  We present a complete analysis of the observational constraints and
cosmological implications of our Bound Dark Energy (BDE) model aimed to explain
the late-time cosmic acceleration of the universe. BDE is derived from particle
physics and corresponds to the lightest meson field $\phi$ dynamically formed
at low energies due to the strong gauge coupling constant. The evolution of the
dark energy is determined by the scalar potential
$V(\phi)=\Lambda_c^{4+2/3}\phi^{-2/3}$ arising from non-perturbative effects at
a condensation scale $\Lambda_c$ and scale factor $a_c$, related each other by
$a_c\Lambda_c/\mathrm{eV}=1.0934\times 10^{-4}$. We present the full background
and perturbation evolution at a linear level. Using current observational data,
we obtain the constraints $a_c=(2.48 \pm 0.02)\times10^{-6}$ and
$\Lambda_c=(44.09 \pm 0.28) \textrm{ eV}$, which is in complete agreement with
our theoretical prediction $\Lambda_c^{th}=34^{+16}_{-11}\textrm{ eV}$. The
bounds on the equation of state today, the dark energy density and the
expansion rate are $w_\mathrm{BDE 0}=-0.929\pm 0.007$,
$\Omega_\mathrm{BDE0}=0.696\pm0.007$ and $H_0=67.82\pm 0.05$ km s$^{-1}$Mpc,
respectively. Even though the constraints on the six Planck base parameters are
consistent at the 1$\sigma$ level between BDE and the concordance $\Lambda$CDM
model, BDE improves the likelihood ratio by 2.1 of the Baryon Acoustic
Oscillations (BAO) measurements with respect to $\Lambda$CDM and has an
equivalent fit for type Ia supernovae and the Cosmic Microwave Background data.
We present the constraints on the different cosmological parameters, and
particularly we show the tension between BDE and $\Lambda$CDM in the BAO
distance ratio $r_\mathrm{BAO}$ vs $H_\mathrm{0}$ and the growth index $\gamma$
at different redshifts, as well as the dark matter density at present time
$\Omega_ch^2$ vs $H_0$.
