Ellis-Bronnikov Wormholes in Asymptotically Safe Gravity
UNIVERSE, (2021)DOI: 10.3390/universe7070238
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, r(0), 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,
omega(r), at r(0), 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.