A joint study of early and late spectral distortions of the cosmic microwave background and of the millimetric foreground

In this work we have compared the absolute temperature data of the cosmic microwave background (CMB) spectrum with models of CMB spectra distorted by a single or two heating processes at different cosmic times. The constraints on the fractional energy injected in the radiation field, Δϵ/ϵ<inf>i</inf>, are mainly provided by the precise measures of the FIRAS instrument on board the <it>COBE</it> satellite, while long-wavelength measures are crucial to set constraints on free–free distortions. We find that the baryon density does not influence the limits on Δϵ/ϵ<inf>i</inf> derived from current data for cosmic epochs corresponding to the same dimensionless time <it>y</it><inf>h</inf> of dissipation epoch, although the redshift corresponding to the same <it>y</it><inf>h</inf> decreases with the baryon density. Under the hypothesis that two heating processes have occurred at different epochs, the former at any <it>y</it><inf>h</inf> in the range 5 ≥<it>y</it><inf>h</inf>≥ 0.01 (this joint analysis is meaningful for <it>y</it><inf>h</inf>≳ 0.1) and the latter at <it>y</it><inf>h</inf>≪ 1, the limits on Δϵ/ϵ<inf>i</inf> are relaxed by a factor ∼2 for both the earlier and the later process with respect to the case in which a single energy injection in the thermal history of the Universe is considered. In general, the constraints on Δϵ/ϵ<inf>i</inf> are weaker for early processes (5 ≳<it>y</it><inf>h</inf>≳ 1) than for relatively late processes (<it>y</it><inf>h</inf>≲ 0.1), because of the subcentimetric wavelength coverage of FIRAS data, relatively more sensitive to Comptonization than to Bose–Einstein like distortions. While from a widely conservative point of view the FIRAS calibration as revised recently by Battistelli et al. only implies a significant relaxation of the constraints on the Planckian shape of the CMB spectrum, the favoured calibrator emissivity law proposed by the authors, quite different from a constant emissivity, implies significant deviations from a Planckian spectrum. An astrophysical explanation of this, although intriguing, seems difficult. We find that an interpretation in terms of CMB spectral distortions should require a proper balance between the energy exchanges at two very different cosmic times or a delicate fine tuning of the parameters characterizing a dissipation process at intermediate epochs, while an interpretation in terms of a relevant millimetric foreground, produced by cold dust, should imply a too large involved mass and/or an increase of the fluctuations at subdegree angular scales. Future precise measurements at longer wavelengths as well as current and future CMB anisotropy space missions will provide independent, direct or indirect, cross-checks. This work is related to <it>Planck</it>-LFI activities.