States of Low Energy are a class of exact Hadamard states for free quantum fields on cosmological spacetimes whose structure is fixed at all scales by a minimization principle. The original construction was for Friedmann–Lemaître geometries and is here generalized to anisotropic Bianchi I geometries relevant to primordial cosmology. In addition to proving the Hadamard property, systematic series expansions in the infrared and ultraviolet are developed. The infrared expansion is convergent and induces in the massless case a leading spatial long distance decay that is always Minkowski-like but anisotropy modulated. The ultraviolet expansion is shown to be equivalent to the Hadamard property, and a non-recursive formula for its coefficients is presented.
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November 2023
Research Article|
November 08 2023
States of Low Energy on Bianchi I spacetimes
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R. Banerjee
;
R. Banerjee
a)
(Formal analysis, Investigation, Software, Writing – original draft, Writing – review & editing)
1
Okinawa Institute of Science and Technology Graduate University
, 1919-1 Tancha, Onna-son, Kunigami-gun, Okinawa, Japan 904-0495a)Author to whom correspondence should be addressed: [email protected]
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M. Niedermaier
M. Niedermaier
b)
(Formal analysis, Investigation, Software, Writing – original draft, Writing – review & editing)
2
Department of Physics and Astronomy, University of Pittsburgh
, 100 Allen Hall, Pittsburgh, Pennsylvania 15260, USA
Search for other works by this author on:
R. Banerjee
1,a)
M. Niedermaier
2,b)
1
Okinawa Institute of Science and Technology Graduate University
, 1919-1 Tancha, Onna-son, Kunigami-gun, Okinawa, Japan 904-0495
2
Department of Physics and Astronomy, University of Pittsburgh
, 100 Allen Hall, Pittsburgh, Pennsylvania 15260, USA
a)Author to whom correspondence should be addressed: [email protected]
b)
Electronic mail: [email protected]
J. Math. Phys. 64, 113503 (2023)
Article history
Received:
May 30 2023
Accepted:
October 11 2023
Citation
R. Banerjee, M. Niedermaier; States of Low Energy on Bianchi I spacetimes. J. Math. Phys. 1 November 2023; 64 (11): 113503. https://doi.org/10.1063/5.0160180
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