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Interacting radiation after Planck and its implications for the Hubble Tension

Nikita Blinov, Gustavo Marques-Tavares

TL;DR

This paper analyzes extensions of ΛCDM that include an extra non-free-streaming radiation component, parameterized by $N_ ext{eff}$, $N_ ext{fld}$, and the free-streaming fraction $f_ ext{fs}$, using Planck 2018 data plus BAO and $H_0$ measurements. It shows that, with the total radiation fixed to the standard value $N_ ext{tot}=3.046$, Planck polarization and TT data require $f_ ext{fs}>0.8$, effectively ruling out significant self-interactions for neutrinos at recombination; when $N_ ext{tot}$ is allowed to vary, $N_ ext{fld}$ is constrained to be small ($<0.6$ at 95% CL) but a mild increase in total radiation can modestly improve the fit and help alleviate the $H_0$ tension. The authors connect these cosmological constraints to concrete particle-physics scenarios, notably non-Abelian dark radiation and late equilibration of a dark sector, showing that Planck data place strong bounds on such models (e.g., excluding large $N_d$ in equilibrium with the SM) while highlighting parameter regions where small non-free-streaming components could still be viable. Overall, the results favor predominantly free-streaming radiation and demonstrate that while non-free-streaming components can slightly ease the $H_0$ tension, they do so without compelling evidence and must satisfy tight particle-physics-inspired constraints.

Abstract

Standard cosmology predicts that prior to matter-radiation equality about 41% of the energy density was in free-streaming neutrinos. In many beyond Standard Model scenarios, however, the amount and free-streaming nature of this component is modified. For example, this occurs in models with new neutrino self-interactions or an additional dark sector with interacting light particles. We consider several extensions of the standard cosmology that include a non-free-streaming radiation component as motivated by such particle physics models and use the final Planck data release to constrain them. This release contains significant improvements in the polarization likelihood which plays an important role in distinguishing free-streaming from interacting radiation species. Fixing the total amount of energy in radiation to match the expectation from standard neutrino decoupling we find that the fraction of free-streaming radiation must be $f_\mathrm{fs} > 0.8$ at 95% CL (combining temperature, polarization and baryon acoustic oscillation data). Allowing for arbitrary contributions of free-streaming and interacting radiation, the effective number of new non-free-streaming degrees of freedom is constrained to be $N_\mathrm{fld} < 0.6$ at 95% CL. Cosmologies with additional radiation are also known to ease the discrepancy between the local measurement and CMB inference of the current expansion rate $H_0$. We show that including a non-free-streaming radiation component allows for a larger amount of total energy density in radiation, leading to a mild improvement of the fit to cosmological data compared to previously discussed models with only a free-streaming component.

Interacting radiation after Planck and its implications for the Hubble Tension

TL;DR

This paper analyzes extensions of ΛCDM that include an extra non-free-streaming radiation component, parameterized by , , and the free-streaming fraction , using Planck 2018 data plus BAO and measurements. It shows that, with the total radiation fixed to the standard value , Planck polarization and TT data require , effectively ruling out significant self-interactions for neutrinos at recombination; when is allowed to vary, is constrained to be small ( at 95% CL) but a mild increase in total radiation can modestly improve the fit and help alleviate the tension. The authors connect these cosmological constraints to concrete particle-physics scenarios, notably non-Abelian dark radiation and late equilibration of a dark sector, showing that Planck data place strong bounds on such models (e.g., excluding large in equilibrium with the SM) while highlighting parameter regions where small non-free-streaming components could still be viable. Overall, the results favor predominantly free-streaming radiation and demonstrate that while non-free-streaming components can slightly ease the tension, they do so without compelling evidence and must satisfy tight particle-physics-inspired constraints.

Abstract

Standard cosmology predicts that prior to matter-radiation equality about 41% of the energy density was in free-streaming neutrinos. In many beyond Standard Model scenarios, however, the amount and free-streaming nature of this component is modified. For example, this occurs in models with new neutrino self-interactions or an additional dark sector with interacting light particles. We consider several extensions of the standard cosmology that include a non-free-streaming radiation component as motivated by such particle physics models and use the final Planck data release to constrain them. This release contains significant improvements in the polarization likelihood which plays an important role in distinguishing free-streaming from interacting radiation species. Fixing the total amount of energy in radiation to match the expectation from standard neutrino decoupling we find that the fraction of free-streaming radiation must be at 95% CL (combining temperature, polarization and baryon acoustic oscillation data). Allowing for arbitrary contributions of free-streaming and interacting radiation, the effective number of new non-free-streaming degrees of freedom is constrained to be at 95% CL. Cosmologies with additional radiation are also known to ease the discrepancy between the local measurement and CMB inference of the current expansion rate . We show that including a non-free-streaming radiation component allows for a larger amount of total energy density in radiation, leading to a mild improvement of the fit to cosmological data compared to previously discussed models with only a free-streaming component.

