The cosmic equation of state
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 p...
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| Language: | en |
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Springer Verlag
2014
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| Online Access: | http://hdl.handle.net/10150/614766 http://arizona.openrepository.com/arizona/handle/10150/614766 |
| Summary: | 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, $w=-1/3$. |
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