JWST has revealed a population of compact and extremely red galaxies at
z>4, which likely host active galactic nuclei (AGN). We present a sample of
434 ``little red dots'' (LRDs), selected from the 0.54 deg2 COSMOS-Web
survey. We fit galaxy and AGN SED models to derive redshifts and physical
properties; the sample spans z∼5-9 after removing brown dwarf
contaminants. We consider two extreme physical scenarios: either LRDs are all
AGN, and their continuum emission is dominated by the accretion disk, or they
are all compact star-forming galaxies, and their continuum is dominated by
stars. If LRDs are AGN-dominated, our sample exhibits bolometric luminosities
∼1045−47 erg\,s−1, spanning the gap between JWST AGN in the
literature and bright, rare quasars. We derive a bolometric luminosity function
(LF) ∼100 times the (UV-selected) quasar LF, implying a non-evolving black
hole accretion density of ∼10−4 M⊙ yr−1 Mpc−3 from
z∼2-9. By contrast, if LRDs are dominated by star formation, we derive
stellar masses ∼108.5−10M⊙. MIRI/F770W is key to deriving
accurate stellar masses; without it, we derive a mass function inconsistent
with ΛCDM. The median stellar mass profile is broadly consistent with
the maximal stellar mass surface densities seen in the nearby universe, though
the most massive ∼50\% of objects exceed this limit, requiring substantial
AGN contribution to the continuum. Nevertheless, stacking all available X-ray,
mid-IR, far-IR/sub-mm, and radio data yields non-detections. Whether dominated
by dusty AGN, compact star-formation, or both, the high masses/luminosities and
remarkable abundance of LRDs implies a dominant mode of early galaxy/SMBH
growth.Comment: 27 pages, 13 figures. Submitted to ApJ, comments welcome! Data access
at https://github.com/hollisakins/akins24_c