From Non-Thermal to Thermal: Cosmological Imprints of Self-Interacting Secluded Dark Matter

arXiv:2610.21817 · hep-ph, astro-ph.CO, gr-qc · Submitted 2026-10-15 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: We're looking at the paper: "From Non-Thermal to Thermal".

Jocelyn: The gist Dark matter (DM), secluded from the Standard Model (SM), can attain internal thermalization through self-interactions, and this process has cosmological implications for its mass constraints.

Vera: First, who's behind it and why it matters.

Paper summary: Vera: We're looking at the paper "From Non-Thermal to Thermal: Cosmological Imprints of Self-Interacting Secluded Dark Matter" again, focusing on how dark matter thermalizes through self-interactions #pg4. The core idea is taking dark matter that starts out non-thermal and seeing what happens when it gets these self-interactions #pg3.

Jocelyn: The authors investigate a real scalar dark matter field with a quartic self-coupling #pg4, and they set up this thermalization process by solving the Boltzmann equation for the momentum distribution function in presence of two to two DM elastic self-scatterings #pg4.

Subrahmanyan: The big takeaway is that the resulting thermalized dark sector has a temperature and a chemical potential determined by the inflaton mass and reheat temperature #pg4. They also find that if the inflaton mass is greater than or smaller than its reheat temperature, this dark matter temperature can be higher or lower than the standard model temperature during Big Bang Nucleosynthesis without breaking any of our cosmological constraints #pg4.

Vera: That effect isn't just about the temperature; it’s tied to how they calculate the chemical potential and how that relates to the production history #pg3. The paper says that in a high reheat scenario with TR equal to five times ten to the sixth GeV, the dark matter chemical potential is always positive #pg4.

Jocelyn: And for a low reheat scenario with TR equal to five MeV, it takes a negative value in the relativistic regime #pg3. This correlation between temperature and chemical potential is driven by how the total dark matter number is fixed at production #pg3.

Subrahmanyan: But when you look at the constraints from BBN and CMB radiation, they find those limits on dark matter mass are actually independent of how strong these self-interactions are #pg4. This independence holds true for the basic bounds because the initial temperature is set by the inflaton mass and reheat temperature rather than by all those collision details #pg3.

Vera: That's what makes it interesting, because that independence breaks down when you look at the co-moving free-streaming length #pg4. The effect of elastic scatterings becomes apparent there, weakening that lower bound on the dark matter mass by about forty percent #pg4.

Conclusion: Jocelyn: So we've been looking at "From Non-Thermal to Thermal: Cosmological Imprints of Self-Interacting Secluded Dark Matter" and how it shows that the post-inflationary history and how those dark matter particles interact are what really decide what we can constrain about this secluded dark sector with a nonzero chemical potential #pg3.

Vera: The authors looked at a real scalar DM field with a quartic self-coupling, setting up this thermalization process by solving the Boltzmann equation for the momentum distribution function in presence of two to two DM elastic self-scatterings #pg4. They found that the resulting thermalized dark sector has a temperature and a chemical potential determined by the inflaton mass and reheat temperature #pg4.

Subrahmanyan: The paper shows that depending on whether the inflaton mass is bigger or smaller than its reheat temperature, this dark matter temperature can be higher or lower than the standard model temperature during Big Bang Nucleosynthesis without breaking any of our cosmological constraints #pg4. But that effect isn't just about the temperature; it’s tied to how they calculate the chemical potential and how that relates to the production history #pg3.

Jocelyn: And when you look at the constraints, they find that for BBN and CMB radiation, those limits on dark matter mass are actually independent of how strong these self-interactions are #pg4. That independence holds true for the basic bounds because the initial temperature is set by the inflaton mass and reheat temperature rather than by all those collision details #pg3.

Vera: But that's where things get interesting, because that independence breaks down when you look at the co-moving free-streaming length #pg4. The effect of elastic scatterings becomes apparent there, weakening that lower bound on the dark matter mass by about forty percent #pg4.

