  In this study, we investigate a cosmological model involving a negative
cosmological constant (AdS vacua in the dark energy sector). We consider a
quintessence field on top of a negative cosmological constant and study its
impact on cosmological evolution and structure formation. We use the power
spectrum of the redshifted HI 21 cm brightness temperature maps from the
post-reionization epoch as a cosmological probe. The signature of baryon
acoustic oscillations (BAO) on the multipoles of the power spectrum is used to
extract measurements of the angular diameter distance $D_A(z)$ and the Hubble
parameter $H(z)$. The projected errors on these are then subsequently employed
to forecast the constraints on the model parameters ($\Omega_\Lambda, w_0,
w_a$) using Markov Chain Monte Carlo techniques. We find that a negative
cosmological constant with a phantom dark energy equation of state (EoS) and a
higher value of $H_0$ is viable from BAO distance measurements data derived
from galaxy samples. We also find that BAO imprints on the 21cm power spectrum
obtained from a futuristic SKA-mid like experiment yield a $1-\sigma$ error on
a negative cosmological constant and the quintessence dark energy EoS
parameters to be $\Omega_\Lambda=-1.030^{0.589}_{-1.712}$ and
$w_0=-1.023^{0.043}_{-0.060}$, $w_a=-0.141^{0.478}_{-0.409}$ respectively.
