Erratum to: Noncommutative geometry and fluid dynamics

1 Erratum to: Eur. Phys. J. C (2016) 76:627 DOI 10.1140/epjc/s10052-016-4488-8

There are several corrections related to our paper, as given below.

The correct form of (17) is,

$$\begin{aligned} \{j^i(\mathbf{r}),j^j(\mathbf{r}^{\prime })\}=j^j(\mathbf{r})\partial _i\delta (\mathbf{r}-\mathbf{r}^{\prime })+ j^i(\mathbf{r}^{\prime })\partial _j\delta (\mathbf{r}-\mathbf{r}^{\prime }). \end{aligned}$$

(1)

There is a crucial change of sign in the Dirac bracket of (37),

$$\begin{aligned} \{\rho (\mathbf{r}),\rho (\mathbf{r}^{\prime })\}=-\theta _{ij} \partial _i \rho (\mathbf{r})\partial _j\delta (\mathbf{r}-\mathbf{r}^{\prime }) \end{aligned}$$

(2)

with (37, 38) remaining unchanged. This leads to a canonical form of the continuity equation,

$$\begin{aligned} \dot{\rho }=\{H,\rho \}=-\partial _i(\rho v_i) \end{aligned}$$

(3)

instead of (54). However the noncommutative extension of the Euler equation (56) remains unchanged. Subsequently, contrary to our results of a noncommutativity-modified Friedmann equation in (84, 85), in the present model, to first order in noncommutative parameter $\theta _{ij}$, the Friedmann equation remains unmodified.

We thank Rabin Banerjee and Arpan Krishna Mitra for pointing out the errors.