Forecast constraints on null tests of the $Λ$CDM model with SPHEREx

TL;DR

This paper evaluates SPHEREx's capability to constrain BAO observables and test the internal consistency of ΛCDM using Fisher-matrix forecasts, model-independent reconstructions, and machine learning. It introduces a suite of null tests (Om_H, curvature, global shear) to probe homogeneity and isotropy, and demonstrates how a neural network can detect subtle model dependence in the Fisher information. The authors forecast sub-percent precision on angular diameter distance and ~1% precision on the Hubble rate across 11 redshift bins, and find no evidence for deviations from ΛCDM in the null tests. They further show that covariance structures carry measurable model-dependent information, which a neural network can exploit to distinguish ΛCDM from wCDM, highlighting the need for simulation-based inference in future cosmological analyses.

Abstract

In this work we quantify the ability of the upcoming SPHEREx survey to constrain cosmological observables and test the internal consistency of the cosmological constant and cold dark matter ($Λ$CDM) model. Using Fisher matrix forecasting, we assess the expected precision on Baryon Acoustic Oscillations (BAO) observables, such as the angular diameter distance $D_\mathrm{A}(z)$ and the Hubble parameter $H(z)$. We further explore SPHEREx's potential to probe some of the fundamental assumptions of large-scale spatial homogeneity and isotropy, through model-independent reconstructions of several consistency tests of the $Λ$CDM model. In addition, we also examine the effect of the model dependence of the resulting Fisher and covariance matrices, using a neural network (NN) classification approach. We find that, while it is commonly assumed the covariance matrix depends weakly on the model, in fact the NN can very accurately ($\sim 98\%$) detect the underlying fiducial cosmological model based solely on the covariance matrix of the data, thus challenging this assumption. This model dependence, often neglected in standard analyses, can be naturally incorporated within simulation-based inference frameworks, which offer a flexible alternative for capturing such effects.

Figures (5)

• Figure 1: Flowchart of the iterative processes followed by the GA (left) and the NN architecture (right), as implemented in our analysis.
• Figure 2: We show the theoretical values of the angular diameter distance (left) and the Hubble parameter over $(1+z)^{3/2}$ (right) as functions of redshift (black dashed lines), alongside the theoretical values of Table \ref{['fid_params']} (green points with error bars). In the bottom of each panels we show the values normalized to unity, with respect to the fiducial model.
• Figure 3: GA reconstructions of the consistency tests mentioned in Section \ref{['sec::consist_sect']}. The black dashed line corresponds to the best-fit $\Lambda$CDM model, the red line is the GA fit and the orange shaded region corresponds to the 1$\sigma$ GA uncertainties.
• Figure 4: Confusion matrix results from the $\Lambda$CDM - $w$CDM classification. The top left and bottom right correspond to the true negatives (TN) and true positives (TP), representing correct classifications. The off-diagonal terms represent the false positives (FP) and false negatives (FN).
• Figure 5: Loss (left) and accuracy (right) curves for both the training (blue) and validation (orange) data for the NN model implemented.