We present an introductory review of the standard cosmological model i
n the framework of Einstein's theory of gravitation. We show that the
standard model while succeeding in predicting many features of the evo
lution of the Universe, cannot, however, explain some other recent obs
ervations. In particular, some inconsistencies arise between the prese
nt values of the cosmological parameters, the age of the Universe, the
nature of the so-called dark matter, and the standard inflationary pr
ediction Omega = 1. Neither can the standard cosmology explains the re
cent discovery of a galactic periodicity in pencil beam surveys. In th
is paper we review the alternative oscillating G model proposed as an
explanation of this phenomena, and also as a candidate to reconcile th
e cosmological parameters with the cosmological dark matter problem.