Subrahmanyan: So to summarize this paper, we're looking at how self-interactions shift the thermalized constraints on dark matter mass from BBN and CMB observations #pg4. We need to keep looking at these constraints because understanding how this thermalization happens is crucial for designing experiments that look for these kinds of exotic dark matter properties in the future #pg3.

Koushik Dutta, Deep Ghosh, Ahamadullah Khana

Department of Physical Sciences, Indian Institute of Science Education and Research · Theory Division, Saha Institute of Nuclear Physics

hep-ph, astro-ph.CO, gr-qc

Submitted: 2026-10-15

Updated: 2026-10-15

Comments: 35 pages, 7 figures

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 82/100

The gist: The gist Dark matter (DM), secluded from the Standard Model (SM), can attain internal thermalization through self-interactions, and this process has cosmological implications for its mass constraints.

Key concepts

Thermalization via Self-Interactions: This process describes how dark matter particles, initially produced non-thermally from an inflaton decay, reach a state where their momentum distribution is thermalized through elastic collisions between the DM particles themselves. This self-interaction is crucial because it changes the DM's final temperature and chemical potential, which in turn affects cosmological constraints.
Chemical Potential ($\mu$): The chemical potential is a measure related to the net number of particles in a system, even when the total number of particles is fixed. In this study, it becomes correlated with the DM temperature and mass, depending on whether the reheat temperature is high or low, influencing how constraints are calculated.
Co-moving Free-Streaming Length: This length describes how far dark matter particles can travel freely in space before being affected by gravitational structure formation. Self-interactions suppress this length compared to a non-thermal scenario without collisions, which is important for determining the minimum allowed mass of the dark matter particle.
Reheat Temperature ($T_R$): The reheat temperature is the temperature of the universe immediately after inflation ends, which sets an initial condition for DM production. The final thermal state and resulting cosmological constraints on DM mass are directly determined by this value, showing different results for high ($5 imes 10^6$ GeV) versus low ($5$ MeV) scenarios.

Summary

The gist Dark matter (DM), secluded from the Standard Model (SM), can attain internal thermalization through self-interactions, and this process has cosmological implications for its mass constraints.

Scalar dark matter production and its thermalization

The study investigates a real scalar DM field with a quartic self-coupling, initially produced from the perturbative decay of the coherently oscillating inflaton field during reheating The initial phase-space distribution is non-thermal, peaked at half the inflaton mass for a two-body decay Thermalization is studied by solving the Boltzmann equation in presence of 2 → 2 DM elastic self-scatterings The thermalized dark sector is characterized by a temperature and a nonzero chemical potential, determined by the inflaton mass and the reheat temperature

Evolution of DM temperature and chemical potential

The initial DM temperature for sufficiently large quartic self-coupling is set by the inflaton mass, i.e., T iDM = mϕ/6 The ratio of DM temperature to the SM one is completely determined by mϕ and TR The DM chemical potential becomes correlated with the DM temperature and the DM mass since the total DM number is fixed at the production For a high reheat scenario with TR = 5 × 10 6 GeV, the DM chemical potential is always positive, whereas for a low reheat scenario with TR = 5 MeV, it takes negative value in the relativistic regime

Cosmological constraints

The lower limits on the DM mass from BBN and CMB radiation turn out to be independent of self-interaction strength because the DM temperature is set by the inflaton mass and reheat temperature The effect of elastic scattering, in turn, becomes apparent in the DM co-moving free-streaming length, which weakens the lower bound on the DM mass by approximately 40% due to elastic scatterings In our scenario, for high reheat scenario, mχ ≥ 10-12 GeV and for low reheat scenario, mχ ≥ 10-3 GeV

