Running the small-correlated-against-large estimator at scale: Applications of small-scale CMB lensing estimators on realistic simulations

TL;DR

This paper extends the Small-Correlated-Against-Large Estimator (SCALE) to full-sky CMB analyses and integrates SCALE into cosmological parameter inference via a neural network emulator and a dedicated likelihood. The authors build a single emulator predicting lensed TT spectra, lensing power, reconstruction biases, and SCALE cross-spectra for 174 band-powers, trained on 8192 Latin-hypercube samples and achieving sub-percentage accuracy with large speedups. Full-sky simulations (NSIDE=8192) generate realistic covariances for TT, QE, and SCALE observables, which are used in a multivariate normal likelihood that also incorporates BAO priors and a prior on $\tau$. The results demonstrate that SCALE provides additional, largely independent information about small-scale lensing, enabling tighter constraints on the neutrino mass $m_\nu$ (potentially up to $4\sigma$ for minimal mass cases with cosmic-variance $\tau$ priors) and enabling tests of exotic dark matter models via scale-dependent lensing suppression; SCALE thus offers a valuable, efficient complement to conventional lensing reconstruction for future CMB surveys.

Abstract

The Small-Correlated-Against-Large Estimator (SCALE) for small-scale lensing of the cosmic microwave background (CMB) provides a novel method for measuring the amplitude of CMB lensing power without the need for reconstruction of the lensing field. In our previous study, we showed that the SCALE method can outperform existing reconstruction methods to detect the presence of lensing at small scales ($\ell \gg 3000$). Here we develop a procedure to include information from SCALE in cosmological parameter inference. We construct a precise neural network emulator to quickly map cosmological parameters to desired CMB observables such as temperature and lensing power spectra and SCALE cross spectra. We also outline a method to apply SCALE to full-sky maps of the CMB temperature field, and construct a likelihood for the application of SCALE in parameter estimation. SCALE supplements conventional observables such as the CMB power spectra and baryon acoustic oscillations in constraining parameters that are sensitive to the small-scale lensing amplitude such as the neutrino mass $m_ν$. We show that including estimates of the small-scale lensing amplitude from SCALE in such an analysis provides enough constraining information to measure the minimum neutrino mass at $4σ$ significance in the scenario of minimal mass, and higher significance for higher mass. Finally, we show that SCALE will play a powerful role in constraining models of clustering that generate scale-dependent modulation to the distribution of matter and the lensing power spectrum, as predicted by models of warm or fuzzy dark matter.

Figures (9)

• Figure 1: Summary of the steps involved in the Small-Correlated-Against-Large Estimator for small-scale CMB lensing. Small-scale features $\varsigma$ are correlated against large-scale features $\lambda$ which are dominated by the primary signal. The presence of lensing at small-scales necessarily generates a positive cross-spectrum $C_{\check{L}}^{\lambda\varsigma}$.
• Figure 2: Top: The lensing convergence power spectrum $C_L^{\kappa\kappa}$ for the fiducial cosmology as computed from CAMB is compared to a model with a suppression of lensing power applied at small scales. Also shown are the three small-scale filter ranges for the applications of SCALE chosen to recover information about the lensing suppression. Bottom: The lensing amplitude $A_{\rm lens}$ applied to $C_L^{\kappa\kappa}$ in our suppression model is shown in dark purple (see parameters in Table \ref{['tab:Fiducial']}). A version with lower $L_0 = 7\,000$ is shown in yellow. A version with higher $B = 0.005$ is shown in red. A version with higher $A_{\rm min} = 0.5$ is shown in green. Also shown is the fiducial model with no suppression obtained by setting $A_{\rm min} = 1$.
• Figure 3: A validation of the emulator for our CMB observables. The % error represented here is computed as the difference between the emulator prediction and the computed output (with CAMB for $\{ C_\ell^{TT}, C_L^{\kappa\kappa} \}$, and Monte Carlo integration with CAMB spectra for $\{ N_L^{(1),\kappa\kappa}, \Psi_{\check{L}} \}$) divided by the computed output. We perform training using 7168 out of a set of 8192 band-powers spanning a large range of cosmological parameters outlined in Table \ref{['tab:TrainingPriors']}. We perform validation tests using the remaining 1024 sets of band-powers unseen by the emulator during training. The filled rectangles indicate the expected 68-percentile precision centered on the median, and the bin-to-bin scatter of emulator predictions is uncorrelated. The precision of each predicted $C_\ell^{TT}$ band-power is generally within $0.05\%$, and these rectangles are not visible on this $y$-scale. Error bars indicate the expected observational variance of band-powers, comparable to the diagonal of the covariance matrix underlying \ref{['fig:BaseCorrelation']}. There is no significant bias from the emulator's predictions within our chosen range of cosmological parameter space, and the precision is generally better than the expected observational variance of all band-powers at our chosen level of noise.
• Figure 4: The correlation matrix between simulated CMB temperature, reconstructed lensing, and SCALE band-powers at the fiducial cosmology (see Table \ref{['tab:Fiducial']}). The correlations are computed from 600 simulations. The band-powers are binned similarly to the Planck scheme for $\hat{C}_\ell^{TT}$Planck:2019nip: i.e., unbinned for $2 \leq \ell \leq 31$ (sectioned with dashed lines) and with width $\Delta\ell = 30$ for $32 \leq \ell \leq 3002$. The reconstructed lensing band-powers $\hat{C}_L^{\kappa\kappa,\mathrm{rec}}$ are binned with width $\Delta L=71$ for $2 \leq L \leq 1208$. SCALE band-powers $\hat{\Psi}_{\check{L}}$ are binned with width $\Delta{\check{L}}=71$ for $2 \leq {\check{L}} \leq 1989$. Combinations of contributing components $\{ \hat{C}_\ell^{TT}, \hat{C}_L^{\kappa\kappa,\mathrm{rec}}, \hat{\Psi}_{\check{L}} \}$ and their underlying covariance matrix are used in our likelihoods combining conventional CMB observables and SCALE band-powers.
• Figure 5: The correlation matrix between SCALE band-powers at the fiducial cosmology (see Table \ref{['tab:Fiducial']}). The correlations between three applications of SCALE are depicted here, with shared large-scale filters $2 \leq \ell_L \leq 3000$ and different small-scale filters indicated by superscripts. The correlations are computed from 600 simulations. The strongest off-diagonal entries indicate that SCALE band-powers at the same ${\check{L}}$ are approximately 20-50% correlated between applications of small-scale filters which share half of their multipole coverage. Correlations between SCALE with the other $\ell_S$ filters $\{ \hat{\Psi}_{\check{L}}^{9\mathrm{k}- 11\mathrm{k}}, \hat{\Psi}_{\check{L}}^{10\mathrm{k}- 12\mathrm{k}} \}$ and the other CMB observables $\{ \hat{C}_\ell^{TT}, \hat{C}_L^{\kappa\kappa,\mathrm{rec}} \}$ are similar to those of $\hat{\Psi}_{\check{L}}^{8\mathrm{k}- 10\mathrm{k}}$ in \ref{['fig:BaseCorrelation']}.