We calculate the bispectrum of primordial curvature perturbations, ζ, generated during ''open inflation.'' Inflation occurs inside a bubble nucleated via quantum tunneling from the background false vacuum state. Our universe lives inside the bubble, which can be described as a Friedmann-Lemaȋtre-Robertson-Walker (FLRW) universe with negative spatial curvature, undergoing slow-roll inflation. We pay special attention to the issue of an initial state for quantum fluctuations. A ''vacuum state'' defined by a positive-frequency mode in de Sitter space charted by open coordinates is different from the Euclidean vacuum (which is equivalent to the so-called ''Bunch-Davies vacuum'' defined by a positive-frequency mode in de Sitter space charted by flat coordinates). Quantum tunneling (bubble nucleation) then modifies the initial state away from the original Euclidean vacuum. While most of the previous study on modifications of the initial quantum state introduces, by hand, an initial time at which the quantum state is modified as well as the form of the modification, an effective initial time naturally emerges and the form is fixed by quantum tunneling in open inflation models. Therefore, open inflation enables a self-consistent computation of the effect of a modified initial state on the bispectrum. We find a term which goes as (ζ{submore » k{sub 1}}ζ{sub k{sub 2}}ζ{sub k{sub 3}})∝1/k{sub 1}{sup 2}k{sub 3}{sup 4} in the so-called squeezed configurations, k{sub 3} << k{sub 1} ≈ k{sub 2}, in agreement with the previous study on modifications of the initial state. The bispectrum in the exact folded limit, e.g., k{sub 1} = k{sub 2}+k{sub 3}, is also enhanced and remains finite. However, these terms are exponentially suppressed when the wavelength of ζ is smaller than the curvature radius of the universe. The leading-order bispectrum is equal to the usual one from single-field slow-roll inflation; the terms specific for open inflation arise only in the sub-leading order when the wavelength of ζ is smaller than the curvature radius.« less

Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto (Japan)

Max-Planck-Institut für Astrophysik, Karl-Schwarzschild Str. 1, 85741 Garching (Germany)

Publication Date:

OSTI Identifier:

22369890

Resource Type:

Journal Article

Resource Relation:

Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2013; Journal Issue: 11; Other Information: Country of input: International Atomic Energy Agency (IAEA)

Country of Publication:

United States

Language:

English

Subject:

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; BUBBLES; COORDINATES; DE SITTER SPACE; EUCLIDEAN SPACE; MODIFICATIONS; PERTURBATION THEORY; QUANTUM STATES; TUNNEL EFFECT; UNIVERSE; VACUUM STATES; WAVELENGTHS