In 2002, Salvatore Capozziello proposed the fundamental new point of view to dark energy: dark Energy is caused by a modification of gravitational theory. Based on this idea and developing it Odintsov and Shin'ichi Nojiri proposed the first fundamental unified picture for the evolution of the universe based on modified gravity. According to this the evolution of the universe changes the gravitational theory, so that modified gravity changes the evolution of the universe making it to be accelerating at the very early and very late epoch. Later, they also demonstrated that such unified inflationary-dark Energy universe may be achieved in modified Gauss-Bonnet gravity and non-local gravity. This picture became even more popular recently due to the increasing possibility that inflation is caused by modified gravity which differs from the usual General Relativity.
In 2011, Odintsov was included in the list of the top 10 most well-known Scientists of Russian origin according to Forbes. In 2014, he was included in the list of The World's Most Influential Scientific Minds: 2014 according to Thomson Reuters.
Odintsov has published 500 research articles with about 22.000–25.000 citations with an h-index of 73–76.