Conclusion and future outlook

The lower limits on the DM mass from BBN and CMB are independent of self-interaction strength because the DM temperature is set by the initial condition rather than by the details of thermalization The effect of collisions becomes apparent only in the co-moving free-streaming length, where elastic scatterings weaken the lower bound on the DM mass by about 40% and introduce an explicit dependence on the self-interaction strength We obtain lower limits on the thermal DM mass of 2.2 × 10-10 GeV and 0.47 GeV for TR = 5 × 10 6 GeV and 5 MeV respectively, with mϕ = 103 GeV The post-inflationary history and the poorly constrained DM self-interaction are the deciding factors in constraining secluded DM with a non-zero chemical potential

Details of the Boltzmann Equation

The Boltzmann equation in terms of the scaled comoving momentum becomes xH˜ (x) d/dx fχ(x, ξ1) = C[fχ] The collision term of Eq. A.37 shows that C[nχ] = 0 for elastic scattering of identical particles The energy density is only diluted by the expansion, leading to dρ chi/dt + 4Hρ chi = 0 in the relativistic regime

Decoupling time for calculating free-streaming length

The decoupling time of elastic scatterings is obtained by comparing the self-interaction rate, Γint ∼ nχλ 2 χ/E 2 χ as in Eq. 2.14 with the Hubble rate, i.e., H ∼ T 2 SM ∝ a-2 The lower limit of the free-streaming integral is thus set by the condition Γint(adec) = H(adec)

Cosmological constraints on self-interacting secluded DM

The lower bound on the DM mass from BBN (blue solid line) and CMB (green dashed line) observations have been shown to be independent of thermalization process as long as DM particles are participating in only elastic scatterings The observational difference between thermal and nonthermal distribution may be seen in matter power spectrum, which requires a dedicated study in cosmological perturbation theory The lower limit on the DM mass from BBN is approximately 10-12 GeV for high reheat scenario and 10-3 GeV for low reheat scenario The lower limit on the DM mass from the CMB is approximately 9 orders of magnitude stronger than that of the BBN, shown in Eq.3.9 The lower bound on the DM mass from BBN is independent of self-interaction strength, since the DM temperature is set by the initial condition rather than by thermalization The effect of collisions becomes apparent only in the co-moving free-streaming length, where elastic scatterings weaken the lower bound on the DM mass by about 40% and introduce an explicit dependence on the self-interaction strength

Bullet Cluster constraints

The lower limit on the DM mass from the Bullet cluster bound is shown by red dot-dashed line The Bullet cluster bound becomes stronger for λ 2 χ ≥ 10-15 than the CMB bound The observational difference between thermal and nonthermal distribution may be seen in matter power spectrum, which requires a dedicated study in cosmological perturbation theory

Summary of findings

The lower limits on the DM mass from BBN and CMB, ∼ 10-12 GeV and ∼ 10-3 GeV for TR = 5 × 10 6 GeV and 5 MeV respectively, are independent of the self-interaction strength The CMB bound turns out to be about 32% stronger than the BBN one, in contrast to the canonical thermal DM case, where BBN yields the stronger bound The effect of collisions becomes apparent only in the co-moving free-streaming length, where elastic scatterings weaken the lower bound on the DM mass by about 40% and introduce an explicit dependence on the self-interaction strength We obtain lower limits on the thermal DM mass of 2.2 × 10-10 GeV and 0.47 GeV for TR = 5 × 10 6 GeV and 5 MeV respectively, with mϕ = 103 GeV The post-inflationary history and the poorly constrained DM self-interaction are the deciding factors in constraining secluded DM with a non-zero chemical potential

Acknowledgement

DG acknowledges the Post-doctoral Fellowship from SINP Kolkata. AK acknowledges the Senior Research Fellowship (SRF) awarded by the University Grants Commission (UGC), Government of India

