The cosmic equation of state

The cosmic spacetime is often described in terms of the Friedmann-Robertson-Walker (FRW) metric, though the adoption of this elegant and convenient solution to Einstein’s equations does not tell us much about the equation of state, p=wρ, in terms of the total energy density ρ and pressure p of the cosmic fluid. ΛCDM and the R_h=ct Universe are both FRW cosmologies that partition ρ into (at least) three components, matter ρ_m, radiation ρ_r, and a poorly understood dark energy ρ_de, though the latter goes one step further by also invoking the constraint w=−1/3. This condition is apparently required by the simultaneous application of the Cosmological principle and Weyl’s postulate. Model selection tools in one-on-one comparisons between these two cosmologies favor R_h=ct, indicating that its likelihood of being correct is ∼90 % versus only ∼10 % for ΛCDM. Nonetheless, the predictions of ΛCDM often come quite close to those of R_h=ct, suggesting that its parameters are optimized to mimic the w=−1/3 equation-of-state. In this paper, we explore this hypothesis quantitatively and demonstrate that the equation-of-state in R_h=ct helps us to understand why the optimized fraction Ω_m≡ρ_m/ρ in ΛCDM today must be ∼0.27, an otherwise seemingly random variable. We show that when one forces ΛCDM to satisfy the equation-of-state w=(ρ_r/3−ρ_de)/ρ, the value of the Hubble radius today, c/H₀, can equal its measured value ct₀ only with Ω_m∼0.27 when the equation-of-state for dark energy is w_de=−1. (We also show, however, that the inferred values of Ω_m and w_de change in a correlated fashion if dark energy is not a cosmological constant, so that w_de≠-1.) This peculiar value of Ω_m therefore appears to be a direct consequence of trying to fit the data with the equation-of-state w=(ρ_r/3−ρ_de)/ρ in a Universe whose principal constraint is instead R_h=ct or, equivalently, w=−1/3.