Borde–Guth–Vilenkin theorem

The Borde–Guth–Vilenkin theorem, or the BGV theorem, is a theorem in physical cosmology which deduces that any universe that has, on average, been expanding throughout its history cannot be infinite in the past but must have a past spacetime boundary.[1] It is named after the authors Arvind Borde, Alan Guth and Alexander Vilenkin, who developed its mathematical formulation in 2003.[2][1] The BGV theorem is also popular outside physics, especially in religious and philosophical debates.[1][3][4]

The theorem does not assume any specific mass content of the universe and it does not require gravity to be described by Einstein field equations.[1] Theoretical cosmologist Sean M. Carroll argues that the theorem only applies to classical spacetime, and may not hold under consideration of quantum theory.[5]