  The cosmic spacetime is often described in terms of the 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. LCDM and the
R_h=ct Universe are both FRW cosmologies that partition rho into (at least)
three components, matter rho_m, radiation rho_r, and a poorly understood dark
energy rho_de, though the latter goes one step further by also invoking the
constraint w=-1/3. This condition is required by the simultaneous application
of the Cosmological principle and Weyl's postulate. Model selection tools in
one-on-one comparisons favor R_h=ct with a likelihood of ~90% versus only ~10%
for LCDM. Nonetheless, the predictions of LCDM 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 demonstrate that the equation of state in
R_h=ct helps us to understand why the optimized fraction Omega_m=rho_m/rho in
LCDM must be ~0.27, an otherwise seemingly random variable. We show that when
one forces LCDM to satisfy the equation of state w=(rho_r/3-rho_de)/rho, the
value of the Hubble radius today, c/H_0, can equal its measured value ct_0 only
with Omega_m~0.27 when the equation of state for dark energy is w_de=-1. This
peculiar value of Omega_m therefore appears to be a direct consequence of
trying to fit the data with the equation of state w=(rho_r/3-rho_de)/rho in a
Universe whose principal constraint is instead R_h=ct or, equivalently, w=-1/3.
