### Abstract

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/H_{0}, can equal its measured value ct_{0} 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.

Original language | English (US) |
---|---|

Pages (from-to) | 393-398 |

Number of pages | 6 |

Journal | Astrophysics and Space Science |

Volume | 356 |

Issue number | 2 |

DOIs | |

State | Published - 2015 |

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### Keywords

- 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

### Cite this

*Astrophysics and Space Science*,

*356*(2), 393-398. https://doi.org/10.1007/s10509-014-2211-5

**The cosmic equation of state.** / Melia, Fulvio.

Research output: Contribution to journal › Article

*Astrophysics and Space Science*, vol. 356, no. 2, pp. 393-398. https://doi.org/10.1007/s10509-014-2211-5

}

TY - JOUR

T1 - The cosmic equation of state

AU - Melia, Fulvio

PY - 2015

Y1 - 2015

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

UR - http://www.scopus.com/inward/record.url?scp=84925503579&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84925503579&partnerID=8YFLogxK

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 -