The cosmic equation of state

Abstract

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.