  We investigate anisotropic fluid cosmology in a situation where the spacetime
metric back-reacts in a local, time-dependent way to the presence of
inhomogeneities. We derive exact solutions to the Einstein field equations
describing Friedmann-Lemaitre-Robertson-Walker (FLRW) large scale cosmological
evolution in the presence of local inhomogeneities and time-dependent back
reaction. We use our derivation to tackle the cosmological constant problem. A
cosmological constant emerges by averaging the back reaction term on spatial
scales of the order of $100 \ \text{Mpc}$, at which our universe begins to
appear homogeneous and isotropic. We find that the order of magnitude of the
"emerged" cosmological constant agrees with astrophysical observations and is
related in a natural way to baryonic matter density. Thus, there is no
coincidence problem in our framework.
