TY - JOUR
T1 - Vacua and correlators in hyperbolic de Sitter space
AU - Dimitrakopoulos, Fotios V.
AU - Kabir, Laurens
AU - Mosk, Benjamin
AU - Parikh, Maulik
AU - van der Schaar, Jan Pieter
N1 - Publisher Copyright:
© 2015, The Author(s).
PY - 2015/6/19
Y1 - 2015/6/19
N2 - Abstract: We study the power- and bi-spectrum of vacuum fluctuations in a hyperbolic section of de Sitter space, comparing two states of physical interest: the Bunch-Davies and hyperbolic vacuum. We introduce a one-parameter family of de Sitter hyperbolic sections and their natural vacua, and identify a limit in which it reduces to the planar section and the corresponding Bunch-Davies vacuum state. Selecting the Bunch-Davies vacuum for a massless scalar field implies a mixed reduced density matrix in a hyperbolic section of de Sitter space. We stress that in the Bunch-Davies state the hyperbolic de Sitter n-point correlation functions have to match the planar de Sitter n-point correlation functions. The expressions for the planar and hyperbolic Bunch-Davies correlation functions only appear different because of the transformation from planar to hyperbolic coordinates. Initial state induced deviations from the standard inflationary predictions are instead obtained by considering the pure hyperbolic vacuum, as we verify explicitly by computing the power- and bi-spectrum. For the bi-spectrum in the hyperbolic vacuum we find that the corrections as compared to the standard Bunch-Davies result are not enhanced in specific momentum configurations and strongly suppressed for momenta large compared to the hyperbolic curvature scale. We close with some final remarks, in particular regarding the implications of these results for more realistic inflationary bubble scenarios.
AB - Abstract: We study the power- and bi-spectrum of vacuum fluctuations in a hyperbolic section of de Sitter space, comparing two states of physical interest: the Bunch-Davies and hyperbolic vacuum. We introduce a one-parameter family of de Sitter hyperbolic sections and their natural vacua, and identify a limit in which it reduces to the planar section and the corresponding Bunch-Davies vacuum state. Selecting the Bunch-Davies vacuum for a massless scalar field implies a mixed reduced density matrix in a hyperbolic section of de Sitter space. We stress that in the Bunch-Davies state the hyperbolic de Sitter n-point correlation functions have to match the planar de Sitter n-point correlation functions. The expressions for the planar and hyperbolic Bunch-Davies correlation functions only appear different because of the transformation from planar to hyperbolic coordinates. Initial state induced deviations from the standard inflationary predictions are instead obtained by considering the pure hyperbolic vacuum, as we verify explicitly by computing the power- and bi-spectrum. For the bi-spectrum in the hyperbolic vacuum we find that the corrections as compared to the standard Bunch-Davies result are not enhanced in specific momentum configurations and strongly suppressed for momenta large compared to the hyperbolic curvature scale. We close with some final remarks, in particular regarding the implications of these results for more realistic inflationary bubble scenarios.
KW - Cosmology of Theories beyond the SM
KW - Effective field theories
KW - Models of Quantum Gravity
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U2 - 10.1007/JHEP06(2015)095
DO - 10.1007/JHEP06(2015)095
M3 - Article
AN - SCOPUS:84935038561
SN - 1126-6708
VL - 2015
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 6
M1 - 95
ER -