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Shedding Light on the Small-Scale Crisis with CMB Spectral Distortions

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Shedding Light on the Small-Scale Crisis with CMB Spectral Distortions The University of Manchester Research Shedding light on the small-scale crisis with CMB spectral distortions DOI: 10.1103/PhysRevD.95.121302 Document Version Final published version Link to publication record in Manchester Research Explorer Citation for published version (APA): Nakama, T., Chluba, J., & Kamionkowski, M. (2017). Shedding light on the small-scale crisis with CMB spectral distortions. Physical Review D, 95(12). https://doi.org/10.1103/PhysRevD.95.121302 Published in: Physical Review D Citing this paper Please note that where the full-text provided on Manchester Research Explorer is the Author Accepted Manuscript or Proof version this may differ from the final Published version. If citing, it is advised that you check and use the publisher's definitive version. 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Sep. 2021 RAPID COMMUNICATIONS PHYSICAL REVIEW D 95, 121302(R) (2017) Shedding light on the small-scale crisis with CMB spectral distortions Tomohiro Nakama,1 Jens Chluba,2 and Marc Kamionkowski1 1Department of Physics and Astronomy, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, USA 2Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom (Received 31 March 2017; published 28 June 2017) The small-scale crisis, discrepancies between observations and N-body simulations, may imply suppressed matter fluctuations on subgalactic distance scales. Such a suppression could be caused by some early-universe mechanism (e.g., broken scale invariance during inflation), leading to a modification of the primordial power spectrum at the onset of the radiation-domination era. Alternatively, it may be due to nontrivial dark-matter properties (e.g., new dark-matter interactions or warm dark matter) that affect the matter power spectrum at late times, during radiation domination, after the perturbations reenter the horizon. We show that early- and late-time suppression mechanisms can be distinguished by measurement of the μ distortion to the frequency spectrum of the cosmic microwave background. This is because the μ distortion is suppressed, if the power suppression is primordial, relative to the value expected from the dissipation of standard nearly scale-invariant fluctuations. We emphasize that the standard prediction of the μ distortion remains unchanged in late-time scenarios even if the dark-matter effects occur before or during the era (redshifts 5 × 104 ≲ z ≲ 2 × 106) at which μ distortions are generated. DOI: 10.1103/PhysRevD.95.121302 I. INTRODUCTION There has been exploration of different astrophysical The canonical ΛCDM model of cosmic structure for- consequences of suppressed small-scale power, and con- mation, in which structures grow from a nearly scale- straints to models are already being derived. For example, invariant spectrum of primordial adiabatic perturbations, WDM provides a particularly well-studied example of a has achieved many successes. Still, there are discrepancies late-time-suppression mechanism, and some recent work between observations on subgalactic scales and predictions [27,28] suggests tensions between WDM solutions to the from N-body simulations of structure and galaxy forma- small-scale crisis and observations. Even if a WDM-only tion. We refer to these discrepancies collectively as the scenario for resolving the small-scale crisis is in tension α “small-scale crisis” (see Ref. [1] for a review), which with Lyman- observations, a mixture of cold DM and includes the missing-satellite problem [2], the cusp-vs-core WDM (mixed dark matter) can still evade Lyman-α problem [3], and the too-big-to-fail problem [4]. While constraints while helping to solve problems associated further elucidation of the relevant baryonic physics may with the small-scale crisis [29–32]. There is thus still good help solve these problems [5–7], the small-scale crisis may reason to consider solutions to the small-scale crisis based also imply a suppression of density fluctuations below or on power suppression. around subgalactic scales [1]. For a primordial suppression, the shape of the suppressed Exotic mechanisms to suppress small-scale power can be spectrum on small scales depends on unknown and largely classified into those that involve modification of the unconstrained early-universe physics. In the framework of primordial power in the early Universe and those that single-field inflation, for instance, it is determined by the suppress power at later times. Examples of primordial slope of the inflaton potential [8]. Hence, even