Analytical solution of traversable wormholes in the presence of positive cosmological constant

Abstract

The construction of traversable wormholes with a cosmological constant, $\Lambda$, introduces significant challenges and leads to non-trivial modifications of the spacetime geometry. In this work, we obtain an analytical solution describing a locally traversable wormhole for $\Lambda >0$ following a perturbative approach. Starting from the Ellis-Bronnikov wormhole geometry, we derive the metric deformation induced by the cosmological constant at linear order, assuming $\Lambda r_0^2\ll 1$, where $r_0$ represents the throat of the Ellis-Bronnikov wormhole. We further identify the radial domain of validity of the perturbative solution, which is restricted to $r\ll \sqrt{3/\Lambda }$. Within this domain, we find that the Ellis-Bronnikov wormhole is modified by the cosmological constant; interestingly, the shape function takes a de Sitter-like form. Nevertheless, we verify that the flare-out condition holds at the deformed throat and find a violation of the null energy condition in its vicinity, as required for traversable WHs. Traversability is further analyzed by evaluating tidal forces and deriving constraints on the velocity required for safe human passage. Additionally, we discuss the possibility of constructing a global extension by matching the perturbative wormhole solution to a Schwarzschild-de Sitter exterior spacetime. Given the recent advances in the observational study of astrophysical compact objects, together with a variety of astrophysical and cosmological observations indicating the existence of a positive cosmological constant, the analytical solution presented here may be of considerable phenomenological interest.

20 pages,5 figures, revised version, JCAP

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