Large-scale effect of Krein quantization method on the matter density perturbations. (English) Zbl 1323.83039
Summary: According to the theoretical results obtained in usual quantum cosmology in which the field operator is constructed on the Hilbert space, the power spectrum of the scalar field fluctuations is scale invariant in the inflationary epoch. On the other hand, the observational data predict some deviation from scale-invariance in the power spectrum. It has been shown previously that by using Krein quantization method for constructing field operator, the power spectrum is obtained scale dependent [M. Mohsenzadeh et al., ibid. 48, No. 3, 755–762 (2009; Zbl 1176.83163)]. The main goal in this work is to investigate the effect of Krein quantization method on the matter density perturbation at present. The results show if one uses covariant two point function for mass-less minimally coupled scalar field in de Sitter space-time which is calculated via Krein quantization method, the power spectrum of primordial gravitational potential set up during inflation and the power spectrum of matter density perturbation at present deviate from scale-invariant result.
MSC:
| 83F05 | Relativistic cosmology |
| 81S05 | Commutation relations and statistics as related to quantum mechanics (general) |
| 46C20 | Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.) |
Citations:
Zbl 1176.83163References:
| [1] | Mohsenzadeh, M., Rouhani, S., Takook, M.V.: Power spectrum in Krein space quantization. IJTP 755, 48 (2009) · Zbl 1176.83163 |
| [2] | Danielsson, U.H.: A note on inflation and trans-Planckian physics. Phys. Rev. D 66, 023511 (2002) · doi:10.1103/PhysRevD.66.023511 |
| [3] | Martin, J., Brandenberger, R.H.: On the dependence of the spectra of fluctuation in inflationary cosmology on trans-Planckian physics. Phys. Rev. D 68, 063513 (2003) · doi:10.1103/PhysRevD.68.063513 |
| [4] | Kaloper, N., Kleban, M., Lawrence, A.E., Shenker, S.: Signatures of short distance physics in the cosmic microwave background. Phys. Rev. D66, 123510 (2002) |
| [5] | Kaloper, N., Kaplinghat, M.: Primeval corrections to the CMB anisotropies. Phys. Rev. D 68, 123522 (2003) · doi:10.1103/PhysRevD.68.123522 |
| [6] | Collins, H., Holman, R.: Trans-Planckian signals from the breaking of local Lorentz invariance. Phys. Rev. D 77, 105016 (2008) · doi:10.1103/PhysRevD.77.105016 |
| [7] | Gazeau, J.P., Renaud, J., Takook, M.V.: Gupta-Bleuler quantization for minimally coupled scalar fields in de Sitter space. Class. Quantum Gravity 17, 1415 (2000) · Zbl 1131.83301 · doi:10.1088/0264-9381/17/6/307 |
| [8] | Rouhani, S., Takook, M.V.: A naturally renormalized quantum field theory. Int. J. Theor. Phys. 48, 2740 (2009) · Zbl 1177.83072 · doi:10.1007/s10773-009-0064-4 |
| [9] | Takook, MV: A natural renormalization of the one-loop effective action for scalar field in curved space-time. Int. J. Mod. Phys. E 14, 2 (2005) · doi:10.1142/S0218301305002953 |
| [10] | Refaei, A., Takook, M.V.: Scalar effective action in Krein space quantization. Mod. Phys. Lett. A 26, 31 (2011) · Zbl 1208.83044 · doi:10.1142/S0217732311034505 |
| [11] | Refaei, A., Takook, M.V.: QED effective action in krein space quantization. Phys. Lett. B 704 (2011) · Zbl 1208.83044 |
| [12] | Birrel, N.D., Davies, P.C.: Quantum Field Theory in Curved Space. Cambridge University Press, Cambridge (1982) · Zbl 0972.81605 · doi:10.1017/CBO9780511622632 |
| [13] | Kaku, M.: Quantum Field Theory. Oxford University Press, Oxford (1993) |
| [14] | Takook, M.V.: Negative norm states in de Sitter space and QFT without Renormalization procedure. Int. J. Mod. Phys. E 11, 6 (2002) · doi:10.1142/S0218301302001071 |
| [15] | Murdin, P.: Correlation Function and Power Spectra in Cosmology. Encyclopedia of Astronomy and Astrophysics. IOP Publishing Ltd (2006). doi:10.1888/0333750888/2136 · Zbl 1131.83301 |
| [16] | Ade, P.A.R., et al.: Planck 2013 Results-Cosmological parameters. A&A 571 (2014) |
| [17] | Liddle, A., Lyth, D.H.: Cosmological Inflation and Large-Scale Structure. Cambridge University Press, Cambridge (2000) · Zbl 0952.83001 · doi:10.1017/CBO9781139175180 |
| [18] | Takook, M.V.: Covariant two-point function for minimally coupled scalar field in de Sitter space-time. Mod. Phys. Lett. A 16, 26 (2001) · Zbl 1138.81489 · doi:10.1142/S0217732301004996 |
| [19] | Dodelson, S.: Modern Cosmology. Academic Press, New York (2003) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
