A New Theory of Cosmology That Preserves the Generally Recognized Symmetries of Cosmos, Explains the Origin of the Energy for Matter Field, but Excludes the Existence of the Big Bang

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