LSS constraints with controlled theoretical uncertainties

TL;DR

This work develops a systematic method to include theoretical uncertainties in forecasts for large-scale structure and CMB lensing analyses. Using an EFT-based perturbative framework and a correlated envelope for theory errors, the authors quantify how nuisance parameters and modeling imperfections degrade constraints on the sum of neutrino masses and primordial non-Gaussianities, including equilateral and local shapes. The results show that while neutrino-mass bounds can remain competitive with high-redshift surveys and one-loop corrections, reaching $f_{ m NL}^{\rm eq.}\sim1$ remains challenging; local NG remains accessible due to its orthogonality to gravitational signals, and CMB lensing offers a robust, complementary path to neutrino constraints. The framework provides a practical, generalizable pipeline for realistic forecasting and data analysis in the presence of theoretical uncertainties.

Abstract

Forecasts and analyses of cosmological observations often rely on the assumption of a perfect theoretical model over a defined range of scales. We explore how model uncertainties and nuisance parameters in perturbative models of the matter and galaxy spectra affect constraints on neutrino mass and primordial non-Gaussianities. We provide a consistent treatment of theoretical errors and argue that their inclusion is a necessary step to obtain realistic cosmological constraints. We find that galaxy surveys up to high redshifts will allow a detection of the minimal neutrino mass and local non-Gaussianity of order unity, but improving the constraints on equilateral non-Gaussianity beyond the CMB limits will be challenging. We argue that similar considerations apply to analyses where theoretical models are based on simulations.

Figures (9)

• Figure 1: Cumulative constraints on the power spectrum amplitude using linear theory, if the one loop matter power spectrum describes the truth. The red line with error band shows the constraint without considering the theoretical error and leads to inconsistent constraints. The black line and error bound includes the theoretical errors into the parameter estimation and leads to an unbiased estimate of the amplitude of the power spectrum. The plot is made assuming a single redshift bin at $z=0$ and an ideal survey with volume $V=(2.5\; h^{-1} {\rm Gpc})^3$.
• Figure 2: Theoretical errors for the linear theory and one-loop power spectrum (see Eq. \ref{['eq:power_spectrum_error']}) as a function of $k$. The cosmic variance is plotted for the redshift bin $1<z<2$. Three solid lines are relative suppression of the power spectrum for three different $M_\nu$.
• Figure 3: One sigma error bar on the neutrino mass from a galaxy survey up to $z_{\rm max}=2$ as a function of $k_{\rm max}$. The two horizontal lines correspond to $M_{\nu}= 60 \;{\rm meV}$ which is the minimal mass and $M_{\nu}= 20 \;{\rm meV}$ which roughly corresponds to a $3\sigma$ detection. The solid and dashed lines are constraints without marginalization over nuisance parameters, coming from linear and one-loop power spectrum respectively with corresponding theoretical errors. The dot-dashed line is the ideal case with no theoretical errors. The dotted line is the constraint with marginalization over the EFT and bias parameters, combining the one-loop power spectrum and tree-level bispectrum and accounting for the theoretical errors. In all cases where the theoretical error is included, the constraints saturate at some $k_{\rm max}$. The constraint using the one-loop power spectrum is roughly equivalent to the ideal case with no theoretical error and shot noise $n \approx 10^{-4} \;h^3 {\rm Mpc}^{-3}$.
• Figure 4: One sigma error bar on the neutrino mass from a galaxy survey as a function of the maximal redshift $z_{\rm max}$. The two horizontal lines correspond to $M_{\nu}= 60 \;{\rm meV}$ which is the minimal mass and $M_{\nu}= 20 \;{\rm meV}$ which roughly corresponds to a $3\sigma$ detection. Left panel: Constraints without marginalization over nuisance parameters. The solid and dashed line are predictions from linear and one-loop power spectrum with corresponding theoretical errors respectively. The dot-dashed line is the ideal case with no theoretical errors. Central and right panel: Constraints with marginalization over the EFT and bias parameters for two different galaxy samples. The lines correspond to different combinations of the tree-level and the one-loop power spectrum and bispectrum accounting for the theoretical errors. The tree level bispectrum significantly improves the constraints at low redshifts and further improvements arise from the one-loop bispectrum.
• Figure 5: Unmarginalized relative errors of different parameters as a function of maximal redshift $z_{\rm max}$.