- Access by Xinjiang University
Minimum-length deformed quantization of a free field on the de Sitter background and corrections to the inflaton perturbations
Phys. Rev. D 85, 125026 – Published 19 June, 2012
DOI: https://doi.org/10.1103/PhysRevD.85.125026
Abstract
The effect of string- and quantum-gravity-inspired minimum-length deformed quantization on a free, massless scalar field is studied on the de Sitter background at the level of second quantization. An analytic solution of a field operator is obtained to the first order in deformation parameter. Using this solution, we then estimate the two-point and four-point correlation functions (with respect to the Bunch-Davies vacuum). The field operator shows up a nonlinear dependence on creation and annihilation operators, therefore the perturbation spectrum proves to be non-Gaussian. The correction to the power spectrum is of the same order as obtained previously in a similar study that incorporates the minimum-length deformed momentum operator into the first quantization picture and then proceeds in the standard way for second quantization. The non-Gaussianity comes at the level of four-point correlation function; its magnitude appears to be suppressed by the factor , where is the number of e-foldings.
Article Text
References (20)
- J. Martin and R. H. Brandenberger, Phys. Rev. D 63, 123501 (2001).
- R. H. Brandenberger and J. Martin, Mod. Phys. Lett. A 16, 999 (2001).
- A. Kempf, Phys. Rev. D 63, 083514 (2001).
- A. Kempf and J. C. Niemeyer, Phys. Rev. D 64, 103501 (2001).
- J. C. Niemeyer and R. Parentani, Phys. Rev. D 64, 101301 (2001).
- J. C. Niemeyer, arXiv:astro-ph/0201511.
- S. F. Hassan and M. S. Sloth, Nucl. Phys. B674, 434 (2003).
- A. Ashoorioon, A. Kempf, and R. B. Mann, Phys. Rev. D 71, 023503 (2005).
- G. A. Palma and S. P. Patil, J. High Energy Phys. 04 (2009) 005.
- D. Mania and M. Maziashvili, Phys. Lett. B 705, 521 (2011).
- M. S. Berger and M. Maziashvili, Phys. Rev. D 84, 044043 (2011).
- G. Veneziano, Europhys. Lett. 2, 199 (1986); D. J. Gross and P. F. Mende, Nucl. Phys. B303, 407 (1988); D. Amati, M. Ciafaloni, and G. Veneziano, Phys. Lett. B 216, 41 (1989); K. Konishi, G. Paffuti, and P. Provero, 234, 276 (1990); R. Guida, K. Konishi, and P. Provero, Mod. Phys. Lett. A 6, 1487 (1991).
- M. Maggiore, Phys. Lett. B 304, 65 (1993); F. Scardigli, 452, 39 (1999); R. J. Adler and D. I. Santiago, Mod. Phys. Lett. A 14, 1371 (1999).
- A. Kempf and G. Mangano, Phys. Rev. D 55, 7909 (1997).
- A. Kempf, J. Phys. A 30, 2093 (1997).
- A. Kempf, arXiv:hep-th/9405067; J. Math. Phys. (N.Y.) 38, 1347 (1997); Phys. Rev. D 54, 5174 (1996); 55, 1114(E) (1997).
- N. N. Bogolyubov and D. V. Shirkov, Introduction to the Theory of Quantized Fields (Interscience, New York, 1959); N. N. BogolyubovD. V. Shirkov Quantum Fields (Benjamin/Cummings Publishing Co., San Francisco, 1982).
- D. Polarski and A. A. Starobinsky, Classical Quantum Gravity 13, 377 (1996).
- A. D. Linde, Particle Physics and Inflationary Cosmology, Contemporary Concepts in Physics Vol. 5 (Harwood, Chur, Switzerland, 1990), p. 362,
- N. Bartolo, E. Komatsu, S. Matarrese, and A. Riotto, Phys. Rep. 402, 103 (2004).