Constraints on the speed of sound in the k-essence model of dark energy

We consider a particular k-essence scalar field model for the late-time cosmic acceleration in which the sound speed, parametrized as $c_s$ is constant. We compute the relevant background and perturbation quantities corresponding to the observables like cosmic microwave background, type Ia supernova, cosmic chronometers, baryon acoustic oscillations, and the $f{\sigma }_8$. We put constraints on the $c_s^2$ parameter from these observations along with other parameters. We find lower values of $c_s^2$ which are close to zero are tightly constrained. Particularly, we find mean value of ${\log }_{10}(c_s^2)$ to be $-0.61$ and $c_s^2\le {10}^{-3}$ is more than 3$\sigma$ away from this mean value. This means these observations favor a homogeneous dark energy component compared to the clustering one.