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Multipole fine structure of the cosmic microwave background: reconstruction of the temperature power spectrum




The fine structure of the temperature power spectrum of the cosmic microwave background (CMB) radiation is investigated in the presently accessible multipole range up to l ∼ 104. The temperature fluctuations are reproduced by an isotropic Gaussian random field on the unit sphere, whose Green function is defined by a Hermitian matrix kernel inferred from the data sets by way of spectral fits. The reconstruction of the temperature autocorrelation function from the measured multipole moments Cl is a classical inverse problem, which does not require specification of cosmic evolution equations for the photon density. The scale-invariant correlation function admits a multipole expansion in zonal spherical harmonics. The multipole coefficients are obtained as averages over Hermitian spectral matrices determining the angular power spectrum of the spherical random field. The low-l multipole regime of the CMB temperature fluctuations is composed of overlapping Gaussian peaks, followed by an intermediate oscillatory regime manifested by a modulated exponentially decaying Cl slope. The high-l regime above l ∼ 4000 comprises a power-law ascent with exponential cut-off. The fine structure of the Gaussian, oscillatory and high-l regimes is reproduced by zooming into the respective l intervals on linear and logarithmic scales.

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