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Quintessential power-law cosmology: dark energy equation of state

Power-law cosmology with scale factor as power of cosmic time, $a \propto t^{\a}$, is investigated. We review and discuss value of $\a$ obtained from various types of observation. Considering dark energy dominant era in late universe from $z < 0.5$, we use observational derived results from Cosmic Microwave Background (WMAP7), Baryon Acoustic Oscillations (BAO) and observational Hubble data to find power exponent $\a$ and other cosmological variables. $\a$ is found to be $0.99 \pm 0.02$ (WMAP7+BAO+$H_0$) and $0.99 \pm 0.04$ (WMAP7). These values do not exclude possibility of acceleration at 1$σ$ hence giving viability to power-law cosmology in general. When considering scenario of canonical scalar field dark energy with power-law cosmology, we derive scalar field potential, exact scalar field solution and equation of state parameter. We found that the scenario of power-law cosmology containing dynamical canonical scalar field predicts present equation of state parameter $w_{ϕ, 0} = -0.449 \pm 0.030 $ while the $w$CDM with WMAP7 data (model independent, $w$ constant) allows a maximum (+1$σ$) value of $w_{ϕ, 0}$ at -0.70 which is off the prediction range. However, in case of varying $w_ϕ$, the $w_{ϕ, 0}$ value predicted from quintessential power-law cosmology is allowed within 1$σ$ uncertainty.