  While the generally recognized symmetries of cosmos are preserved,
conservation laws for gravitational system are reconsidered and the Lagrangian
density of pure gravitational field is revised. From these considerations, some
of the theoretical foundations of the current cosmology are extended or
revised, and a new theory of cosmology is established. This new theory leads to
the following distinct properties of cosmos: the energy of matter field might
originate from the gravitational field; the big bang might not have occurred;
the fields of the dark energy and some parts of the dark matter would not be
matter fields but might be gravitational fields, they would only interact with
gravitational force but could not interact with other forces. These distinct
properties can be tested by future experiments and observations.
