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At variance with the authors' statement [L. P\'{a}lov\'{a}, P. Chandra and P.Coleman, Phys. Rev. B 79, 075101 (2009)], we show that the behavior of theuniversal scaling amplitude of the gap function in the phonon dispersionrelation as a function of the dimensionality $d$, obtained within aself--consistent one--loop approach, is consistent with some previousanalytical results obtained in the framework of the $\epsilon$--expansion inconjunction with the field theoretic renormalization group method [S. Sachdev,Phys. Rev. B 55, 142 (1997)] and the exact calculations corresponding to thespherical limit i.e. infinite number $N$ of the components of the orderparameter [H. Chamati. and N. S. Tonchev, J. Phys. A: Math. Gen. 33, 873(2000)]. Furthermore we determine numerically the behavior of the "temporal"Casimir amplitude as a function of the dimensionality $d$ between the lower andupper critical dimension and found a maximum at $d=2.9144$. This is confirmedvia an expansion near the upper dimension $d=3$.

Comment on "Quantum critical paraelectrics and the Casimir effect in time"