The $R_{\mathrm{h}}=ct$ universe and quintessence
  Over the last few years the $R_{\mathrm{h}}=ct$ universe has received a lot
of attention, particularly when observational evidence seems to favor this over
the standard $\Lambda$ cold dark matter ($\Lambda CDM$) universe. Like the
$\Lambda CDM$, the $R_{\mathrm{h}}=ct$ universe is based on a
Friedmann-Robertson-Walker (FRW) cosmology where the total energy density
$\rho$ and pressure $p$ of the cosmic fluid contain a dark energy component
besides the usual (dark and baryonic) matter and radiation components. However
unlike the $\Lambda CDM$ this model has the simple equation of state (EOS)
$\rho + 3p = 0$, i.e., its total active gravitational mass vanishes, which
would therefore exclude a cosmological constant as the source of its dark
energy component. Faced with this issue, in this paper we examine various
possible sources for the dark energy component of the $R_{\mathrm{h}}=ct$
universe and show that quintessence which has been used in other various
dynamical dark energy models could also be a possible source in this case.
