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We present 307 Type Ia supernova (SN) light curves from the first four yearsof the TESS mission. We use this sample to characterize the shapes of the earlytime light curves, measure the rise times from first light to peak, and searchfor companion star interactions. Using simulations, we show that light curvesmust have noise $<$10% of the peak to avoid biases in the early time lightcurve shape, restricting our quantitative analysis to 74 light curves. We findthat the mean power law index $t^{\beta_1}$ of the early time light curves is1.93$\pm$ 0.57 and the mean rise time to peak is 15.7 $\pm$ 3.5 days. We alsoestimate the underlying population distribution and find a Gaussian componentwith mean $\beta_1 = 2.29$, width 0.34, and a tail extending to values lessthan 1.0. We use model comparison techniques to test for the presence ofcompanion interactions. In contrast to recent results in the literature, wefind that the data can rarely distinguish between models with and withoutcompanion interactions, and caution is needed when claiming detections of earlytime flux excesses. Nevertheless, we find three high-quality SN light curvesthat tentatively prefer the addition of a companion interaction model, but thestatistical evidence is not robust. We also find two SNe that disfavor theaddition of a companion interaction model to a curved power law model. Takingthe 74 SNe together, we calculate 3$\sigma$ upper limits on the presence ofcompanion signatures to control for orientation effects that can hidecompanions in individual light curves. Our results rule out common progenitorsystems with companions having Roche lobe radii $>$ 31 R$_{\odot}$ (99.9%confidence level) and disfavor companions having Roche lobe radii $>$ 10R$_{\odot}$ (95% confidence level). Lastly, we discuss the implications of ourresults for the intrinsic fraction of single degenerate progenitor systems.

Four years of Type Ia Supernovae Observed by TESS: Early Time Light Curve Shapes and Constraints on Companion Interaction Models