ΛCDM Or Self-Interacting Neutrinos? - How CMB Data Can Tell the Two Models Apart

ΛCDM or self-interacting neutrinos? - how CMB data can tell the two models apart Minsu Park,1, 2, ∗ Christina D. Kreisch,2, y Jo Dunkley,1, 2 Boryana Hadzhiyska,3 and Francis-Yan Cyr-Racine3, 4 1Department of Physics, Princeton University, Princeton, New Jersey 08544 USA 2Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544 USA 3Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA 4Department of Physics and Astronomy, University of New Mexico, 1919 Lomas Blvd NE, Albuquerque, New Mexico 87131, USA (Dated: April 24, 2019) Of the many proposed extensions to the ΛCDM paradigm, a model in which neutrinos self- interact until close to the epoch of matter-radiation equality has been shown to provide a good fit to current cosmic microwave background (CMB) data, while at the same time alleviating tensions with late-time measurements of the expansion rate and matter fluctuation amplitude. Interestingly, CMB fits to this model either pick out a specific large value of the neutrino interaction strength, or are consistent with the extremely weak neutrino interaction found in ΛCDM, resulting in a bimodal posterior distribution for the neutrino self-interaction cross section. In this paper, we explore why current cosmological data select this particular large neutrino self-interaction strength, and by consequence, disfavor intermediate values of the self-interaction cross section. We show how it is the ` & 1000 CMB temperature anisotropies, most recently measured by the Planck satellite, that produce this bimodality. We also establish that smaller scale temperature data, and improved polarization data measuring the temperature-polarization cross-correlation, will best constrain the neutrino self-interaction strength. We forecast that the upcoming Simons Observatory should be capable of distinguishing between the models. I. INTRODUCTION New neutrino interactions have become a topic of increasing interest due their impact on cosmological observ- Within the Standard Model of particle physics, neu- ables via altering neutrino free-streaming during the radi- trinos remain elusive. While universally present, their ation dominated era (see e.g. Refs. [10{43]). Past studies weak interactions with other particles make them difficult [44{49] have explored the viability of stronger neutrino to study directly. Neutrino oscillation experiments have self-scattering, using a Yukawa interaction model param- shown that neutrinos have mass [1, 2], but the Standard eterized by an interaction strength, Geff . Here the rate of 2 5 scattering, Γν , scales as Γν G T where Tν is the tem- Model does not account for the mechanism that gener- / eff ν ates this mass [3{6]. This presents the neutrino sector as perature of the cosmic neutrino background [44{48]. In- an intriguing source of new physics. creasing Geff strengthens the neutrino-neutrino coupling In the Standard Model we assume neutrinos interact in the early Universe. Thus, increasing Geff ultimately only through the electroweak interaction and decouple delays neutrino free-streaming to epochs of lower energies from the cosmic plasma at a temperature of 1.5 MeV [7]. and lower redshifts. Once decoupled, the neutrinos freely streamed through A delay in the onset of neutrino free-streaming affects the early universe, interacting only through gravity. The the amplitude and phases of the CMB power spectrum free-streaming of these gravitationally coupled neutri- (see [45, 50] for more details.). A model with non-zero nos imposes a shear stress on the matter as it streams value of Geff has been shown to fit current cosmological past, damping acoustic oscillations in the photon-baryon data and produce a bimodal posterior probability for the plasma and boosting CDM fluctuations at horizon entry interaction rate: a `weak' mode with low self-scattering [8]. Recent observations of the Cosmic Microwave Back- strength Geff , essentially indistinguishable from no self- ground (CMB), most recently by the Planck satellite [9], scattering (ΛCDM), and a `strong' self-interacting mode −2 −2 have put bounds on neutrino parameters, including the with Geff of order 10 MeV , where the neutrinos de- arXiv:1904.02625v2 [astro-ph.CO] 23 Apr 2019 effective number of neutrino species (Neff = 2:99 0:17) couple at neutrino temperatures as low as 25 eV [44{ P ± and the sum of the species' masses ( mν < 0:24 eV 46]. The strong mode is particularly interesting as it P at 95% confidence, or mν < 0:12 eV combined with has a larger predicted Hubble constant [51] than the baryon acoustic oscillation data). This is approaching usual ΛCDM model, and a lower predicted amplitude of the lower mass limit for the inverted neutrino hierarchy, structure [52], which are preferred by other