Smoothing Out Spatially Closed Cosmologies

Classical back reaction of low-frequency cosmic gravitational radiation

“…to consider a fluid with the components ρ m = Λ 8πG , p m = − Λ 8πG . Considering again the case lim k→0 ǫ 0 = 0, we arrive at (77) as before, but the field equations (12) and (13) lead now to an exponential increase or decrease of the scale factor (in the η-coordinate): a = a 1 exp (±η 4πk 5 1 q/3 ).…”

“…How averages can be formulated consistently in general relativity, is a basic and still not completely solved problem [5]. Our assumption is to interprete the perturbations of the geometry as random functions as in optical coherence theory [6] or in the Monin-Yaglom approach to statistical fluid mechanics [7].…”

Observational Evidence for Dark Matter and Dark Energy

“…Whatever smoothing process is adopted, the Einstein field equations with a smoothed energy-momentum tensor cannot yield the smoothed metric of the CS simply because the are highly non-linear. As a consequence, the so-called back-reaction shows up [54,55], which is unfortunately generally ignored. Hence we get the Friedmann equations…”

Ricci Flow Gravity

“…4 Flow-like equations are also not unfamiliar to physicists, the earliest and most well-known being the renormalization group equations in quantum field theory (for an introduction, see Mitter [14]), and also the nonlinear σ -model (e.g., Lott [15], Oliynyk, Suneeta and Woolgar [16], Tseytlin [17]). After Ellis [18] called attention to the cosmological "fitting problem", the usefulness of the Ricci flow to deal with volume-averaged inhomogeneities was immediately recognized and continues to be an active area of research (e.g., Carfora and Marzuoli [19], Buchert and Carfora [20], and the recent review by Buchert [21]). An overview of flow techniques in physics is given in Bakas [22].…”