[1] It is named after the authors Arvind Borde, Alan Guth and Alexander Vilenkin, who developed its mathematical formulation in 2003.
[2][3] The BGV theorem is also popular outside physics, especially in religious and philosophical debates.
[3][4][5] In general relativity, the geodesics represent the paths that free-falling particles or objects follow in curved spacetime.
The theorem only applies to classical spacetime, but it does not assume any specific mass content of the universe and it does not require gravity to be described by Einstein field equations.
Here is an example of derivation of the BGV theorem for an expanding homogeneous isotropic flat universe (in units of speed of light c=1).
However, this derivation can be generalized to an arbitrary space-time with no appeal to homogeneity or isotropy.
Along a timeline geodesic xi = constant, we can consider the universe to be filled with comoving particles.
[7] Some physical theories do not discard the possibility of a non-accelerated expansion before a certain moment in time.
Vilenkin and Audrey Mithani have argued that none of these models escape the implications of the theorem.
[8] In 2017, Vilenkin stated that he does not think there are any viable cosmological models that escape the scenario.
[9] Sean M. Carroll argues that the theorem only applies to classical spacetime, and may not hold under consideration of a complete theory of quantum gravity.
He added that Alan Guth, one of the co-authors of the theorem, disagrees with Vilenkin and believes that the universe had no beginning.
[10][11] Vilenkin argues that the Carroll–Chen model constructed by Carroll and Jennie Chen, and supported by Guth, to elude the BGV theorem's conclusions persists to indicate a singularity in the history of the universe as it has a reversal of the arrow of time in the past.
[12] Joseph E. Lesnefsky, Damien A. Easson and Paul Davies constructed an uncountable infinite class of classical solutions which have
[13] The authors claim that the geodesic incompleteness of inflationary spacetime is still an open issue.
Furthermore, there are examples of infinite cyclic models solving the problem of unbounded entropy growth which are geodesically complete.
[14] In both of these studies, the authors argue that the previous investigations often did not use mathematically precise formulations of the BGV theorem and thus reached incomplete conclusions.
In October 2015, Vilenkin responded to arguments made by theist William Lane Craig and the New Atheism movement regarding the existence of God.