Possible signature of entanglement in null-energy-condition-violating inflation

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In recent years, the classical version of the null energy condition (NEC) has been enhanced into its quantum generalization, the quantum null energy condition (QNEC). The right-hand side of the QNEC inequality is non-zero; it is multiplied by a factor of ћ and recovers the standard NEC in the classical limit. Moreover, the second derivative of entanglement entropy also plays a role in determining the right-hand side. In this work, we study several examples of theories of inflation that violate the standard NEC, yet still, possibly obey the QNEC. This suggests that the deviation of the standard NEC arises due to the existence of entanglement between regions inside and outside of the cosmological horizon. Possible connection to quantum fluctuations of de Sitter spacetime is also studied.