The Cosmic Evolution of Fast Radio Bursts Inferred from the CHIME/FRB Baseband Catalog 1

Redshift and luminosity distributions are essential for understanding the cosmic evolution of extragalactic objects and phenomena, such as galaxies, gamma-ray bursts, and fast radio bursts (FRBs). For FRBs, these distributions are primarily estimated using the fluence and the Dispersion Measure (DM). Calibrating their joint distribution has been challenging due to a lack of accurate fluences in the intensity data of the CHIME/FRB survey. Using the baseband update of CHIME/FRB Catalog 1, we calibrate the 2D fluence-DM distribution for the first time. We find the energy distribution is described well by a Schechter function with power-law slope of $-1.94^{+0.14}_{-0.12}$. Testing two types of redshift evolution models suggests a likely combination of young and old formation channels. $31^{+31}_{-21}$% of FRB sources may track star formation, or correspondingly, FRB sources may have delay times of $1.94^{+1.54}_{-1.31}$ Gyr. A pure star formation tracking population is excluded by only one model at $> 2\sigma$ confidence. An updated cosmic star formation rate density evolution up to redshift 14 is constrained by compiling results from several JWST studies. The furthest FRB detection with planned radio facilities is expected to be at $z \approx 5$. A radio telescope operating at 200 MHz with a system-equivalent flux density of $\leq 0.07$ Jy (equivalent to a detection threshold of 1 mJy ms) and instantaneous sky coverage of $\gtrsim 400$ square degrees should be able to detect $630^{+730}_{-485}$ FRBs year$^{-1}$ at $z \gtrsim 6$ and $53^{+83}_{-43}$ FRBs year$^{-1}$ at $z\gtrsim 8$, which is sufficient to differentiate between reionization histories.