm exhibits versatility, making it applicable across a diverse array of variational Bayes domains, including Gaussian approximation and normalizing flow Variational Bayes. We offer a range of numerical examples to demonstrate the efficiency and reliability of the proposed variational Bayes method. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Weighing massive neutrinos with Lyman-α observations

The presence of massive neutrinos has still not been revealedby the cosmological data. We considera novel method based on the two-point line-of-sight correlation function ofhigh-resolution Lyman-α data to achieve this end in the paper.We adopt semi-analytic models of Lyman-αclouds for the study. We employ Fisher matrix technique to show thatit is possible to achieve a scenario in whichthe covariance of the two-point function nearly vanishes for both the spectroscopic noise and the signal.We analyze this near `zero noise' outcome in detail to argue it might be possible to detect neutrinosof mass range m ν ≃ 0.05–0.1 eV with signal-to-noise of unity witha single QSO line of sight. We show that this estimate can be improved to SNR ≃ 3–6 with data along multiple line of sightswithin the redshift range z ≃ 2–2.5.Such data sets already exist in the literature.We further carry outprincipal component analysis of the Fisher matrix to study the degeneraciesof the neutrino mass with otherparameters. We show that Planck priors lift the degeneracies betweenthe neutrino mass and other cosmological parameters.However, the prospects of the detection of neutrino mass are driven by the poorly-determined parameters characterizing the ionization and thermal state of Lyman-α clouds. We have also mentioned the possible limitations andobservational challenges posed in measuring the neutrino mass using our method.

Uncertainty of Line-of-sight Velocity Measurements of Faint Stars from Low- and Medium-resolution Optical Spectra

Massively multiplexed spectrographs will soon gather large statistical samples of stellar spectra. The accurate estimation of uncertainties on derived parameters, such as the line-of-sight velocity v los, especially for spectra with low signal-to-noise ratios (S/Ns), is paramount. We generated an ensemble of simulated optical spectra of stars as if they were observed with low- and medium-resolution fiber-fed instruments on an 8 m class telescope, similar to the Subaru Prime Focus Spectrograph, and determined v los by fitting stellar templates to the simulated spectra. We compared the empirical errors of the derived parameters—calculated from an ensemble of simulations—to the asymptotic errors determined from the Fisher matrix, as well as from Monte Carlo sampling of the posterior probability. We confirm that the uncertainty of v los scales with the inverse square root of the S/N, but also show how this scaling breaks down at low S/N and analyze the error and bias caused by template mismatch. We outline a computationally optimized algorithm to fit multiexposure data and provide a mathematical model of stellar spectrum fitting that maximizes the so called significance, which allows for calculating the error from the Fisher matrix analytically. We also introduce the effective line count, and provide a scaling relation to estimate the errors of v los measurements based on stellar type. Our analysis covers a range of stellar types with parameters that are typical of the Galactic outer disk and halo, together with analogs of stars in M31 and in satellite dwarf spheroidal galaxies around the Milky Way.

Measurable parameter combinations of environmentally-dephased EMRI gravitational-wave signals

The future space-borne Laser Interferometer Space Antenna (LISA) is expected to detect gravitational waves (GW) from Extreme Mass Ratio Inspiral (EMRI) binaries which may live in nontrivial environments such as accretion disks. In this work, we apply the Fisher matrix Principal Component Analysis (PCA) method to assess how well LISA observations can jointly constrain the source parameters and environmental densities around EMRIs. Specifically, we calculate the Fisher matrix from the post-Newtonian parameters of an EMRI binary embedded in a fluid with a constant density profile. We determine that the most dominant measurable parameter combination is dominated by contributions from environmental effects, namely, gravitational drag, accretion, and gravitational pull (in order of contribution). The proposed reparameterization of the PN parameters can be used to improve the power and efficiency of future detection and parameter estimation methods.

Forecast Cosmological Constraints with the 1D Wavelet Scattering Transform and the Lyman-α Forest.

