  We consider a nonrelativistic cosmological model introduced in [1] and
derived as the nonrelativistic limit (or approximation at sub-Hubble scales) of
a general relativistic model in [3, 4]. The latter is defined by an
energy-momentum tensor containing only dust and a nontrivial energy flow. The
nonrelativistic limit contains in leading order a 1st-order relativistic
contribution to the spatial curvature whose time-dependence drives the
accelerated expansion of the Universe (we do not need any kind of dark energy).
Analytic solutions of the model are fixed by three constants (initial
conditions). In the present paper we use our model as a toy model by adjusting
the three constants in two different ways to a second order polynomial fit by
Montenari and R\"as\"anen [5] to the observed expansion rate $H(z)$ for $z
\lesssim 2$ (mainly cosmic chronometer data). In scenario 1 we adjust our model
to this fit and its derivative at the self-consistently determined transition
redshift $z_t$. In scenario 2 we use the same fit at $z_t$ and in addition
$H(z)$ at decoupling $(z = 1089)$. The Hubble parameter $H_0$ is taken from the
polynomial fit in [5]: $H_0 = 64.2 km/s/Mpc$. For both scenarios we obtain a
satisfactory agreement between predicted and observed $H(z)$ values. But the
outcomes for the curvature function $k(z)$ are completely different: In
scenario 1 we obtain a strong variation of $k(z)$ ranging from $k(0) = - 1.216$
up to $k(2.33) = 0.718$. On the other hand scenario 2 shows an almost constant
value for $k(z) \sim - 1$ for all $z \lesssim 2$ in agreement with the
polynomial fit to one of the FRW consistency conditions performed in [5].
