The article critically examines modern model of the Universe evolution constructed by efforts of a group of scientists (mathematicians, physicists and cosmologists) from the world's leading universities (Oxford and Cambridge Universities, Yale, Columbia, New York, Rutgers and the UC Santa Cruz). The author notes its strengths, but also points to shortcomings. Author believes that this model does not take into account the most important achievements in the field of biochemistry and biology (molecular, physical, developmental, etc.), as well as neuroscience and psychology. Author believes that in the construction of model of the Universe evolution, scientists must take into account (with great reservations) the impact of living and intelligent matter on space processes. As an example, the author gives his theoretical model "Evolving matter". In this model, he shows not only the general dependence of the interaction of cosmic processes with inert, living and intelligent matter, but also he attempts to show the direct influence of systems of living and intelligent matter on the acceleration of the Universe's expansion.