Paper Structure

This paper contains 20 sections, 30 equations, 12 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Models of Dark Radiation
  3. Non-Abelian Dark Radiation
  4. Late Equilibration of a Dark Sector
  5. Impact of Interacting Radiation
  6. Boltzmann Equations
  7. Impact on the CMB Power Spectrum
  8. Cosmological Constraints
  9. Testing the free-streaming hypothesis for neutrinos
  10. Models with varying Ntot
  11. Extra radiation and H0
  12. Interacting versus free-streaming radiation
  13. Implications for the Hubble and sigma8 Tensions
  14. Variation of primordial helium fraction Yp
  15. Particle Physics Interpretation
  16. ...and 5 more sections

Figures (12)

  • Figure 1: Marginalized posteriors of the fraction of energy in free-streaming radiation, $f_\mathrm{fs}$, in the model with fixed $N_\mathrm{tot}=3.046$ using only Planck data. The dashed black and solid red lines correspond to the results using Planck TT, and TT, TE, EE data sets, respectively. The solid points denote the 95.4% CL lower limit on $f_\mathrm{fs}$ for each data set taken from Tab. \ref{['tab:ntot_fixed_results']}.
  • Figure 2: Marginalized posterior of the total radiation degrees of freedom $N_\mathrm{tot}$ and the present value of the Hubble rate, $H_0$, in different models. In the left panel we combine Planck and BAO data, while in the right we add the distance ladder measurement of $H_0$Riess:2019cxk. In both panels the gray horizontal band represents this measurement and the black dot is the $\Lambda$CDM value with $2\sigma$ uncertainties. The darker inner (lighter outer) regions correspond to 68% (95%) confidence regions.
  • Figure 3: Marginalized posterior of the additional radiation degrees of freedom (either $\Delta N_\mathrm{tot}= N_\mathrm{eff} - 3.046$, or $\Delta N_\mathrm{tot} = N_\mathrm{fld}$ with $N_\mathrm{eff} = 3.046$) and the angular scale of the sound horizon $\theta_s$ as derived from the Planck + BAO data sets. Free-streaming ($N_\mathrm{eff}$) and non-free-streaming ($N_\mathrm{fld}$) radiation exhibit different correlation with $\theta_s$ due to their opposite effects on the phase shift of acoustic peaks in the CMB. Supersonic propagation of free-streaming radiation perturbations shifts acoustic peaks to larger angular scales; in order to keep the physical peak locations the same $\theta_s$ must be decreased. Conversely, non-free-streaming radiation reduces this phaseshift, requiring $\theta_s$ to increase to keep peak location the same. The darker inner (lighter outer) regions correspond to 68% (95%) confidence regions.
  • Figure 4: Marginalized posterior for the model with free-streaming and non-free-streaming species for different combinations of cosmological data. In the left panel the posterior is shown as a function of the total radiation degrees of freedom $N_\mathrm{tot}$ and their free-streaming fraction $f_\mathrm{fs}$, while the right panel instead uses the number of free-streaming and non-free-streaming relativistic degrees of freedom, $N_\mathrm{eff}$ and $N_\mathrm{fld}$, respectively. In all cases, the darker inner (lighter outer) regions correspond to 68% (95%) confidence regions.
  • Figure 5: Marginalized posteriors of the fraction of energy in free-streaming radiation $f_\mathrm{fs}$ (left panel) and the number of non-free-streaming degrees of freedom $N_\mathrm{fld}$ (right panel) in models with fixed and varying $N_\mathrm{tot}$ (solid, and dashed or dotted lines, respectively) for the Planck TT, TE, EE + BAO data set. The solid dots denote the 95.4% CL lower (upper) limit on $f_\mathrm{fs}$ ($N_\mathrm{fld}$) in the left (right) panel. These limits happen to coincide for the $(N_\mathrm{tot}=3.046,f_\mathrm{fs})$ and $(N_\mathrm{tot}, f_\mathrm{fs})$ models -- see Tabs. \ref{['tab:ntot_fixed_results']} and \ref{['tab:ntot_planck_bao']}.
  • ...and 7 more figures