Emergence of a cosmological constant in anisotropic fluid cosmology

In this paper, we investigate anisotropic fluid cosmology in a situation where the space-time 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-Lemaítre-Robertson-Walker (FLRW) large-scale cosmological evolution in the presence of local inhomogeneities and time-dependent backreaction. We use our derivation to tackle the cosmological constant problem. A cosmological constant emerges by averaging the backreaction term on spatial scales of the order of 100 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.