Cosmic evolution with delay differential equations

Abstract

Inflation driven by scalar fields is standard in modern cosmology, though not without shortcomings. Noting nonlocal quantum effects, Choudhury et al. modified the Friedmann equation with a time delay and showed that inflation is possible without such fields. We revisit this delayed cosmology scheme and demonstrate the role of the delay parameters more clearly. We find that in the delayed Friedmann model with an initial power-law history, the universe always prefers an expansion. In fact, inflation is generic and its strength is proportional to the initial energy density. The inflationary period lasts as long as the delay. But interestingly, the universe makes up for a short-lived inflation (due to a short delay) by very slowly decelerating after the rapid expansion, thereby still growing even after inflation.