Connecting the Dots: Prospects for Detecting Multi-Source Inflation through Scale-Dependent and Stochastic Bias of Little Red Dots

Recent work has proposed using the spatial clustering of Little Red Dots (LRDs) as a high-redshift cosmological probe. In this paper, we investigate the feasibility of obtaining a LRD sample with a future space experiment, and forecast LRD constraints on primordial local-type non-Gaussianity, $f_{\mathrm{N}\mathrm{L}}^{\mathrm{l}\mathrm{o}\mathrm{c}}$, and the collapsed-limit trispectrum amplitude, ${\tau }_{\mathrm{N}\mathrm{L}}^{\mathrm{l}\mathrm{o}\mathrm{c}}$. LRDs are ideally suited to probe these inflationary parameters because they span a large cosmological volume, have high bias and are easily identifiable. We perform idealised joint $f_{\mathrm{N}\mathrm{L}}^{\mathrm{l}\mathrm{o}\mathrm{c}}$–${\tau }_{\mathrm{N}\mathrm{L}}^{\mathrm{l}\mathrm{o}\mathrm{c}}$ Fisher forecasts assuming the universality relation, Gaussian covariance, Poisson shot-noise and a normalised redshift dispersion, $\sigma (z)\mathrm{/}\left(1+z\right)=0.03$. We quantify the significance at which one would detect multi-source inflation under the Suyama–Yamaguchi relation, ${\tau }_{\mathrm{N}\mathrm{L}}^{\mathrm{l}\mathrm{o}\mathrm{c}}>{\left(6\mathrm{/}5f_{\mathrm{N}\mathrm{L}}\right)}^2$, across the $f_{\mathrm{N}\mathrm{L}}^{\mathrm{l}\mathrm{o}\mathrm{c}}$–${\tau }_{\mathrm{N}\mathrm{L}}^{\mathrm{l}\mathrm{o}\mathrm{c}}$ plane. We find that a LRD analysis could robustly detect multi-source inflation at high-significance over a large region of parameter space, and would be more constraining than all other past or present experiments.