Because of these remarkable agreements between observation and theory, most work in the field of physical cosmology (see Section 4) has utilized the standard model as the background spacetime in which the large scale structure evolves, with the ambition to further constrain parameters and structure formation scenarios through numerical simulations. The most widely accepted form of the model is described by a set of dimensionless density parameters which sum to for a more in-depth review of the standard model, and to [128, 154] for a summary of observed cosmological parameter constraints and best fit “concordance” models. Peebles and Ratra  provide a comprehensive literature survey and an excellent review of the standard model, cosmological tests, and the evidence for dark energy and the cosmological constant.
However, some important unanswered questions about the standard model concern the nature of the special conditions that produced an essentially geometrically flat Universe that is also homogeneous and isotropic to a high degree over large scales. In an affort to address these questions, it should be noted that many other cosmological models can be constructed with a late time behavior similar enough to the standard model that it is difficult to exclude them with absolute certainty. Consider, for example, the collection of homogeneous but arbitrarily anisotropic vacuum spacetimes known as the Bianchi models [141, 69]. There are nine unique models in this family of cosmologies, ranging from simple Bianchi I models representing the Kasner class of spacetimes (the flat FLRW model, sometimes referred to as Type I-homogeneous, belongs to this group), to the more complex and chaotic Bianchi IX or Mixmaster model (which also includes the closed FLRW model, Type IX-homogeneous). Several of these models will be discussed in the first section on relativistic cosmology (Section 3) dealing pre-dominately with the early Universe, where the models differ the most.
Anisotropic solutions, as well as more general (and in some cases exact) inhomogeneous cosmological models with initial singularities, can isotropize through anisotropic damping mechanisms and adiabatic cooling by the expansion of the Universe to resemble the standard FLRW model at late times. Furthermore, if matter is included in these spacetimes, the effective energy of anisotropy, which generally dominates matter energy at early times, tends to become less important over time as the Universe expands. The geometry in these matter-filled anisotropic spacetimes thus evolves towards an isotropic state. Quantum mechanical effects have also been proposed as a possible anisotropy damping mechanism that takes place in the early Universe to convert vacuum geometric energy to radiation energy and create particles. All of this suggests that the early time behavior and effects of local and global geometry are highly uncertain, despite the fact that the standard FLRW model is generally accepted as accurate enough for the late time description of our Universe.
Further detailed information on homogeneous (including Bianchi) universes, as well as more general classes of inhomogeneous cosmological models can be found in [105, 158, 70].
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