Ellis–Bronnikov Wormholes in Asymptotically Safe Gravity

Abstract

In this paper, we investigate the simplest wormhole solution—the Ellis–Bronnikov one—in the context of the asymptotically safe gravity (ASG) at the Planck scale. We work with three models, which employ the Ricci scalar, Kretschmann scalar, and squared Ricci tensor to improve the field equations by turning the Newton constant into a running coupling constant. For all the cases, we check the radial energy conditions of the wormhole solution and compare them with those that are valid in general relativity (GR). We verified that asymptotic safety guarantees that the Ellis–Bronnikov wormhole can satisfy the radial energy conditions at the throat radius, r0, within an interval of values of the latter, which is quite different from the result found in GR. Following this, we evaluate the effective radial state parameter, ω(r), at r0, showing that the quantum gravitational effects modify Einstein’s field equations in such a way that it is necessary to have a very exotic source of matter to generate the wormhole spacetime–phantom or quintessence-like matter. This occurs within some ranges of the throat radii, even though the energy conditions are or are not violated there. Finally, we find that, although at r0 we have a quintessence-like matter, upon growing r, we inevitably came across phantom-like regions. We speculate whether such a phantom fluid must always be present in wormholes in the ASG context or even in more general quantum gravity scenarios.