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Possible Nonequilibrium Imprint in the Cosmic Background at Low Frequencies

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Possible Nonequilibrium Imprint in the Cosmic Background at Low Frequencies PHYSICAL REVIEW RESEARCH 2, 013210 (2020) Possible nonequilibrium imprint in the cosmic background at low frequencies Marco Baiesi ,1,2 Carlo Burigana ,3,4,5 Livia Conti ,2,* Gianmaria Falasco,6 Christian Maes ,7 Lamberto Rondoni ,8,9 and Tiziana Trombetti3,10 1Dipartimento di Fisica e Astronomia, Università degli Studi di Padova, 35121 Padova, Italy 2Sezione di Padova, Istituto Nazionale di Fisica Nucleare, 35131 Padova, Italy 3Istituto di Radioastronomia, Istituto Nazionale di Astrofisica, 40129 Bologna, Italy 4Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, 44122 Ferrara, Italy 5Sezione di Bologna, Istituto Nazionale di Fisica Nucleare, 40126 Bologna, Italy 6Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, 1511 Luxembourg, Luxembourg 7Instituut voor Theoretische Fysica, KU Leuven, 3001 Leuven, Belgium 8Dipartimento di Scienze Matematiche, Politecnico di Torino, 10129 Torino, Italy 9Sezione di Torino, Istituto Nazionale di Fisica Nucleare, 10125 Torino, Italy 10Istituto di Scienze Marine, Consiglio Nazionale delle Ricerche, 40129 Bologna, Italy (Received 26 August 2019; accepted 3 February 2020; published 26 February 2020) Cosmic background radiation has been observed to deviate from the Planck law expected from a blackbody at ∼ 2.7 K at frequencies below ∼3 GHz. We discuss the abundance of the low-energy photons from the perspective of nonequilibrium statistical mechanics. We propose a mechanism of stochastic frequency diffusion, the counterpart to stochastic acceleration for charged particles in a turbulent plasma, to modify the standard Kompaneets equation. The resulting violation of the Einstein relation allows us to take advantage of low-frequency localization and finally leads to photon cooling. The modified equation predicts a frequency distribution in agreement with the absolute temperature measurements of the cosmic background radiation down to about 20 MHz, for which we offer an updated compilation. In that sense, the so-called space roar we observe today is interpreted as a nonequilibrium echo of the early universe and more specifically of nonequilibrium conditions in the primordial plasma. DOI: 10.1103/PhysRevResearch.2.013210 I. INTRODUCTION structures (see [3,4] for reviews and [5,6] for recent analyses). As a result, the distribution function of the CMB photons at The cosmic microwave background (CMB) is a prime later times t is supposed to follow the blackbody spectrum at witness to the physics of the early universe. According to the an equilibrium temperature T (t ). After a delicate subtraction standard model of physical cosmology, it carries information of the intervening astrophysical emissions, the cosmic back- about an epoch before neutral atoms were formed, dating from ground appears today very close to a blackbody radiation [7] some 105 years after the Big Bang (see [1,2] for reviews). at a temperature of about 2.7 K, peaking at about 160 GHz, It is generally assumed then that matter and radiation were in very good agreement with the Planck spectrum from about approximately in thermodynamic equilibrium, owing to the 10 GHz up to about 600 GHz. high efficiency of Compton scattering, bremsstrahlung, and However, there is evidence of a systematic deviation from radiative Compton processes, with characteristic timescales the Planck law of a blackbody at about 2.7 K at low fre- much shorter than the cosmic expansion timescale. At the quencies, in the radio tail of the cosmic background. That recombination era, when electrons and protons formed hy- aspect was brought to attention by two independent types of drogen atoms, light decoupled from matter and the photons observations: the CMB absolute temperature excess measured started to move almost freely through the expanding universe, by the second generation absolute radiometer for cosmology, influenced by secondary effects only, such as the cosmological astrophysics, and diffuse emission instrument (ARCADE 2) reionization associated with the formation of early stars and [8] and the anomalously strong absorption of the redshifted galaxies and the weak gravitational lensing induced by cosmic 21-cm line from neutral hydrogen measured by the exper- iment to detect the global epoch of reionization signature (EDGES) [9]. After consideration of possible instrumental *[email protected] errors and after subtracting galactic and extragalactic sources of low-frequency radiation, a strong residual emission remains Published by the American Physical Society under the terms of the in ARCADE 2 data [10], which is much larger than predicted Creative Commons Attribution 4.0 International license. Further by the