Emergence of a Cosmological Constant in Anisotropic Fluid Cosmology

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.