Rare Poisson processes (PP) during cosmic inflation can lead to signatures that are localized in position space and are not well-captured by the standard two- or higher-point correlation functions of primordial density perturbations. As an example, PP can lead to localized overdense regions that are far denser than the ones produced through standard inflationary fluctuations. As a result, such overdense regions collapse earlier than expected based on the standard $\mathrm{\Lambda }\mathrm{CDM}$ model and would host anomalously high-redshift galaxies. We describe some general aspects of such PP and consider a particular realization in the context of inflationary particle production. We then show that the masses and redshifts of the resulting galaxies can lie in a range discoverable by the James Webb Space Telescope and future surveys, while being consistent with existing constraints on the matter power spectrum and UV luminosity functions at lower redshifts.

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• Cosmology
• Inflation
• Particle production
• Quantum fields in curved spacetime
• Galaxies