The cosmic equation of state

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15 Scopus citations


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 Rh=ct Universe are both FRW cosmologies that partition ρ into (at least) three components, matter ρm, radiation ρr, and a poorly understood dark energy ρde, 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 Rh=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 Rh=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 Rh=ct helps us to understand why the optimized fraction Ωm≡ρm/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=(ρr/3−ρde)/ρ, the value of the Hubble radius today, c/H0, can equal its measured value ct0 only with Ωm∼0.27 when the equation-of-state for dark energy is wde=−1. (We also show, however, that the inferred values of Ωm and wde change in a correlated fashion if dark energy is not a cosmological constant, so that wde≠-1.) This peculiar value of Ωm therefore appears to be a direct consequence of trying to fit the data with the equation-of-state w=(ρr/3−ρde)/ρ in a Universe whose principal constraint is instead Rh=ct or, equivalently, w=−1/3.

Original languageEnglish (US)
Pages (from-to)393-398
Number of pages6
JournalAstrophysics and Space Science
Issue number2
StatePublished - Apr 2015


  • Cosmic microwave background
  • Cosmological parameters
  • Cosmology: dark matter
  • Cosmology: observations
  • Cosmology: redshift
  • Cosmology: theory
  • Gravitation

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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