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 } , 0 } can be identified with \Omega _ { \omega, 0 } ( only dust fluid is admissible ) and rotation can exist with \Omega _ { \text { r } , 0 } = \Omega _ { \omega, 0 } \leq 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 of 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 } \geq - 0.01 
( or \omega _ { 0 } < 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 ) .