# The cosmic equation of state

http://hdl.handle.net/10150/614766
Title:
The cosmic equation of state
Author:
Melia, F.
Affiliation:
The University of Arizona
Issue Date:
2014-12-04
Publisher:
Springer Verlag
Citation:
The cosmic equation of state 2014, 356 (2):393 Astrophysics and Space Science
Journal:
Astrophysics and Space Science
Rights:
Collection Information:
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
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, $p=w\rho$, in terms of the total energy density $\rho$ and pressure $p$ of the cosmic fluid. $\Lambda$CDM and the $R_{\rm h}=ct$ Universe are both FRW cosmologies that partition $\rho$ into (at least) three components, matter $\rho_{\rm m}$, radiation $\rho_{\rm r}$, and a poorly understood dark energy $\rho_{\rm de}$, 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 $R_{\rm h}=ct$, indicating that its likelihood of being correct is $\sim 90\%$ versus only $\sim 10\%$ for $\Lambda$CDM. Nonetheless, the predictions of $\Lambda$CDM often come quite close to those of $R_{\rm h}=ct$, 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 $R_{\rm h}=ct$ helps us to understand why the optimized fraction $\Omega_{\rm m}\equiv \rho_m/\rho$ in $\Lambda$CDM must be $\sim 0.27$, an otherwise seemingly random variable. We show that when one forces $\Lambda$CDM to satisfy the equation of state $w=(\rho_{\rm r}/3-\rho_{\rm de})/\rho$, the value of the Hubble radius today, $c/H_0$, can equal its measured value $ct_0$ only with $\Omega_{\rm m}\sim0.27$ when the equation-of-state for dark energy is $w_{\rm de}=-1$. (We also show, however, that the inferred values of $\Omega_{\rm m}$ and $w_{\rm de}$ change in a correlated fashion if dark energy is not a cosmological constant, so that $w_{\rm de}\not= -1$.) This peculiar value of $\Omega_{\rm m}$ therefore appears to be a direct consequence of trying to fit the data with the equation of state $w=(\rho_{\rm r}/3-\rho_{\rm de})/\rho$ in a Universe whose principal constraint is instead $R_{\rm h}=ct$ or, equivalently, $w=-1/3$.
ISSN:
0004-640X; 1572-946X
DOI:
10.1007/s10509-014-2211-5
Version:
Final accepted manuscript

# Full metadata record

DC FieldValue Language
dc.contributor.authorMelia, F.en
dc.date.accessioned2016-06-25T00:34:32Z-
dc.date.available2016-06-25T00:34:32Z-
dc.date.issued2014-12-04-
dc.identifier.citationThe cosmic equation of state 2014, 356 (2):393 Astrophysics and Space Scienceen
dc.identifier.issn0004-640X-
dc.identifier.issn1572-946X-
dc.identifier.doi10.1007/s10509-014-2211-5-
dc.identifier.urihttp://hdl.handle.net/10150/614766-
dc.description.abstractThe 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, $p=w\rho$, in terms of the total energy density $\rho$ and pressure $p$ of the cosmic fluid. $\Lambda$CDM and the $R_{\rm h}=ct$ Universe are both FRW cosmologies that partition $\rho$ into (at least) three components, matter $\rho_{\rm m}$, radiation $\rho_{\rm r}$, and a poorly understood dark energy $\rho_{\rm de}$, 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 $R_{\rm h}=ct$, indicating that its likelihood of being correct is $\sim 90\%$ versus only $\sim 10\%$ for $\Lambda$CDM. Nonetheless, the predictions of $\Lambda$CDM often come quite close to those of $R_{\rm h}=ct$, 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 $R_{\rm h}=ct$ helps us to understand why the optimized fraction $\Omega_{\rm m}\equiv \rho_m/\rho$ in $\Lambda$CDM must be $\sim 0.27$, an otherwise seemingly random variable. We show that when one forces $\Lambda$CDM to satisfy the equation of state $w=(\rho_{\rm r}/3-\rho_{\rm de})/\rho$, the value of the Hubble radius today, $c/H_0$, can equal its measured value $ct_0$ only with $\Omega_{\rm m}\sim0.27$ when the equation-of-state for dark energy is $w_{\rm de}=-1$. (We also show, however, that the inferred values of $\Omega_{\rm m}$ and $w_{\rm de}$ change in a correlated fashion if dark energy is not a cosmological constant, so that $w_{\rm de}\not= -1$.) This peculiar value of $\Omega_{\rm m}$ therefore appears to be a direct consequence of trying to fit the data with the equation of state $w=(\rho_{\rm r}/3-\rho_{\rm de})/\rho$ in a Universe whose principal constraint is instead $R_{\rm h}=ct$ or, equivalently, $w=-1/3$.en
dc.language.isoenen
dc.publisherSpringer Verlagen
dc.titleThe cosmic equation of stateen
dc.typeArticleen
dc.contributor.departmentThe University of Arizonaen
dc.identifier.journalAstrophysics and Space Scienceen
dc.description.collectioninformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.en
dc.eprint.versionFinal accepted manuscripten
All Items in UA Campus Repository are protected by copyright, with all rights reserved, unless otherwise indicated.
• # Files 1

• ms.pdf
116KB

Final Accepted Manuscript