Non-perpetual eternal inflation and the emergent de Sitter Swampland conjecture

Abstract We introduce a novel correlation, $$n_{\text {s}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>n</mml:mi> <mml:mtext>s</mml:mtext> </mml:msub> </mml:math> - $$\Delta N$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> , connecting CMB parameters to the required total e-folds for eternal inflation. This correlation provides a robust tool for evaluating eternal (string) inflation models using CMB data and explores the impact of quantum fluctuations on non-attractor phases. By generalizing eternal inflation criteria, our parameterization simplifies rigorous testing of predictions and reveals a link between refined de Sitter conjecture parameters and the eternal nature of the cosmic landscape. This points to a general tendency towards eternal behavior in low-energy effective field theories within the landscape, opening the possibility for our cosmic stage to potentially embrace a ’multiverse’ scenario.