  The equations of motion for matter fields are invariant under the shift of
the matter lagrangian by a constant. Such a shift changes the energy momentum
tensor of matter by T^a_b --> T^a_b +\rho \delta^a_b. In the conventional
approach, gravity breaks this symmetry and the gravitational field equations
are not invariant under such a shift of the energy momentum tensor. I argue
that until this symmetry is restored, one cannot obtain a satisfactory solution
to the cosmological constant problem. I describe an alternative perspective to
gravity in which the gravitational field equations are [G_{ab} -\kappa T_{ab}]
n^an^b =0 for all null vectors n^a. This is obviously invariant under the
change T^a_b --> T^a_b +\rho \delta^a_b and restores the symmetry under
shifting the matter lagrangian by a constant. These equations are equivalent to
G_{ab} = \kappa T_{ab} + Cg_{ab} where C is now an integration constant so that
the role of the cosmological constant is very different in this approach. The
cosmological constant now arises as an integration constant, somewhat like the
mass M in the Schwarzschild metric, the value of which can be chosen depending
on the physical context. These equations can be obtained from a variational
principle which uses the null surfaces of spacetime as local Rindler horizons
and can be given a thermodynamic interpretation. This approach turns out to be
quite general and can encompass even the higher order corrections to Einstein's
gravity and suggests a principle to determine the form of these corrections in
a systematic manner.
