  The second derivative of the luminosity distance with respect to the redshift
is written in terms of the deceleration parameter $q_0$. We point out that the
third derivative contains the information regarding the sound speed of cosmic
matter as well as the curvature of the universe. We restrict physically
possible parameter ranges of the coefficients. It is found that there is a
relation between the coefficients in a flat universe model with matter such
that $c_{s0}(1+w_{\rm x0})=0$ ($c_{s0}$ is the total sound speed of the matter
component and $w_{\rm x0}$=$p_{\rm x0}/\rho_{\rm x0}$).
