  We discuss the problem of universe acceleration driven by global rotation.
The redshift-magnitude relation is calculated and discussed in the context of
SN Ia observation data. It is shown that the dynamics of considered problem is
equivalent to the Friedmann model with additional non-interacting fluid with
negative pressure. We demonstrate that the universe acceleration increase is
due to the presence of global rotation effects, although the cosmological
constant is still required to explain the SN Ia data. We discuss some
observational constraints coming from SN Ia imposed on the behaviour of the
homogeneous Newtonian universe in which matter rotates relative local
gyroscopes. In the Newtonian theory $\Omega_{\text{r},o}$ can be identified
with $\Omega_{\omega,0}$ (only dust fluid is admissible) rotation can exist
with $\Omega_{\text{r},0}=\Omega_{\omega,0} \le 0$. However, the best-fit flat
model is the model without rotation, i.e., $\Omega_{\omega,0}=0$. In the
considered case we obtain the limit for $\Omega_{\omega,0}>-0.033$ at 1\sigma$
level$. We are also beyond the model and postulate the existence od additional
matter which scales like radiation matter and then analyse how that model fits
the SN Ia data. In this case the limits on rotation coming from BBN and CMB
anisotropies are also obtained. If we assume that the current estimates are
$\Omega_{\text{m},0}\sim 0.3$, $\Omega_{\text{r},0} \sim 10^{-4}$, then the SN
Ia data show that $\Omega_{\omega,0} \ge -0.01$ (or $\omega < 2.6 \cdot
10^{-19} \text{rad}/\text{s}$). The statistical analysis gives us that the
interval for any matter scaling like radiation is $\Omega_{\text{r},0} in
(-0.01, 0.04)$.
