  The expression of gravitational time advancement (negative time delay) for
particles with non-zero mass in Schwarzschild geometry has been obtained. The
influences of the gravitational field that describes the observed rotation
curves of spiral galaxies and that of dark energy (in the form of cosmological
constant) on time advancement of particles have also been studied. The present
findings suggest that in presence of dark matter gravitational field the time
advancement may take place irrespective of gravitational field of the observer,
unlike the case of pure Schwarzschild geometry where gravitational time
advancement takes place only when the observer is situated at stronger
gravitational field compare to the gravitational field encountered by the
particle during its journey. When applied to the well known case of SN 1987a,
it is found that the net time delay of a photon/gravitational wave is much
smaller than quoted in the literature. In the presence of dark matter field,
the photon and neutrinos from SN 1987a should have been suffered gravitational
time advancement rather than the delay.
