Aspects of Duality in Cosmology
  In the first part of this article, given the intent to stay at a popular
level, it has been introduced and explained briefly basic concepts of
Einstein's General Relativity, Dark Matter, Dark Energy, String Theory, Quantum
Gravity and Extended Theories of Gravity. The core of this research is based on
selecting a class of f(R) theories of gravity, which exhibits scale factor
duality transformations. The starting point of this theory is the effective
theory of gravity derived from Bosonic String Theory, which is called tree
level effective theory of gravity. It is shown that this theory can be cast in
a class of f(R) theories of gravity (modified theories of Einstein's General
Relativity). It is imposed that FLRW metric be solution of this class of $f(R)$
theories, and, using the Noether symmetry approach, it is found that the
cosmological model has scale factor duality like the Pre-Big Bang cosmology of
Gasperini and Veneziano.
