The Peculiar Growth of Structure: Validating $f\sigma_8$ Measurements from TITAN Type Ia Supernovae and the Uchuu Simulations
The growth rate of cosmic structure, parameterized by $f\sigma_8$, is a fundamental test of $\Lambda$CDM and general relativity. Using Type Ia supernova (SN Ia) peculiar velocities in conjunction with galaxy redshift surveys may be one of the most precise pathways to measuring $f\sigma_8$ in the local Universe, yet existing analyses have not quantified its systematic uncertainties. Here, we present an end-to-end simulated $f\sigma_8$ measurement tailored to the Type Ia Supernova Trove from ATLAS in the Nearby Universe (TITAN) survey, using ~2000 simulated SNe Ia at $z < 0.067$. We use the Uchuu $N$-body simulations to generate mock galaxy catalogs and SN Ia simulations with realistic, correlated peculiar velocities, and use these catalogs to reconstruct density fields that replicate the 2M++ redshift survey. Using a modified forward likelihood framework across eight mock realizations, we recover $\langle f\sigma_8 \rangle = 0.429 \pm 0.038$ ($\sigma_{\rm stat} = 0.030$, $\sigma_{\rm sys} = 0.023$), consistent with the Uchuu simulation input $f\sigma_8 = 0.428$ to within 0.1%. The mock-to-mock scatter of 0.031 is consistent with our uncertainties, highlighting the reliability of our error estimates. Our measurement is dominated by the statistical uncertainty, with approximately equal contributions from SN Ia ($\sigma_{\rm sys}^{\rm SN}=0.017$) and density reconstruction ($\sigma_{\rm sys}^{\rm recon}=0.016$) systematic uncertainties. The assumed intrinsic scatter model is the largest single systematic contribution, and a different model choice can shift $f\sigma_8$ to lower values, largely driven by red SNe with a skewed color distribution. Our analysis provides the first systematic uncertainty budget for the "reconstruction-and-scaling" method of measuring $f\sigma_8$ with SNe Ia, and demonstrates that SNe Ia are a competitive probe of the growth of structure in the local Universe.