The paper is 2610.21817. Every sentence must end with a reference token. The initial DM temperature for sufficiently large quartic self-coupling is set by the inflaton mass, i.e., T iDM = mϕ/6 The ratio of DM temperature to the SM one is completely determined by mϕ and TR The DM chemical potential becomes correlated with the DM temperature and the DM mass since the total DM number is fixed at the production For a high reheat scenario with TR = 5 × 10 6 GeV, the DM chemical potential is always positive, whereas for a low reheat scenario with TR = 5 MeV, it takes negative value in the relativistic regime The lower limits on the DM mass from BBN and CMB radiation turn out to be independent of self-interaction strength because the DM temperature is set by the inflaton mass and reheat temperature The effect of elastic scattering, in turn, becomes apparent in the DM co-moving free-streaming length, which weakens the lower bound on the DM mass by approximately 40% due to elastic scatterings In our scenario, for high reheat scenario, mχ ≥ 10-12 GeV and for low reheat scenario, mχ ≥ 10-3 GeV The lower limit on the DM mass from BBN is independent of self-interaction strength since the DM temperature is set by the initial condition rather than by thermalization The CMB bound turns out to be about 32% stronger than the BBN one, in contrast to the canonical thermal DM case, where BBN yields the stronger bound We obtain lower limits on the thermal DM mass of 2.2 × 10-10 GeV and 0.

Improvements for AI systems

Improved AI can perform detailed numerical simulations of dark matter momentum distribution functions by solving Eq. A.35, allowing for a direct assessment of thermalization history based on specific parameter choices for quartic self-coupling and inflaton mass (e.g., In Fig.1, we show the DM momentum distribution functions in three different epochs).
The improved system can accurately determine the effective DM temperature and chemical potential by solving the evolution of these quantities using analytical expressions like Eq. 2.11 and 2.12, ensuring that constraints on BBN and CMB are correctly applied to the energy density of additional relativistic species during BBN.
The AI system can calculate the co-moving free-streaming length in both thermal (collisional) and non-thermal (collisionless) cases by comparing the self-interaction rate to the Hubble rate, as detailed in Eq. 2.15, which is crucial for distinguishing between scenarios where the lower limit on the DM mass originates from the free-streaming length.
The system can map out a multi-dimensional parameter space for secluded DM by analyzing Figure 4, identifying regions where DM particles never thermalize and regions that are allowed from cosmologically observations, providing a comprehensive view of allowed physics beyond canonical scenarios.
The AI can quantify the impact of self-interaction on cosmological bounds by calculating how the lower limit on DM mass is modified, noting that the effect of elastic scattering, in turn the history of thermalization becomes apparent in the DM co-moving free-streaming length, weakening it by about 40%.

Abstract

Dark matter (DM), secluded from the Standard Model (SM), can attain internal thermalization through self-interactions. We investigate the thermalization of a real scalar DM field with a quartic self-coupling, initially produced from the perturbative decay of the coherently oscillating inflaton field during reheating. The thermalization process has been studied numerically by solving Boltzmann equation of the DM momentum distribution function in presence of 2 to2 DM elastic self-scatterings. In the absence of number-changing processes, the thermalized dark sector is characterized by a temperature and a nonzero chemical potential, determined by the inflaton mass and the reheat temperature. We find that if the inflaton mass is greater (smaller) than the reheat temperature, the DM temperature can be greater (smaller) than the SM temperature during Big Bang Nucleosynthesis, without violating any cosmological constraints. This is realized with a negative (positive) chemical potential for the DM temperature greater (smaller) than the SM one. Depending on DM production history, we can achieve the lower limit on the DM mass much below than in warm DM scenarios. The thermalization via self-scatterings tends to suppress the DM co-moving free-streaming length, compared to the non-thermal scenario without any collisions. Consequently, the lower limit on the DM mass weakens approximately by 40% for a suitable choice of quartic self-coupling than in the non-thermal scenario. We obtain the lower limits on the thermal DM mass to be 2.2 times10-10 GeV and 0.47 GeV for reheat temperatures, 5 times 10 6 GeV and 5 MeV respectively, while the inflaton mass is set at 10 cubed GeV.