In this paper we examine the effects introduced in the luminosity
function of white dwarf stars by a change of the gravitational
constant during the life of the Universe. A decrease of G induces
the expansion of the star and accelerates its cooling. This effect
has noticeable effects on the luminosity function and can be used to
set upper bounds on the rate of change of G. Preliminary results
indicate that Ġ/G ≤ 10-13 yr-1. These values are the
best ever obtained and will improve as the white dwarf luminosity
function will improve.