It is shown that a first-order cosmological perturbation theory for Friedmann-Lemaître-Robertson-Walker universes admits one and only one gauge-invariant variable which describes the perturbation to the energy density and which becomes equal to the usual energy density of the Newtonian theory of gravity in the limit that all particle velocities are negligible with respect to the speed of light .
The same holds true for the perturbation to the particle number density .

A cosmological perturbation theory based on these particular gauge-invariant quantities is more precise than any earlier first-order perturbation theory .
In particular , it explains star formation in a satisfactory way , even in the absence of cold dark matter .
In a baryon-only universe , the earliest stars , the so-called Population III stars , are found to have masses between 400 and 100,000 solar masses with a peak around 3400 solar masses .
If cold dark matter is present then the star masses are between 130 and 13,000 solar masses with a peak around 450 solar masses .
They come into existence between 100 Myr and 1000 Myr .
At much later times , star formation is possible only in high density regions , for example within galaxies .
Late time stars may have much smaller masses than early stars .
The smallest stars that can be formed have masses of 0.2–0.8 solar mass , depending on the initial internal relative pressure perturbation .

It is demonstrated that the Newtonian theory of gravity can not be used to study the evolution of cosmological density perturbations .