Bunch–Davies vacuum explained

In quantum field theory in curved spacetime, there is a whole class of quantum states over a background de Sitter space which are invariant under all the isometries: the alpha-vacua. Among them there is a particular one whose associated Green functions verify a condition (Hadamard condition) consisting to behave on the light-cone as in flat space. This state is usually called the Bunch–Davies vacuum or Euclidean vacuum,^[1] actually was first obtained by N.A. Chernikov and E. A. Tagirov, in 1968^[2] and later by C. Schomblond and P. Spindel, in 1976, in the framework of a general discussion about invariant Green functions on de Sitter space.^[3] The Bunch–Davies vacuum can also be described as being generated by an infinite time trace from the condition that the scale of quantum fluctuations is much smaller than the Hubble scale.^[4] The state possesses no quanta at the asymptotic past infinity.^[5]

The Bunch–Davies state is the zero-particle state as seen by a geodesic observer, that is, an observer who is in free fall in the expanding state.^[6] The state explains the origin of cosmological perturbation fluctuations in inflationary models.

See also

• Quantum field theory in curved spacetime
• Unruh effect
• Hawking radiation
• Inflation (cosmology)

Further reading

• Greene. Brian R . Parikh, Maulik K . van der Schaar, Jan Pieter . Universal correction to the inflationary vacuum. Journal of High Energy Physics. 28 April 2006. 2006. 4. 057. 10.1088/1126-6708/2006/04/057. hep-th/0512243. 2006JHEP...04..057G . 16290999 .

Notes and References

1. Bunch. Timothy Stephen. Davies. Paul. Paul Davies. 1978. Quantum Field Theory In De Sitter Space: Renormalization By Point Splitting. Proceedings of the Royal Society of London. 360. A. 1700. 117–134. 10.1098/rspa.1978.0060. 1978RSPSA.360..117B . 121912658.
2. Chernikov. N.A.. Tagirov. E. A. . 1968. Quantum theory of scalar field in de Sitter space-time. Annales de l'Institut Henri Poincaré. IX, 2. A. 109 . 1968AnHP....9..109C.
3. Schomblond. Christiane. Spindel. Philippe. 1976. Conditions d'unicit e pour le propagateur Delta 1(x; y) du champ scalaire dans l'univers de de Sitter. Annales de l'Institut Henri Poincaré. XXV, 1. A. 67 .
4. Danielsson. Ulf H. Olsson, Martin E. On thermalization in de Sitter space. Journal of High Energy Physics. 15 March 2004. 2004. 3. 036. 10.1088/1126-6708/2004/03/036. hep-th/0309163. 2004JHEP...03..036D . 16226660.
5. Armendariz-Picon. C. Why should primordial perturbations be in a vacuum state?. Journal of Cosmology and Astroparticle Physics. 26 February 2007. 2007. 2. 031. 10.1088/1475-7516/2007/02/031. astro-ph/0612288. 2007JCAP...02..031A . 33049406.
6. Greene. Brian R . Parikh, Maulik K . van der Schaar, Jan Pieter . Universal correction to the inflationary vacuum. Journal of High Energy Physics. 28 April 2006. 2006. 4. 057. 10.1088/1126-6708/2006/04/057. hep-th/0512243. 2006JHEP...04..057G . 16290999 .