  In order to understand the nature of the accelerating expansion of the
late-time universe, it is important to experimentally determine whether dark
energy is a cosmological constant or dynamical in nature. If dark energy
already exists prior to inflation, which is a reasonable assumption, then one
expects that a dynamical dark energy would leave some footprint in the
anisotropy of the late-time accelerated expansion. To demonstrate the viability
of this notion, we invoke the quintessence field with the exponential potential
as one of the simplest dynamical dark energy models allowed by observations. We
investigate the effects of its quantum fluctuations (the physical origin of the
perturbation being isocurvature) generated during inflation and having fully
positive correlation with the primordial curvature perturbations, and estimate
the anisotropy of the cosmic expansion so induced. We show that the primordial
amplitude of quantum fluctuations of quintessence field {\delta\phi}_P can be
related to the tensor-to-scalar ratio r, and we calculate the perturbed
luminosity distance to first order and the associated luminosity distance power
spectrum, which is an estimator of anisotropicity of late-time accelerated
expansion. We find that the gravitational potential at large scales and late
times is less decayed in QCDM compared to that in {\Lambda}CDM so that the
smaller the redshift and multipole, the more relative deficit of power in QCDM.
Our results of luminosity distance power spectrum also show the similar
conclusions of suppression as that of the previous investigation regarding the
effect of quantum fluctuations of quintessence field on the CMB temperature
anisotropies.