We make forecasts for the constraining power of the 1D wavelet scattering transform when used with a Lyman-α forest cosmology survey. Using mock simulations and a Fisher matrix, we show that there is considerable cosmological information in the scattering transform coefficients not captured by the flux power spectrum. We estimate mock covariance matrices assuming uncorrelated Gaussian pixel noise for each quasar at a level drawn from a simple log-normal model. The extra information comes from a smaller estimated covariance in the first-order wavelet power and from second-order wavelet coefficients that probe non-Gaussian information in the forest. Forecast constraints on cosmological parameters from the wavelet scattering transform are more than an order of magnitude tighter than for the power spectrum, shrinking a 4D parameter space by a factor of 10^{6}. Should these improvements be realized with the Dark Energy Spectroscopic Instrument, inflationary running would be constrained to test common inflationary models predicting α_{s}=-6×10^{-4} and neutrino mass constraints would be improved enough for a 5-σ detection of the minimal neutrino mass.

Candl: cosmic microwave background analysis with a differentiable likelihood

We present candl, an automatically differentiable python likelihood for analysing cosmic microwave background power spectrum measurements. candl is powered by JAX, which makes it fast and easy to calculate derivatives of the likelihood. This facilitates, for example, robust Fisher matrices without finite-difference methods. We show the benefits of candl through a series of example calculations, covering forecasting, robustness tests, and gradient-based Markov chain Monte Carlo sampling. These also include optimising the band power bin width to minimise parameter errors of a realistic mock data set. Moreover, we calculate the correlation of parameter constraints from correlated and partially overlapping subsets of the SPT-3G 2018 TT/TE/EE data release. In a traditional analysis framework, these tasks are slow and require careful fine-tuning to obtain stable results. As such, a fully differentiable pipeline allows for a higher level of scrutiny; we argue that this is the paradigm shift required to leverage incoming data from ground-based experiments, which will significantly improve the cosmological parameter constraints from the Planck mission. candl comes with the latest primary and lensing power spectrum data from the South Pole Telescope and Atacama Cosmology Telescope collaborations and will be used as part of the upcoming SPT-3G TT/TE/EE and ϕϕ data releases. Along with the core code, we release a series of auxiliary tools, which simplify common analysis tasks and interface the likelihood with other cosmological software. candl is pip-installable and publicly available on Github.

Fisher matrix based fault detection for PMUs data in power grids

In this paper, using the data collected from phasor measurement units (PMUs), two methods based on Fisher random matrix are proposed to detect faults in power grids. Firstly, the fault detection matrix is constructed and the event detection problem is reformatted as a testing problem for two-sample covariance matrices, which is related with the so-called Fisher matrix. To save computing resources, the screening step of fault interval based on the test statistic is designed to check the existence of faults. Then two point-by-point methods are proposed to determine the time of the fault in the selected interval. One method detects faults by the limiting spectral distribution of the standard Fisher matrix, which can detect the faults with higher accuracy. The other method tests the faults based on the proposed test statistic , which has a faster detection speed. Compared with existing works, the simulation results illustrate that two methods proposed in this paper cost less computational time and provide a higher degree of accuracy and sensitivity.

Forecast constraints on the baryonic feedback effect from the future kinetic Sunyaev-Zel'dovich effect detection

The baryonic feedback effect is an important systematic error in the weak lensing (WL) analysis. It contributes partly to the S 8 tension in the literature. With the next generations of large scale structure (LSS) and CMB experiments, the high signal-to-noise kinetic Sunyaev-Zel'dovich (kSZ) effect detection can tightly constrain the baryon distribution in and around dark matter halos, and quantify the baryonic effect in the weak lensing statistics. In this work, we apply the Fisher matrix technique to predict the future kSZ constraints on 3 kSZ-sensitive Baryon Correction Model (BCM) parameters. Our calculations show that, in combination with next generation LSS surveys, the 3rd generation CMB experiments such as AdvACT and Simon Observatory can constrain the matter power spectrum damping S(k) to the precision of σ S (k) < 0.8%√(37.8 Gpc3h-3-3/V) at k ≲ 10h/Mpc, where V is the overlapped survey volume between the future LSS and CMB surveys. For the 4th generation CMB surveys such as CMB-S4 and CMB-HD, the constraint will be enhanced to σ S (k) < 0.4%√(37.8 Gpc3h-3/V). If extra-observations, e.g. X-ray detection and thermal SZ observation, can effectively fix the gas density profile slope parameter δ, the constraint on S(k) will be further boosted to σ S (k) < 0.3%√(37.8 Gpc3 h -3/V) and σ S (k) < 0.1%√(37.8 Gpc3 h -3/V) for the 3rd and 4th generation CMB surveys.

