Abstract
The notion that dust might have formed the cosmic microwave background (CMB) has been strongly refuted on the strength of four decades of observation and analysis, in favour of recombination at a redshift \(z\sim 1080\). But tension with the data is growing in several other areas, including measurements of the Hubble constant H(z) and the BAO scale, which directly or indirectly impact the physics at the surface of last scattering (LSS). The \(R_\mathrm{h}=ct\) universe resolves at least some of this tension. We show in this paper that—if the BAO scale is in fact equal to the acoustic horizon—the redshift of the LSS in this cosmology is \(z_\mathrm{cmb} \sim 16\), placing it within the era of Pop III star formation, prior to the epoch of reionization at \(15\gtrsim z \gtrsim 6\). Quite remarkably, the measured values of \(z_\mathrm{cmb}\) and \(H_0\equiv H(0)\) in this model are sufficient to argue that the CMB temperature today ought to be \(\sim 3\) K, so \(H_0\) and the baryon-to-photon ratio are not independent free parameters. This scenario might have resulted from rethermalization of the CMB photons by dust, presumably supplied to the interstellar medium by the ejecta of Pop III stars. Dust rethermalization may therefore yet resurface as a relevant ingredient in the \(R_\mathrm{h}=ct\) universe. Upcoming high-sensitivity instruments should be able to readily distinguish between the recombination and dust scenarios by either (i) detecting recombination lines at \(z\sim 1080\) or (ii) establishing a robust frequency-dependent variation of the CMB power spectrum at the level of \(\sim \) 2–4% across the sampled frequency range.
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Notes
In the context of \(R_\mathrm{h}=ct\), we know that radiation alone cannot sustain an equation of state \(p=-\rho /3\), so dark energy is a necessary ingredient.
In this expression, we have adopted the Planck optimized value of the Hubble constant, \(H_0=67.6\pm 0.9\) km \(\hbox {s}^{-1} \hbox {Mpc}^{-1}\) [79]. To be fair, this is the value measured in the context of \(\Lambda \)CDM, and while a re-analysis of the Planck data in the context of \(R_\mathrm{h}=ct\) will produce a somewhat different result for \(H_0\), the differences are likely to be too small to affect the discussion in this paper.
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Acknowledgements
I am grateful to the anonymous referee for several helpful suggestions to improve the presentation in the manuscript. I am also very happy to acknowledge helpful discussions with Daniel Eisenstein and Anthony Challinor regarding the acoustic scale, and with Martin Rees, José Alberto Rubino-Martin, Ned Wright and Craig Hogan for insights concerning the last-scattering surface. I thank Amherst College for its support through a John Woodruff Simpson Lectureship and Purple Mountain Observatory in Nanjing, China, for its hospitality while part of this work was being carried out. This work was partially supported by Grant 2012T1J0011 from the Chinese Academy of Sciences Visiting Professorships for Senior International Scientists, and Grant GDJ20120491013 from the Chinese State Administration of Foreign Experts Affairs.
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F. Melia: John Woodruff Simpson Fellow.
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Melia, F. Reassessing dust’s role in forming the CMB. Eur. Phys. J. Plus 135, 511 (2020). https://doi.org/10.1140/epjp/s13360-020-00533-2
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DOI: https://doi.org/10.1140/epjp/s13360-020-00533-2