  The probability representation of quantum mechanics including propagators and
tomograms of quantum states of the universe and its application to quantum
gravity and cosmology are reviewed. The minisuperspaces modeled by oscillator,
free pointlike particle and repulsive oscillator are considered. The notion of
tomographic entropy and its properties are used to find some inequalities for
the tomographic probability determining the quantum state of the universe. The
sense of the inequality as a lower bound for the entropy is clarified.
