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. 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. It is named after the authors Arvind Borde, Alan Guth and Alexander Vilenkin, who developed its mathematical formulation in 2003. The BGV theorem is also popular outside physics, especially in religious and philosophical debates.