Analytic Solutions for the Λ-FRW Model

Abstract

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).

Multi-fluid cosmology in Einstein gravity: analytical solutions

“…This solution is well-known and found in standard cosmology textbooks, e.g., [94,261,404] and as a special case of more complicated solutions [13]. For K = +1, the scale factor is…”

“…In its parametric form using conformal time, the solution is well known (Tauber [389] and Gilman [189] gave the solution for K = 0, ±1) and is found in standard cosmology textbooks, e.g., [94,261,404]. It is rarer to find it expressed in terms of comoving time, in which case it reads [13,395]…”

Cosmic acceleration from second order gauge gravity

“…Our future perspectives include to obtain more accurate values for the parameters using the likelihood function fitted by supernovae data. We also intend to study a perturbative solution for a closed (κ = 1) universe, keeping in mind the exact solution found in the ordinary FLRW case (Aldrovandi et al 2006).…”

Multi-scale perturbation theory. Part I. Methodology and leading-order bispectrum corrections in the matter-dominated era

“…The first step here is straightforward, with known exact solutions available for spatially flat FRW cosmologies with dust and Λ [14]. The second step is more complicated, and could be approached in a number of ways [10,11].…”