Abstract

One of the biggest challenges for current cosmology is the late time speed‐up of the universe. Among the several mechanisms that have been suggested to explain this problem we focus our attention in a model including both a negative cosmological constant Λ and a scalar field evolving under the action of an exponential potential. We conclude that a negative Λ is indeed allowed and could represent a viable mechanism to halt eternal acceleration. We reconstruct the gravity Lagrangian f(R) of a fourth order theory of gravity predicting the same dynamics (scale factor and Hubble parameter) as the starting model. We thus end up with a f(R) theory able to both fit the data and solve the problem of eternal acceleration without the need of an unusual negative Λ and ad hoc scalar fields.