where is the scale factor and is cosmological time.
A de Sitter universe is one with a positive cosmological constant and zero matter density.
There is no Big Bang in a de Sitter universe - expansion is self-similar from an infinite time in the past to an infinite time in the future.
The model has practical implications as an approximation during the future of the Universe when the cosmological constant is likely to dominate (assuming no changes from the present version of the standard Big Bang model), and during the early universe during a hypothesised period of inflation.