  Modified General Relativity (MGR) is the natural extension of General
Relativity (GR). MGR explicitly uses the smooth regular line element vector
field $(\bm{X},-\bm{X}) $, which exists in all Lorentzian spacetimes, to
construct a connection-independent symmetric tensor that represents the
energy-momentum of the gravitational field. It solves the problem of the
non-localization of gravitational energy-momentum in GR, preserves the ontology
of the Einstein equation, and maintains the equivalence principle. The line
element field provides MGR with the extra freedom required to describe dark
energy and dark matter. An extended Schwarzschild solution for the matter-free
Einstein equation of MGR is developed, from which the Tully-Fisher relation is
derived, and the gravitational energy density is calculated. The mass of the
invisible matter halo of galaxy NGC 3198 calculated with MGR is identical to
the result obtained from GR using a dark matter profile. Although dark matter
in MGR is described geometrically, it has an equivalent representation as a
particle with the property of a vector boson or a pair of fermions; the
geometry of spacetime and the quantum nature of matter are linked together by
the unit line element covectors that belong to both the Lorentzian metric and
the spin-1 Klein-Gordon wave equation. The three classic tests of GR provide a
comparison of the theories in the solar system and several parts of the cosmos.
MGR provides the flexibility to describe inflation after the Big Bang and
galactic anisotropies.