standard theory of CMB spectral distortions. Consis- distribution of this work must maintain attribution to the author(s) tently, the intriguing EDGES absorption profile amplitude, and the published article’s title, journal citation, and DOI. about 2–3 times larger than expected, could be explained 2643-1564/2020/2(1)/013210(15) 013210-1 Published by the American Physical Society MARCO BAIESI et al. PHYSICAL REVIEW RESEARCH 2, 013210 (2020) by a much stronger background radiation with respect to one for population selection in various nonequilibrium distri- standard predictions (see [11] for an alternative explanation butions, as has been discussed, for example, for population assuming that the primordial hydrogen gas was much colder inversion in lasers [16], for kinetic proofreading in protein than expected). The scientific literature in fact abounds with synthesis [17], and for suprathermal kappa-distributions in experimental data from low-frequency radio surveys, some space plasma [18]. It may be theoretically summarized in going back a long time: After subtraction for galactic and the so-called blowtorch theorem [19,20]: Here, violating the extragalactic contributions, they all show an excess of soft, Einstein relation and adding a low-frequency diffusion imme- i.e., low-frequency, photons. A concise description of the diately leads to the abundance of soft photons. cosmic background spectrum data considered in this work is Nonequilibrium effects in the early universe have not been given in Sec. II. discussed extensively so far and details on the precise mech- We repeat that the CMB spectrum theory assumes (near-) anism cannot be provided at this point. So far, the origin equilibrium conditions, e.g., up to the time of recombination. of nonequilibrium features can only be thought to reside The equilibrium distribution, the Planck law, is the quantum ultimately with gravitational degrees of freedom that have analog of the Maxwell distribution for a classical ideal gas influenced the nature of light and matter, as may be expected and as emphasized already by the pioneers of statistical me- in strongly non-Newtonian regimes of gravity. Furthermore, chanics, it is the distribution to be typically expected as a the supposed presence of frequency diffusion most likely consequence of counting with Bose statistics. For the kinetics leads to much slower relaxation. and relaxation to the Planck distribution, we recall in Sec. III The hypothesis that the low-frequency excess in the CMB the Kompaneets equation [12], which is used in that context. It is a nonequilibrium imprint, originating at (or ultimately describes the evolution of the photon spectrum due to repeated before) the time of the primordial plasma, does not stand Compton scattering off a thermal bath of nonrelativistic elec- alone though. We mentioned already the blowtorch theo- trons, possibly towards the equilibrium Planck distribution. rem and its relevance to population inversion. We have also In the Kompaneets equation, the Planck law entails zero been led to investigate such an idea by the various analo- current (in frequency space) as a result of the detailed balance gies we see with the phenomenon of low-frequency spectral between diffusion and drift. That arises from the analog of the power enhancement that has been observed in a number of Einstein relation or the second fluctuation-dissipation relation different nonequilibrium systems, including disordered sys- as it is called in the (classical) Fokker-Planck equation. How- tems [21,22], fluids [23,24], driven macromolecules [25], and ever, kinetically, there is localization at low frequencies, as vibrating solids [26]. We also refer to the theoretical models implied by the proportionality ν2 of the kinetic coefficients: in [27,28] for a different type of population inversion. The number (or density) of soft photons does not change easily as the interaction with the plasma is damped at low frequency. It is that kinetic aspect that is crucially important when (even slightly) violating the Einstein relation. II. OBSERVATIONAL FRAMEWORK In this paper we no longer assume that the universe at t 1 s after the Big Bang was in thermodynamic equilibrium Measurements of the absolute temperature of the cosmic for the relevant degrees of freedom. Instead, in Sec. IV, background have been performed since the CMB discovery we propose an additional turbulent diffusion in frequency by Penzias and Wilson [29] at 4.08 GHz. In this paper we space. Its origin is the assumed chaotic nature of the turbulent consider the cosmic background absolute temperature data plasma, where stochastic acceleration is caused by space-time on the basis of the available measurements, including their random force fields [13–15]. Quite independent of the detailed quoted global errors that are related to limited
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