A mathematical proof for the existence of a possible source for dark energy

Abstract

The expansion of the universe has been accepted by scientists for more than a century. However, since the 1990s, observations have suggested that the universe is expanding at an accelerating rate. Although the source of this acceleration is still unknown, cosmologists call it dark energy; a type mysterious energy which exerts a negative pressure on the universe. In this paper, applying different approach from those of classical mathematical physics based mainly on functional analysis, we propose an answer to this question. In fact, we first establish a theorem for multivalued mappings; and as result we apply this theorem to show the existence of a remnant field of high energy in a continuously expanding system of energy. The results may also be applied to the early universe to show the existence of a possible source for dark energy. The answer is partially confirmed by a paper published in Nature Asronomy.