Do the stars in galaxies expand wrt each other because of dark energy?

Question

Expansion of space is observed between galaxies. In the galaxies themselves, the effect is very small obviously. But is space, no matter how little, actually expanding or is it countered by local gravity, so matter, reducing the influence of dark energy, isn't diluting, causing DE to increase in force?

Answer 1

No, space expands based on the Einstein Field Equations, which relates the curvature of spacetime to the stress energy tensor. In regions with high matter density (like within galaxies), the dark energy is negligible, so the behavior of spacetime is dominated by the matter.

Space expands and countered by local gravity, leading to no expansion: False

Dark energy is countered by local matter, leading to no expansion: True

Answer 2

The statement "all space is expanding" is utterly wrong.

The space does not expand at all within galaxies, not even within galactic clusters, because these structures are gravitationally bound (dark energy is irrelevant on these scales). For instance, Andromeda is not moving away from the Milky Way as a result of the cosmic expansion. On the contrary, Andromeda is approaching the Milky Way because of their mutual gravitational atraction. Andromeda–Milky Way collision is predicted to occur in about 5 billion years.

Hubble expansion is only noticeable at much larger scales $\sim 100 \; Mpc$, or greater, the scale of super-clusters of galaxies and cosmic voids, where the Cosmological Principle (CP) applies. The CP is the fundamental assumption underlying all cosmological models that predict the cosmic expansion. You can't apply the Friedmann Equations within a galaxy (or galactic cluster) because on these scales the CP is not valid. The equations that govern the galactic dynamics are not the Friedmann Equations.

Only when viewed on a large enough scale $\sim 100 \; Mpc$, the spatial distribution of matter in the universe is homogeneous and isotropic (on average). On these scales, the CP is a very good approximation, the Friedmann Equations predict the cosmic expansion, and astronomical observations confirm the theoretical prediction.

Answer 3

The mainstream model of cosmology is the Big Bang model, BB,based on the theory of General Relativity. As the words say it, a three dimensional Bang/explosion expands from a center and every part of matter distances from every other part, radially in according to classical mechanics. In GR the analogue is the mathematical model of the BB,observation/data that

Crucially, the theory is compatible with Hubble–Lemaître law—the observation that the farther away a galaxy is, the faster it is moving away from Earth. Extrapolating this cosmic expansion backwards in time using the known laws of physics, the theory describes an increasingly concentrated cosmos preceded by a singularity in which space and time lose meaning (typically named "the Big Bang singularity")

That is the basic expansion of the galaxies receding from each other and fitted with the BB model. Dark energy is the title given to a continuing expansion more than can be fitted with the BB model.

In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the universe does not expand at a constant rate; rather, the universe's expansion is accelerating.

italics mine.