New Light Species and the CMB

TL;DR

This work addresses how new light or massless particles alter the Cosmic Microwave Background through changes in the relativistic energy density, encoded in $g_*$ and $N_{eff}$. It develops a precise, EFT-based map from model parameters to $ riangle g_*$ by numerically solving coupled Boltzmann and Friedmann equations, accounting for decoupling, entropy redistribution, and non-equilibrium effects after the QCD phase transition. By surveying natural, minimal models across spins 0, 1/2, 1, 3/2, and 2, the authors quantify each scenario’s impact on $g_*$ and compare with Planck constraints to carve out viable regions of parameter space. The results show Planck’s power to constrain or exclude several classes (e.g., Goldstones, certain four-fermion and millicharged scenarios) while many models with masses near the eV scale require mass-aware analyses; future CMB polarization measurements could tighten these limits and even illuminate details of the QCD transition. Overall, the paper provides a rigorous framework for linking beyond-Standard-Model light species to observable CMB signatures and demonstrates how current and upcoming data can guide model-building in the early universe.

Abstract

We consider the effects of new light species on the Cosmic Microwave Background. In the massless limit, these effects can be parameterized in terms of a single number, the relativistic degrees of freedom. We perform a thorough survey of natural, minimal models containing new light species and numerically calculate the precise contribution of each of these models to this number in the framework of effective field theory. After reviewing the relevant details of early universe thermodynamics, we provide a map between the parameters of any particular theory and the predicted effective number of degrees of freedom. We then use this map to interpret the recent results from the Cosmic Microwave Background survey done by the Planck satellite. Using this data, we present new constraints on the parameter space of several models containing new light species. Future measurements of the Cosmic Microwave Background can be used with this map to further constrain the parameter space of all such models.

Figures (10)

• Figure 1: Projected CMB anisotropy power spectrum for three different values of $g_*$ (or equivalently $N_{eff}$). The addition of new light degrees of freedom increases the height of the first peak through the early ISW effect and decreases the height of later peaks through Silk damping. The power spectrum, and therefore these effects, are measured by multiple observational experiments, such as the Planck satellite. These spectra were calculated using CAMB LewisEtAlHowlettEtAl. The magenta, blue, and orange curves (dark gray, black, and light gray curves, when viewed in black and white) correspond to an $N_{eff}$ of 3, 4, and 5, respectively.
• Figure 2: Additional light degrees of freedom $\Delta g_*$ at recombination for a new light species as a function of the decoupling temperature (in the instantaneous decoupling approximation), calculated using eq. (\ref{['eq:deltagstar']}). The contribution of various particle species is shown, specifically a real scalar boson (magenta), a Weyl fermion (blue), a real gauge boson (orange), and a Dirac fermion pair (green). The dashed line indicates the current sensitivity of the Planck observational experiment Planck. The gray region corresponds to the QCD phase transition, where the precise evolution of $g_*(T)$ for the SM is not well-understood. The provided values of $\Delta g_*$ should therefore only be interpreted qualitatively in that region.
• Figure 3: Effective degees of freedom $g_*$ in the SM as a function of temperature. The gray region corresponds to the QCD phase transition, where the precise evolution of $g_*(T)$ is not well-understood. The provided values of $g_*$ should therefore only be interpreted qualitatively in that region.
• Figure 4: Dominant interaction process for the Goldstone-lepton coupling.
• Figure 5: $\Delta g_*$ due to a single Goldstone boson which interacts with only pions. The contribution to $g_*$ at recombination is given as a function of the effective scale $\Lambda$, which suppresses this interaction. The gray region for $\Lambda \gtrsim 5 \times 10^6$ GeV corresponds to models which decouple during the QCD phase transition. The provided values of $\Delta g_*$ should therefore only be interpreted qualitatively in that region. Supernova and star cooling constraints on this scenario limit $\Lambda \gtrsim 10^9$ GeV, and so this plot demonstrates that the Goldstone must have decoupled during or before the QCD phase transition.