It's about gravitational radiation emitted by stars and the energy that is contained in gravitational fields. Gravitational radiation is produced when matter is accelerated. However, this applies not only to huge masses such as rotating pulsars, but also to accelerated elementary particles. Even photons, light particles that interact with matter, lead to gravitational radiation because their mass equivalent is accelerated during the interaction.
In the interior of stars, an incredible number of elementary particles and photons collide, but it is assumed that no significant gravitational radiation is emitted from these collisions. Even the best-known physicists assume that gravitational radiation is far too weak in relation to the electromagnetic radiation emitted by accelerated charges to be able to play a role in principle. However, this assumption is based on a serious error in thinking.
The fallacy is that the electromagnetic radiation produced by colliding charged particles does not change the sum of kinetic and electromagnetic energy at all. Only the tiny bit of gravitational radiation disturbs the energy balance and, to make matters worse, can also disappear without interaction.
Only collisions leading to nuclear fusion change the balance of kinetic and electrodynamic energy. In the interior of a star, all collisions that only lead to the emission of gravitational waves are more frequent than fusion collisions by a nearly infinite factor. This factor is so large that it almost balances the ratio between the energy content of fusion reactions and gravitational radiation.
It must be taken into account that the collisions of electrons with each other and their interaction with photons also lead to gravitational radiation. In addition, the free path length of photons inside stars is extremely small and each individual photon is completely decelerated or deflected once per free path length. All these collision events do not change the kinetic and electromagnetic energy balance. However, they lead to the generation of gravitational radiation.
Even if it should ultimately turn out that gravitational radiation does not actually play a significant role, the neglect or, more precisely, the complete disregard of mechanisms that lead to microscopic gravitational radiation is an unforgivable mistake.
But when stars emit microscopic gravitational radiation in significant quantities, it has a direct impact on the concept of dark energy and dark matter.
This influence results from the fact that the energy density or the energy density gradient in the gravitational field leads to gravity. Then it is precisely the gradient of the energy density in the gravitational radiation emitted by stars that leads to gravitational anomalies in galaxies.
It is not the influence of dark matter or of already absurd MOND fantasies.
First of all, dark energy doesn't have anything to do with dark matter. They're distinct notions and it doesn't make sense to mention them together.
The existence of dark energy is inferred from measuring the rate of change of the expansion of the universe as a whole. That the universe is expanding was realized since 1929; the question then became whether the rate was constant or not. And in 1998 it was found that the rate is positive. This can be perfectly well described by the cosmological constant, that's as much a part of general relativity as Newton's constant is. The question now has become whether its contribution is, also, sufficient, to describe the rate of expansion, or, whether additional fields are needed, beyond the metric. For the moment the data can be described by the metric alone.
The inference for the existence of dark matter results from the rotation curves of galaxies, so it doesn't have anything to do with gravitational radiation. The rotation curves of galaxies are not affected by gravitational radiation, any more or less than the motion of the Earth around the Sun is.
The only question pertains to the particle content of dark matter, that must be a new form of matter. However gravitational measurements can't discover this, since gravitation isn't sensitive to the matter content, unless fields, besides the metric, contribute to defining the spacetime geometry of the universe. And whether there can exist such fields is quite constrained by known measurements.
It would be a good idea to learn general relativity, cf. https://arxiv.org/pdf/gr-qc/9712019
Stam Nicolis "The inference for the existence of dark matter results from the rotation curves of galaxies, so it doesn't have anything to do with gravitational radiation. The rotation curves of galaxies are not affected by gravitational radiation, any more or less than the motion of the Earth around the Sun is."
Sorry, but you have ignored an important part im my explanation:
"This influence results from the fact that the energy density or the energy density gradient in the gravitational field leads to gravity. Then it is precisely the gradient of the energy density in the gravitational radiation emitted by stars that leads to gravitational anomalies in galaxies."
The essential point is that strong gravitational radiation has a gravitational impact, which easily can be confused with the gravitational impact of dark matter.
Gravitational radiation does have observable effects-as have been measured. But it doesn't affect the rotation curve of a galaxy in the same way as matter does. It suffices to do the calculation of the rotation curve, Newtonian mechanics is necessary and sufficient.
Stam Nicolis "Gravitational radiation does have observable effects-as have been measured. But it doesn't affect the rotation curve of a galaxy in the same way as matter does."
No, the anti-gravitational effect of gravitational radiation can reach a significant fraction of the mass effect. As soon as the density of the gravitational radiation has decayed to the level of the background density, the anti-gravitational effect vanishes. Then the gravity of the full star mass appears. This appearance is interpreted as dark matter with a significant influence on rotation curves.