MNRAS 000, 1–3 (2015) Preprint 14 October 2020 Compiled using MNRAS L A T E X style file v3.0 Primordial nucleosynthesis constraints on high-  energy releases Gianfranco De Zotti 1 ★ and Matteo Bonato, 2,1 1 INAF–Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy 2 INAF–Istituto di Radioastronomia and Italian ALMA Regional Centre, Via Gobetti 101, I-40129, Bologna, Italy Accepted XXX. Received YYY; in original form ZZZ ABSTRACT The cosmic microwave background (CMB) spectrum provides tight constraints on the thermal history of the universe up to  ∼ 2 × 10 6 . At higher redshifts thermalization processes become very efficient so that even large energy releases do not leave visible imprints in the CMB spectrum. In this paper we show that the consistency between the accurate determinations of the specific entropy at primordial nucleosynthesis and at the electron-photon decoupling implies that no more than 7.8% of the present day CMB energy density could have been released in the post-nucleosynthesis era. As pointed out by previous studies, primordial nucleosynthesis complements model independent constraints provided by the CMB spectrum, extending them by two orders of magnitude in redshift. Key words: Primordial nucleosynthesis – cosmic microwave background – cosmology: theory 1 INTRODUCTION The spectrum of the cosmic microwave background (CMB) carries unique information/constraints on the thermal history of the universe since energy releases occurring over many redshift decades can leave their imprint on it (Zeldovich & Sunyaev 1969; Sunyaev & Zeldovich 1970; Illarionov & Sunyaev 1975; Danese & de Zotti 1977; Burigana et al. 1991; Chluba et al. 2012; Khatri & Sunyaev 2012; Chluba & Jeong 2014; Tashiro 2014; Chluba 2016; De Zotti et al. 2016; Chluba et al. 2019). However, at very high redshifts such imprints are erased by thermalization effects due to the combined action of photon emission processes and of Compton scattering. Small distortions are completely thermalized at > few × 10 6 (Danese & de Zotti 1982; Burigana et al. 1991; Hu & Silk 1993; Chluba 2014). The thermalization is less efficient for large distortions which can keep some visibility up to redshifts higher by factors of several (Chluba et al. 2020). At still higher redshifts, releases of very large amount of energy could have occurred without leaving any visible track in the CMB spectrum. On the other hand, the outcomes of primordial nucle- osynthesis (or big-bang nucleosynthesis, BBN) are sensitive to the radiation energy density. Indeed, just the consideration of the pro- duction of light elements in the early universe led to the prediction of the CMB (Gamow 1948; Alpher ¯ & Herman 1949). The present-day accurate determinations of cosmological param- eters entail strong constraints on the CMB energy density both at the BBN epoch and at electron-photon decoupling, hence on the ad- ditional amount of energy that could have been released after the BBN, at high enough redshifts to ensure a tight coupling between electrons and radiation. Such constraints are quantified in Sect. 2. Our conclusions are summarized in Sect. 3. ★ E-mail: gianfranco.dezotti@inaf.it Figure 1. Upper limit (95% confidence level) to the fractional amount of energy that could have been added to the CMB after the primordial nucle- osynthesis epoch, derived in this paper (black horizontal line), compared with constraints derived by Chluba et al. (2020). The red dotted horizontal lines show the limits obtained from the effective number of neutrino species, as- suming that a fraction   of the total injected energy goes into neutrinos. The lower and upper lines refer to   = 0 and   = 0.5, respectively; note that the value for   = 0 has been corrected as mentioned in the text. Constraints from CMB spectral measurements, as computed by Chluba et al. (2020), are also shown. The upper (blue) and lower (pink) dot-dashed lines show the 95% confidence upper limits implied by CMB spectral measurements from COBE/FIRAS (  /   < 6 × 10 −5 ) and from a future PIXIE-like exper- iment (  /   < 10 −8 ), respectively. The dotted lines deviating from the dot-dashed lines at their right end, again from Chluba et al. (2020), show the corresponding limits obtained under the small-distortion approximation. © 2015 The Authors arXiv:2010.06419v1 [astro-ph.CO] 13 Oct 2020