The high precision attained by cosmological data in the last few years has increased the interest in exact solutions. Analytic expressions for solutions in the Standard Model are presented here for all combinations of Λ = 0, Λ ≠ 0, κ = 0, and κ ≠ 0, in the presence and absence of radiation and nonrelativistic matter. The most complete case (here called the ΛγCDM Model) has Λ ≠ 0, κ ≠ 0, and supposes the presence of radiation and dust. It exhibits clearly the recent onset of acceleration. The treatment includes particular models of interest such as the ΛCDM Model (which includes the cosmological constant plus cold dark matter as source constituents).
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Aldrovandi, R., Cuzinatto, R.R. & Medeiros, L.G. Analytic Solutions for the Λ-FRW Model. Found Phys 36, 1736–1752 (2006). https://doi.org/10.1007/s10701-006-9076-6
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DOI: https://doi.org/10.1007/s10701-006-9076-6