Gravitational wave measurement in the mid-band with atom interferometers

Gravitational Waves (GWs) have been detected in the ∼ 100 Hz and nHz bands, but most of the gravitational spectrum remains unobserved. A variety of detector concepts have been proposed to expand the range of observable frequencies. In this work, we study the capability of GW detectors in the “mid-band”, the ∼ 30 mHz– 10 Hz range between LISA and LIGO, to measure the signals from and constrain the properties of ∼ 1 – 100 M ⊙ compact binaries. We focus on atom-interferometer-based detectors. We describe a Fisher matrix code, AIMforGW, which we created to evaluate their capabilities, and present numerical results for two benchmarks: terrestrial km-scale detectors, and satellite-borne detectors in medium Earth orbit. Mid-band GW detectors are particularly well-suited to pinpointing the location of GW sources on the sky. We demonstrate that a satellite-borne detector could achieve sub-degree sky localization for any detectable source with chirp mass ℳ c ≲ 50 M ⊙. We also compare different detector configurations, including different locations of terrestrial detectors and various choices of the orbit of a satellite-borne detector. As we show, a network of only two terrestrial single-baseline detectors or one single-baseline satellite-borne detector would each provide close-to-uniform sky-coverage, with signal-to-noise ratios varying by less than a factor of two across the entire sky. We hope that this work contributes to the efforts of the GW community to assess the merits of different detector proposals.

Fully non-Gaussian Scalar-Induced Gravitational Waves

Scalar-Induced Gravitational Waves (SIGWs) represent a particular class of primordial signals which are sourced at second-order in perturbation theory whenever a scalar fluctuation of the metric is present. They form a guaranteed Stochastic Gravitational Wave Background (SGWB) that, depending on the amplification of primordial scalar fluctuations, can be detected by GW detectors. The amplitude and the frequency shape of the scalar-induced SGWB can be influenced by the statistical properties of the scalar density perturbations. In this work we study the intuitive physics behind SIGWs and we analyze the imprints of local non-Gaussianity of the primordial curvature perturbation on the GW spectrum. We consider all the relevant non-Gaussian contributions up to fifth-order in the scalar seeds without any hierarchy, and we derive the related GW energy density ΩGW(f). We perform a Fisher matrix analysis to understand to which accuracy non-Gaussianity can be constrained with the LISA detector, which will be sensitive in the milli-Hertz frequency band. We find that LISA, neglecting the impact of astrophysical foregrounds, will be able to measure the amplitude, the width and the peak of the spectrum with an accuracy up to 𝒪(10-4), while non-Gaussianity can be measured up to 𝒪(10-3). Finally, we discuss the implications of our non-Gaussianity expansion on the fraction of Primordial Black Holes.

Euclid preparation

In this paper we investigate the impact of lensing magnification on the analysis of Euclid’s spectroscopic survey using the multipoles of the two-point correlation function for galaxy clustering. We determine the impact of lensing magnification on cosmological constraints as well as the expected shift in the best-fit parameters if magnification is ignored. We considered two cosmological analyses: (i) a full-shape analysis based on the Λ cold dark matter (CDM) model and its extension w0waCDM and (ii) a model-independent analysis that measures the growth rate of structure in each redshift bin. We adopted two complementary approaches in our forecast: the Fisher matrix formalism and the Markov chain Monte Carlo method. The fiducial values of the local count slope (or magnification bias), which regulates the amplitude of the lensing magnification, have been estimated from the Euclid Flagship simulations. We used linear perturbation theory and modelled the two-point correlation function with the public code coffe. For a ΛCDM model, we find that the estimation of cosmological parameters is biased at the level of 0.4–0.7 standard deviations, while for a w0waCDM dynamical dark energy model, lensing magnification has a somewhat smaller impact, with shifts below 0.5 standard deviations. For a model-independent analysis aimed at measuring the growth rate of structure, we find that the estimation of the growth rate is biased by up to 1.2 standard deviations in the highest redshift bin. As a result, lensing magnification cannot be neglected in the spectroscopic survey, especially if we want to determine the growth factor, one of the most promising ways to test general relativity with Euclid. We also find that, by including lensing magnification with a simple template, this shift can be almost entirely eliminated with minimal computational overhead.