In the 1980s, however, when the theory of inflation suggested that the Universe really did undergo a stage of exponential expansion during the first split-second after its birth, this inflationary exponential expansion turned out to be exactly described by the de Sitter model, the first successful cosmological solution to Einstein's equations of the general theory of relativity. It began with the Big Bang 13.8 billion years ago when the Universe was tiny, hot, and dense. During the inflationary epoch about 10 −32 of a second after the Big Bang, the universe suddenly expanded, and its volume increased by a factor of at least 10 78 (an expansion of distance by a factor of at least 10 26 in each of the three dimensions), equivalent to expanding an object 1 nanometer (10 −9 m, about half the width of a molecule of DNA) in length to one approximately 10.6 light years (about 10 17 … It is an intrinsic expansion whereby the scale of space itself changes.The universe does not expand "into" anything and does not require space to exist "outside" it.

Following the inflationary period, the universe continued to expand, but at a slower rate. Technically, neither space nor objects in space move. It proposes a period of extremely rapid (exponential) expansion of the universe prior to the more gradual Big Bang expansion, during which time the energy density of the universe was dominated by a cosmological constant -type of vacuum energy that later decayed to produce the matter and radiation that fill the universe today. The acceleration of this expansion due to dark energy began after the universe was already over 9 billion years old (~4 billion years ago).
The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time. This expansion explains various properties of the current universe that are difficult to account for without such an inflationary epoch.
From about 9.8 billion years of cosmic time, the slowing expansion of space gradually begins to accelerate under the influence of dark energy, which may be a scalar field throughout our universe. It is not known exactly when the inflationary epoch ended, but it is thought to have been between 10 −33 and 10 −32 seconds after the Big Bang.