The phrase “physical cosmology” is generally associated with the large (galaxy and cluster) scale structure of the post-recombination epoch where gravitational effects are modeled approximately by Newtonian physics on an uniformly expanding, matter dominated FLRW background. A discussion of the large scale structure is included in this review since any viable model of our Universe which allows a regime where strongly general relativistic effects are important must match onto the weakly relativistic (or Newtonian) regime. Also, since certain aspects of this regime are directly observable, one can hope to constrain or rule out various cosmological models and/or parameters, including the density (), Hubble (), and cosmological () constants.

Due to the vast body of literature on numerical simulations dealing with the post-recombination epoch, only a very small fraction of published work can be reviewed in this paper. Hence, the following summary is limited to cover just a few aspects of computational physical cosmology, and in particular those that can potentially be used to discriminate between cosmological model parameters, even within the realm of the standard model.

For a general overview of theoretical and observational issues associated with structure formation, the reader is referred to [133, 131], and to [45] for a broad review of numerical simulations (and methods) of structure formation.

4.1 Cosmic microwave background

4.1.1 Primordial black body effects

4.1.2 Primary anisotropies

4.1.3 Secondary anisotropies

4.1.4 Computing CMBR anisotropies with ray-tracing methods

4.2 Gravitational lensing

4.3 First star formation

4.4 Ly forest

4.5 Galaxy clusters

4.5.1 Internal structure

4.5.2 Number density evolution

4.5.3 X-ray luminosity function

4.5.4 SZ effect

4.6 Cosmological sheets

4.1.1 Primordial black body effects

4.1.2 Primary anisotropies

4.1.3 Secondary anisotropies

4.1.4 Computing CMBR anisotropies with ray-tracing methods

4.2 Gravitational lensing

4.3 First star formation

4.4 Ly forest

4.5 Galaxy clusters

4.5.1 Internal structure

4.5.2 Number density evolution

4.5.3 X-ray luminosity function

4.5.4 SZ effect

4.6 Cosmological sheets

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