Constraints on Genesis Cosmology from the Smeared Null Energy Condition

The violation of the null energy condition (NEC) is essential for constructing nonsingular cosmological scenarios, such as Genesis cosmology, which avoids the initial singularity by initiating cosmic evolution from an asymptotically Minkowski state. To address theoretical concerns regarding the accumulation of negative energy, the smeared null energy condition (SNEC) has been proposed as a quantum-motivated, semi-local bound on NEC violation. In this work, we examine the implications of the SNEC conjecture for Genesis models, typically constructed within generalized Galileon theories. Our results demonstrate that SNEC imposes nontrivial restrictions on the viability of Genesis models, highlighting the SNEC conjecture as a powerful tool for constraining nonsingular cosmological scenarios.