On the contribution of density perturbations and gravitational waves to the lower order multipoles of the Cosmic Microwave Background Radiation

Details On the contribution of density perturbations and gravitational waves to the lower order multipoles of the Cosmic Microwave Background Radiation On the contribution of density perturbations and gravitational waves to the lower order multipoles of the Cosmic Microwave Background Radiation

2000-10-24

arxiv.org/abs/gr-qc/0010087v2

Int.J.Mod.Phys. D11 (2002) 259

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

prints to 25 pages including 14 figures, several additional sentences on interpretation, new references, to appear in Int. Jou

Scientific paper

10.1142/S0218271802001652

The important studies of Peebles, and Bond and Efstathiou have led to the formula C_l = const/[l(l +1)] aimed at describing the lower order multipoles of the CMBR temperature variations caused by density perturbations with the flat spectrum. Clearly, this formula requires amendments, as it predicts an infinitely large monopole C_0, and a dipole moment C_1 only 6/2 times larger than the quadrupole C_2, both predictions in conflict with observations. We restore the terms omitted in the course of the derivation of this formula, and arrive at a new expression. According to the corrected formula, the monopole moment is finite and small, while the dipole moment is sensitive to short-wavelength perturbations, and numerically much larger than the quadrupole, as one would expect on physical grounds. At the same time, the function l(l +1)C_l deviates from a horizontal line and grows with l, for l \geq 2. We show that the inclusion of the modulating (transfer) function terminates the growth and forms the first peak, recently observed. We fit the theoretical curves to the position and height of the first peak, as well as to the observed dipole, varying three parameters: red-shift at decoupling, red-shift at matter-radiation equality, and slope of the primordial spectrum. It appears that there is always a deficit, as compared with the COBE observations, at small multipoles, l \sim 10. We demonstrate that a reasonable and theoretically expected amount of gravitational waves bridges this gap at small multipoles, leaving the other fits as good as before. We show that the observationally acceptable models permit somewhat `blue' primordial spectra. This allows one to avoid the infra-red divergence of cosmological perturbations, which is otherwise present.

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