though a suppression are discussed in Refs. [8–12], and predict that wide variety of late-time suppression mechanisms that subgalactic primordial adiabatic perturbations are sup- predict different shapes for a suppressed power spectrum pressed at the onset of the radiation-dominated era. have been proposed, measurement of the shape of the late- Examples of late-time suppression are those discussed, time matter power spectrum on small scales cannot really e.g., in Refs. [13–26]; in such scenarios, subgalactic matter distinguish whether the suppression is primordial or late perturbations are present at the onset of the radiation- time. dominated era but then suppressed at later times, after the Here we point out that primordial and late-time sup- relevant scales reenter the horizon. These mechanisms pression mechanisms can be distinguished by the cosmic include free streaming of dark-matter (DM) particles microwave background (CMB) μ distortion [33–43]. Such (e.g., as in warm dark matter, WDM) or interactions μ distortions are produced by heating of the primordial between DM and standard-model or hidden particles. plasma from dissipation of small-wavelength fluctuations. 2470-0010=2017=95(12)=121302(5) 121302-1 © 2017 American Physical Society RAPID COMMUNICATIONS NAKAMA, CHLUBA, and KAMIONKOWSKI PHYSICAL REVIEW D 95, 121302(R) (2017) The Fourier modes that contribute to the μ distortions have comoving wave numbers 50 Mpc−1 ≲ k ≲ 104 Mpc−1, and the μ distortion arises when these dissipate at redshifts 5 × 104 ≲ z ≲ 2 × 106 (the μ era). In the standard scenario, where the nearly scale-invariant spectrum of perturbations seen in the CMB [44] is extrapolated to smaller scales (as motivated by Occam’s razor and the simplest models of inflation), the induced μ distortion is μ ≃ 2 × 10−8 [38,45–47]. For primordial suppression, the value of μ will be reduced relative to that expected from the standard almost-scale-invariant spectrum. If the suppression is strong enough, the μ parameter could even take a negative μ ≃ −3 10−9 FIG. 1. Examples of primordial power spectra suppressed value, BE × [36,48,49], due to the continuous extraction of energy from CMB photons by the non- below subgalactic scales [Eq. (1)] considered in this paper. For α 1 relativistic baryons to which they are coupled.1 the blue curves, ¼ , and from bottom to top we have k 1; 20; 35 −1 In contrast, for late-time suppression of small-scale s ¼f g Mpc . The gray curve corresponds to the standard spectrum P of Eq. (1) (α 0). perturbations, there are still primordial perturbations to be st ¼ dissipated, and so the standard prediction is unmodified. The argument is not entirely trivial, as in many late-time k ns−1 P k P k P~ k ; P k A ; scenarios, the suppression of the matter power spectrum ð Þ¼ stð Þ ð Þ stð Þ¼ kp occurs during the μ era. For example, in the charged-particle- decay scenario [16], suppression of the matter power 1 þ 10−α 1 − 10−α k P~ ðkÞ¼ − tanh log : ð1Þ spectrum occurs until roughly 3.5 years after the big bang, 2 2 ks at redshifts z ≃ 5 × 105, right when the μ distortion is being produced. This time scale is actually fairly generic, as this is 10−α k ≳ k the redshift at which subgalactic scales are entering the That is, the power is suppressed by for s, P horizon. The crucial point is that the matter density is relative to the standard spectrum st with parameters A 2 2 10−9 k 0 05 −1 n 0 97 negligible compared with the radiation density during the μ ¼ . × , p ¼ . Mpc and s ¼ . [44]. era. There can thus be dramatic smoothing of the matter Examples of the suppressed primordial spectra are shown −1 distribution with little effect on the radiation-density per- in Fig. 1, where we take ks ¼ 1, 20, and 35 Mpc , relevant turbations. Similar arguments apply to the y distortion, for small-scale problems. The above step-type suppression which is created later at z ≲ 5 × 104 [33,34]. Here in would lead to a step-type suppression of the matter addition, distortions are sourced by bulk flows at second spectrum at low redshifts, similarly to mixed-DM scenarios order in the baryon velocity, v. However, these contributions [29,30]. Hence, we can refer to those studies to gain insight are subdominant [38] relative to larger energy release from into structure formation for the suppressed primordial first stars and structure formation, as also recently discussed spectrum we consider here. However, establishing a precise in Ref. [50]. For the same reasons the effects of primordial link between our spectrum and different aspects of the dark-matter isocurvature perturbations on spectral distor- small-scale crisis is beyond the scope of this work, at least tions are limited [51].
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