Indexed on: 26 May '18Published on: 26 May '18Published in: arXiv - General Relativity and Quantum Cosmology
The subject of cosmological backreaction in General Relativity is often approached by coordinate-dependent and metric-based analyses. We present in this Letter an averaging formalism for the scalar parts of Einstein's equations that is coordinate-independent and only functionally depends on a metric, and that is applicable to general $3+1$ foliations of spacetime and an arbitary fluid with tilted flow. We clarify the dependence on spacetime foliation and argue that this dependence is weak in cosmological settings. We also introduce a new set of averaged equations that feature a global cosmological time, and we put the statistical nature of effective cosmologies into perspective.