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Shedding light on the small-scale crisis with CMB spectral distortions

DOI: 10.1103/PhysRevD.95.121302

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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

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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 fluctuations on subgalactic distance scales. Such a suppression could be caused by some early- 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 ) 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 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 () 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 , 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.

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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 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 , 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 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 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]. because of potentially important baryonic processes. Thus, In the next section, we calculate the value for μ assuming we treat α and ks as free parameters and only illustrate that a step-type suppression of primordial power below sub- μ can be significantly smaller than the expected standard −8 galactic scales, and we conclude in Sec. III. value, μ ≃ 2 × 10 . Additional information about the precise position of the transition scale might be accessible with future measure- II. PRIMORDIAL SUPPRESSION μ ments of the exact spectral-distortion shape [38,40,45]. AND CMB DISTORTION However, even if we were only to observe a significant We relate the primordial power suppression to the μ suppression of μ, without additional information about the distortion as follows. We employ the following description spectral-distortion shape, we could connect the small-scale of primordial suppression in terms of the dimensionless crisis to primordial suppression. Ultimately, it will be primordial curvature power spectrum: instructive to investigate small-scale problems with simu- lation of structure formation with the various primordial spectra which are consistent with, e.g., simultaneous 1 −2 This arises because the baryons alone would cool as Tb ∝ a constraints from the Lyman-α forest and μ (and possibly −1 with the scale factor a, as opposed to Tγ ∝ a for photons. taking into account baryonic processes).

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SHEDDING LIGHT ON THE SMALL-SCALE CRISIS WITH … PHYSICAL REVIEW D 95, 121302(R) (2017) roughly balanced. If in the future μ is constrained to be μ ≃ μ ≃ 2 10−8 smaller than what is expected ( ac × ), from the dissipation of the standard fluctuations (in the figure this corresponds to the limit α → 0), then it could serve as a smoking gun for some primordial suppression thereby possibly explaining the small-scale crisis.

III. CONCLUSION The small-scale crisis of ΛCDM may imply suppressed matter fluctuations on subgalactic scales. Such a suppres- sion could result from some new physics that operates during inflation or could be the consequence of new dark- μ α FIG. 2. The dependence of distortions on , which controls a matter physics that operates at later times, after the relevant step-type primordial suppression [see Eq. (1)]. From bottom to −1 distance scales reenter the horizon during radiation domi- top, the suppression wave number is ks 1; 20; 35 Mpc .As ¼f g nation. Although the primordial and late-time suppression α → 0, μ approaches ≃2 × 10−8, the value mostly determined by the dissipation of the standard almost-scale-invariant fluctuations. mechanisms are expected to impact structure formation in a similar fashion, we show here that they could be in In contrast, if ks is relevant to the small-scale crisis and if principle distinguished by measurement of the μ distortion α is sufficiently large, μ can be negative, approaching μBE ≃ −9 −1 μ −3 × 10 for ks ∼ 1 Mpc , determined by the energy extraction to the CMB frequency spectrum. This is because may be from photons to baryons due to their coupling. significantly reduced relative to the canonical value μ ≃ 2 × 10−8 if subgalactic power suppression is primordial. For power suppression sufficiently significant, μ could even μ 2 μ μ μ The distortion can be estimated [52] as ¼ ac þ BE become negative as a consequence of the transfer of energy μ ≃ −3 10−9 with BE × and from photons to baryons. On the other hand, for a late-time Z suppression, the CMB μ distortion would not be affected ∞ dk notably since it is mostly determined by primordial μ ≃ PðkÞWμðkÞ; ð2Þ ac k fluctuations rather than subhorizon dynamics of DM kmin fluctuations during the radiation-dominated era. Thus, with for a late-time suppression, μ is not expected to differ significantly from the standard positive value. k=ˆ 1360 2 If μ is found to be unexpectedly small or negative by W k ≃ 2 8A2 − ½ μð Þ . exp 0 3 future high-sensitivity experiments measuring the energy 1 þ½k=ˆ 260 . þ k=ˆ 340 spectrum of CMB photons, it may serve as a smoking gun kˆ 2 − − ; for a primordial suppression. Note also that the negative exp ð3Þ μ μ 32 contribution to can, in principle, be even smaller than BE due to direct or indirect thermal coupling of nonrelativistic k ≃ 1 −1 A ≃ 0 9 kˆ k where min Mpc , . and ¼ Mpc. This DM with photons, since in this case more energy is approximation is accurate at the ≃20% level and slightly extracted from photons to DM to maintain thermal equi- underestimates the recovered value for μ [47]. Hence, we librium [53]. If on the other hand the standard prediction for μ renormalize the above window function Wμ so that is verified, then it suggests that the small-scale crisis has μ ≃ 2 3 10−8 α 0 to do with late-time physics. If we find μ to have the ac . × when ¼ (i.e. standard fluctuations), which is sufficient for our purposes. standard value, then another possibility, which we leave for The values of μ as a function of α are shown in Fig. 2. future work, is that a matter-radiation isocurvature pertur- −1 bation, correlated with the adiabatic perturbation, sup- When ks is close to ∼1 Mpc and α is sufficiently large, μ μ k ≃ 35 −1 pressed matter perturbations on small scales while becomes negative, approaching BE. For s Mpc , the asymptotic value is μ ≃ 0; that is, the energy injection preserving the primordial curvature (and thus radiation) perturbation on small scales. due to the dissipation of sound waves and energy extraction μ due to interactions between photons and baryons are In this paper, we emphasized that can be small for the primordial suppression scenario. However, ultimately it

2 will be interesting to study the small-scale problems by Here we assume no other energy injection mechanisms in N-body simulations for a variety of primordial spectra the early Universe exist, such as evaporating primordial black α holes, decaying/annihilating particles, cosmic strings, primordial consistent with existing constraints from, e.g., Lyman- magnetic fields and axionlike particles (see Ref. [42] for an observation, simultaneously calculating μ for each spec- overview). trum, possibly taking into account baryonic processes.

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NAKAMA, CHLUBA, and KAMIONKOWSKI PHYSICAL REVIEW D 95, 121302(R) (2017) ACKNOWLEDGMENTS supported by the Royal Society as a Royal Society T. N. acknowledges useful discussions with Teruaki University Research Fellow at the University of Suyama and Jun’ichi Yokoyama. T. N. was supported by Manchester, UK. M. K. is supported by the Simons Grant-in-Aid for JSPS Fellow No. 25.8199 and JSPS Foundation, NSF Grant No. PHY-1214000, and NASA Postdoctoral Fellowships for Research Abroad. J. C. is ATP Grant No. NNX15AB18G.

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