  We determine constraints on spatially-flat tilted dynamical dark energy XCDM
and $\phi$CDM inflation models by analyzing Planck 2015 cosmic microwave
background (CMB) anisotropy data and baryon acoustic oscillation (BAO) distance
measurements. XCDM is a simple and widely used but physically inconsistent
parameterization of dynamical dark energy, while the $\phi$CDM model is a
physically consistent one in which a scalar field $\phi$ with an inverse
power-law potential energy density powers the currently accelerating
cosmological expansion. Both these models have one additional parameter
compared to standard $\Lambda$CDM and both better fit the TT + lowP + lensing +
BAO data than does the standard tilted flat-$\Lambda$CDM model, with $\Delta
\chi^2 = -1.26\ (-1.60)$ for the XCDM ($\phi$CDM) model relative to the
$\Lambda$CDM model. While this is a 1.1$\sigma$ (1.3$\sigma$) improvement over
standard $\Lambda$CDM and so not significant, dynamical dark energy models
cannot be ruled out. In addition, both dynamical dark energy models reduce the
tension between the Planck 2015 CMB anisotropy and the weak lensing $\sigma_8$
constraints.
