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APPC12 B4-PMo-10
The 12th Asia Pacific Physics Conference
CMB Power Spectrum: New Approach to Cosmological Fluctuation
using the Background Field Method
S. Ichinose
Laboratory of Physics, School of Food and Nutritional Sciences, University of Shizuoka, Shizuoka
422-8526, Japan
e-mail: [email protected]
A new field theory formulation is presented for the analysis of the CMB power spectrum distribution in the cosmology. The background-field formalism is fully used. The gravitational (metric)
field gµν is not taken as the quantum field, but as the background field. The statistical fluctuation
of the metric field is taken into account by the path (hyper-surface)-integral over the space-time.
Using a simple scalar model on the curved (dS4 ) space-time, we make the analysis comparing with
the S-matrix calculation of the flat ( 3+1 dim Minkowski) field theory (QED). The concrete new
points are as follows.
1) This is the systematic formulation for the n-point function.
2) Clear separate treatment is done for the classical effect, the statistical effect and the quantum
effect.
3) For the classical part, the perturbation around the homogeneous and isotropic limit (RobertsonWalker universe) is systematically treated using the propagator method.
4) We calculate the quantum effects of the matter-field. Casimir energy of the universe is finitely
obtained. The absolute value is consistent with the observation.
5) We introduce fluctuation around the homogeneous part as the statistically-distributed fluctuation. We introduce a statistical averaging functional using the path-integral method. We make the
functional by use of the area of a 3D hyper surface embedded in 3+1 space-time. We stress that
the fluctuation comes not from the quantum gravity but from the unknown ’statistical’ fluctuation
6) IR parameter (l) is introduced for the time axis as the periodicity for the time axis. Time
reversal(Z2 )-symmetry is introduced in order to treat the problem separately with respect to the
Z2 parity P = ±1. This procedure much helps both UV and IR regularization to work well.
7) The IR divergence problem is closely examined. It is compared with the case of QED.
8) The usual CMB power spectrum is obtained.
[1] S. Ichinose, Jour. Phys. Conf. Ser. 384(2012)012028(1-12), arXiv:1205.1316(hep-th), Proceedings of the 7th International Workshop on the Dark Side of The Universe (DSU2011). (Sep.26-30,
2011, Beijin, China), ”Casimir Energy of the Universe and the Dark Energy Problem”
[2] S. Ichinose, Jour.Phys.:Conf.Scr.222(2010)012048,p1-13, arXiv:1001.0222(hep-th), Proceedings
of the First Mediterranean Conference on Classical and Quantum Gravity. (Sep.14-18,2009, The
Orthodox Academy of Crete, Kolymbari, Crete, Greece). ”Casimir Energy of the Universe and
New Regularization of Higher Dimensional Quantum Field Theories”
[3] S. Ichinose, Prog.Theor.Phys. 121(2009)727-768, ArXiv:0801.3064v8[hep-th]. ”Casimir Energy
of 5D Electromagnetism and New Regularization Based on Minimal Area Principle”
[4] S. Ichinose, ”Geometric Approach to Quantum Statistical Mechanics and Minimal Area Principle”, arXiv:1004.2573(hep-th), 28 pages
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