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

We consider a k-essence scalar field model for the late-time cosmic acceleration in which the sound speed, parametrized as cₛ 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 fσ ₈ f σ 8 . We put constraints on the cₛ² c s 2 parameter from these observations along with other parameters. We find lower values of cₛ² c s 2 which are close to zero are tightly constrained. Particularly, we find mean value of log ₁0 (cₛ²) log 10 ( c s 2 ) to be $$-0.61$$ - 0.61 and cₛ² ≤ 10⁻³ c s 2 ≤ 10 - 3 is more than 3 σ σ away from this mean value. This means these observations favor a homogeneous dark energy component compared to the clustering one.