The severe problem is that an absolute negative energy density of gravitational fields is not possible, because then a field source could not adapt its field via aperiodic radiation to a modified velocity.
Therefor we need a cosmic dark energy field with an extremely high energy density, sufficient to compensate for the negative energy density of gravitational fields around neutron stars.
If we consider that the gravitational field strength around neutron stars is about a factor 2.0E+11 stronger as the earth field, the omnipresent dark energy field must have a giant energy density.
The presence of such a strong field turns cosmology inside out. It even adds a new player to the theory of elementary particles. Such a strong field of gravitational nature could stabilize quarks and electrons.
The discussion should be about the pros and cons of the existence of such an omnipresent dark energy field and about the consequences, if such a field exists.
In standard physics and standard cosmology such a field is not considered.