TY - JOUR

T1 - The cosmic equation of state

AU - Melia, F.

N1 - Funding Information:
I am grateful to the anonymous referee for suggestions that have led to improvements in the manuscript. I am also grateful to Amherst College for its support through a John Woodruff Simpson Lectureship, and to Purple Mountain Observatory in Nanjing, China, for its hospitality while part of this work was being carried out. This work was partially supported by grant 2012T1J0011 from The Chinese Academy of Sciences Visiting Professorships for Senior International Scientists, and grant GDJ20120491013 from the Chinese State Administration of Foreign Experts Affairs.
Publisher Copyright:
© 2014, Springer Science+Business Media Dordrecht.

PY - 2015/4

Y1 - 2015/4

N2 - 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.

AB - 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.

KW - Cosmic microwave background

KW - Cosmological parameters

KW - Cosmology: dark matter

KW - Cosmology: observations

KW - Cosmology: redshift

KW - Cosmology: theory

KW - Gravitation

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U2 - 10.1007/s10509-014-2211-5

DO - 10.1007/s10509-014-2211-5

M3 - Article

AN - SCOPUS:84925503579

VL - 356

SP - 393

EP - 398

JO - Astrophysics and Space Science

JF - Astrophysics and Space Science

SN - 0004-640X

IS - 2

ER -