##### Author

Melia, Fulvio##### Affiliation

The University of Arizona##### Issue Date

2014-12-04

##### Metadata

Show full item record##### Publisher

Springer Verlag##### Citation

The cosmic equation of state 2014, 356 (2):393 Astrophysics and Space Science##### Journal

Astrophysics and Space Science##### Rights

© Springer Science+Business Media Dordrecht 2014##### 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

0004-640X1572-946X

##### Version

Final accepted manuscript##### Additional Links

http://link.springer.com/10.1007/s10509-014-2211-5ae974a485f413a2113503eed53cd6c53

10.1007/s10509-014-2211-5