Ellis-Bronnikov Wormholes in Asymptotically Safe Gravity

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 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 valid in General Relativity (GR). We verify that asymptotic safety guarantees that the Ellis-Bronnikov wormhole can satisfy the radial energy conditions at the throat radius, $r_0$, within an interval of values of this latter. That is quite different from the result found in GR. Following, we evaluate the effective radial state parameter, $\omega(r)$, at $r_0$, showing that the quantum gravitational effects modify Einstein's field equations in such a way that it is necessary a very exotic source of matter to generate the wormhole spacetime -- phantom or quintessence-like. That occurs within some ranges of throat radii, even though the energy conditions are or not violated there. Finally, we find that, although at $r_0$ we have a quintessence-like matter, on growing of $r$ we necessarily come across phantom-like regions. We speculate if such a phantom fluid must always be present in wormholes in the ASG context or even in more general quantum gravity scenarios.