Dark energy contributing to, or modifying, mass estimates?

I have found some papers (like this one: https://www.aanda.org/articles/aa/full_html/2009/45/aa12762-09/aa12762-09.html) which say that dark energy increases the potential energy in a system of a quasi-stationary gravitationally bound many-body system.

It also says that because of this, the virial mass estimate also increases with dark energy.

And also in this other paper (https://arxiv.org/abs/2306.14963) it is said that the presence of a cosmological constant (dark energy) increases the estimate of the mass of the Local Group. Is this because of an increase in the potential energy (as in the previous case)?

Does dark energy increase mass estimates by increasing the potential energy of the system?

Suekdccia said:

Does dark energy increase mass estimates by increasing the potential energy of the system?

In principle, yes. Heuristically, you can think of it as adding a small repulsive potential energy, so that the system is slightly less tightly bound than it would be in the absence of dark energy, and so has a slightly larger mass (because the system's mass gets larger as it gets less tightly bound--the net binding energy is a negative contribution to the mass).

In practice, for systems like our solar system, the effect is too small to measure. The papers you reference appear to be estimating the effect for the Local Group of galaxies, which is just large enough that the effect might be measurable in the data.