Cosmological Radio Beacon Constraints from Fast Radio Burst Surveys: From CHIME to Next-Generation Radio Telescopes

Using current radio telescope surveys, we derive upper bounds on the num- ber of advanced civilizations that could produce radio bursts of high energy and millisecond duration as deliberate beacons. The calculation incorpo- rates the effects of light travel time and cosmological expansion, and gives the probability of detectable signaling as a function of broadcasting lifetime and burst rate. The analysis is calibrated against the Second CHIME/FRB Catalog, which contains 4,539 FRB detections, including 83 confirmed re- peating sources. The argument does not require observed FRBs themselves to be artificial. Using both simplified static-universe models and full ΛCDM volume in- tegration, we derive analytic and numerical expressions for the detectable fraction f(τ) of broadcasting civilizations. We derive an upper limit Nmax on the number of FRB-class broadcasting civilizations as a function of broadcast lifetime T. For a single reference di- rectional beacon and T = 1 Gyr, Nmax is∼700,000. We extend the analysis to a multi-beacon regime and define the combined effective sky-coverage pa- rameter η ≡M·Ω/4π, where M is the number of independent beacons per civilization and Ω/4π is the per-beacon beam fraction; the reference beacon above corresponds to η = 10−3. In the full-sky coverage limit (η = 1), this constraint tightens significantly to Nmax ∼700. In the same effective full-sky coverage limit (η = 1), the projected BURSTT and SKA-Low constraints reach Nmax ∼5 for a broadcasting lifetime of T = 1 Gyr and Nmax ∼5,000 for T = 1 Myr, within their survey volume (z ≲ 0.1). We show that the constraints are on the product of broadcaster abundance and broadcasting longevity rather than either quantity independently.