astronomical P mν 0:1 eV, from neutrino oscillation experiments datasets. [1, 2]. Cosmological≥ data can now put competitive con- In this paper we further explore which aspects of cur- straints on neutrino physics. rent CMB data produce the degeneracy between the two models. We identify the part of the Planck data respon- sible for producing the bimodality, which was not present ∗ [email protected] with the WMAP data, and show how the data exclude y [email protected] models with moderate self-interaction. We then assess 2 FIG. 1. Probability distributions for parameters from a nine-parameter model (ΛCDM plus neutrino self-interaction strength Geff , effective neutrino number, and neutrino mass), using the WMAP and Planck CMB data combined with BAO and Planck lensing data. The parameters derived using Planck are consistent with previous results [45] and show the clear bimodality in the neutrino self-interaction strength. The `strong' and `weak' distributions show the marginalized posteriors when considering each of the bimodal islands separately. For the unseparated distribution, the strong mode has a lower marginalized posterior relative to the weak mode. The distribution using just WMAP data is not bimodal. how upcoming CMB data might distinguish between the data [60], using the same BAO data and optical depth two models. This extends similar investigations in [46]. prior. Additionally, we generate simulated TT, TE and EE spectra representative of the upcoming Simons Ob- servatory (SO), with co-added white noise levels of 5µK- 0 II. METHODS amin over 40% of the sky, a 1.4 beam and maximum multipoles of ` = 3000 in temperature and ` = 5000 in polarization [61]1. We describe the input models for these We use MCMC methods to map out the posterior dis- simulations in Sec. III C. tribution for a 9-parameter cosmological model: 6 parameters are the usual ΛCDM parameters (baryon density, cold dark matter density, angular peak position, spectral III. RESULTS index and amplitude, and optical depth) and we also vary the effective number of neutrino species, Neff , the sum P A. Parameter distributions with current data of neutrino masses, mν , and the interaction strength Geff . We impose linear priors on all parameters, except Geff which takes a logarithmic prior. This prior choice In Figure 1 we show a set of the posterior distribu- is further discussed in Section III A. We use the Cos- tions for the sampled and derived parameters for the moMC sampling code [53] with Multinest [54], which is Planck data compared to the WMAP data. Both data well-suited to multimodal posteriors. We use the same were accompanied by the same BAO data and τ prior. modified Boltzmann code, CAMB, as in [45], and imple- For Planck we find results consistent with [45, 46], with ment the same modifications in the CLASS code as a a bimodal distribution for Geff . One mode is consis- cross-check. tent with ΛCDM, and the other `strong' mode has non- The datasets used are Planck 2015 temperature and zero interactions. We identify the preferred parame- lensing likelihood using the Plik-lite code [55, 56], combined with current BAO data [57{59], and a gaussian prior on the optical depth of τ = 0:058 0:012 from Planck. We also examine the effect of replacing± just the 1 In this study we do not include the non-white noise and residual Planck TT data with the WMAP 9-year TT and TE foregrounds considered in [61]. 3 CMB : plikLite = plik lite v18 TT ) 2 1.5 − 220 − MeV eff 3.0 − 240 (G − 10 2 log 260 4.5 χ − − − 280 − 300 − 320 MC 1.045 − θ 3.5 3.0 2.5 2.0 1.5 − − − 2 − − log(GeffMeV ) 100 FIG. 3. −χ2 values for the Planck ` > 30 data along the 1.040 path shown in Figure 2 to show the clear bimodality and the likelihoods between the two modes. The two modes have the 0.15 0.30 0.45 0.60 2.4 3.0 3.6 4.2 Σmν Neff same likelihood; the difference in posterior distribution for Geff is then due to the volume of well-fitting models in our chosen parameterization. FIG. 2. Illustration of the line connecting the best-fitting models in each mode that we use to compute spectra and likelihoods. The orange stars are the locations of the 4 points in parameter space sampled for Figure 4 and Figure 5 Figure 1 also shows that the WMAP data do not favor the strongly interacting mode, implying that the smaller scale data in the 1200 < ` 2500 range enhance the ≤ ters for each mode by plotting them separately in Fig- preference for the strong mode. ure 1, in addition to the joint distribution. The weak 2 P mode has log(Geff MeV ) < 3:04, mν < 0:2eV, and +0:51 − Neff = 3:19−0:48 at 95% CL whereas the strong mode B. CMB spectra as a function of increasing Geff 2 +0:24 P prefers log(Geff MeV ) = 1:36−0:30 and has mν = +0:26 +0−:78 0:30−0:25eV, Neff = 3:80−1:0 at 95% CL.

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