Hot NEDE: Thermal Triggered Early Dark Energy

• Hot NEDE is a thermal-driven form of New Early Dark Energy where a dark-sector first-order phase transition injects energy to reduce the sound horizon.
• It utilizes finite-temperature corrections from a dark radiation or gauge sector to produce either a transient fluid or strongly interacting dark radiation post-transition.
• The model unifies early-Universe cosmology with neutrino mass generation and dark-matter interactions, offering new insights into the Hubble tension and CMB perturbations.

Hot New Early Dark Energy (Hot NEDE) is a thermally triggered realization of New Early Dark Energy in which a dark-sector first-order phase transition injects energy between Big Bang Nucleosynthesis and recombination, thereby reducing the sound horizon and permitting a larger CMB-inferred value of $H_0$. In contrast to baseline NEDE, where the transition is triggered at zero temperature by a subdominant ultralight field, Hot NEDE uses finite-temperature corrections from a dark radiation bath or dark gauge sector; in explicit constructions it can produce either a transient NEDE fluid with $w_{\rm NEDE}^*\in[1/3,1]$ or a post-BBN bath of strongly interacting dark radiation, and it has been developed together with inverse-seesaw neutrino-mass generation, dark-radiation phenomenology, and interacting dark-matter extensions (Niedermann et al., 2021, Garny et al., 2024).

1. Origin within the NEDE program

New Early Dark Energy was introduced as a first-order phase transition in a dark sector shortly before recombination, with the false vacuum decay modeled as a sudden transition from a cosmological constant source to a decaying fluid with constant equation of state (Niedermann et al., 2019). In that formulation, the false vacuum energy briefly increases $H(z)$, shrinks the comoving sound horizon $r_s$, and raises the inferred Hubble constant while preserving the measured angular acoustic scale.

Hot NEDE retains the first-order phase transition but changes the trigger. Instead of the zero-temperature two-field trigger of baseline or “Cold” NEDE, it relies on thermal corrections that subside as a subdominant radiation fluid in a dark gauge sector cools (Niedermann et al., 2021). The same paper identifies the strong supercooled regime as the scenario favored by phenomenology and emphasizes that the thermal trigger removes the need for an ultralight trigger scalar.

At the phenomenological level, CMB analyses often treat Hot NEDE as a special case of the broader NEDE effective fluid. In that parameterization the post-transition equation of state is varied over $1/3 \le w_{\rm NEDE} \le 1$, with the relativistic “hot” limit corresponding to $w_{\rm NEDE}=1/3$ and $c_s^2=w_{\rm NEDE}$ (Poulin et al., 2021). This makes Hot NEDE both a specific microphysical proposal and, in data analyses, a limiting case of the wider NEDE fluid family.

2. Thermal trigger and dark-sector microphysics

The thermal trigger is most transparently expressed through finite-temperature effective potentials. In the representative Hot NEDE setup of 2021, a complex scalar $\Psi$ with $\psi \equiv \sqrt{2}|\Psi|$ is coupled to a dark gauge sector, and the ring-improved one-loop effective potential takes the schematic form

$$V(\psi; T_D)=D(T_D^2-T_0^2)\psi^2-E T_D\psi^3+\frac{\lambda}{4}\psi^4+V_0(T_D),$$

with $w_{\rm NEDE}^*\in[1/3,1]$0, $w_{\rm NEDE}^*\in[1/3,1]$1, and

$w_{\rm NEDE}^*\in[1/3,1]$2

The regime $w_{\rm NEDE}^*\in[1/3,1]$3 is the large-mass/low-temperature, strongly supercooled regime, in which the false vacuum dominates over the dark radiation background and the transition is very fast, with $w_{\rm NEDE}^*\in[1/3,1]$4 (Niedermann et al., 2021).

A more explicit realization was later given in a dark sector with $w_{\rm NEDE}^*\in[1/3,1]$5 gauge symmetry, $w_{\rm NEDE}^*\in[1/3,1]$6, and one complex scalar $w_{\rm NEDE}^*\in[1/3,1]$7 in the fundamental representation acting as a dark Higgs. After the phase transition the symmetry breaks as $w_{\rm NEDE}^*\in[1/3,1]$8, yielding massless $w_{\rm NEDE}^*\in[1/3,1]$9 gauge bosons that constitute strongly interacting dark radiation and massive gauge bosons associated with the broken generators (Garny et al., 2024). The zero-temperature tree-level scalar potential is

$H(z)$0

while the finite-temperature one-loop effective potential is written as

$H(z)$1

In the high-temperature limit,

$H(z)$2

and the barrier disappears at

$H(z)$3

In the supercooled regime $H(z)$4, the transition occurs shortly before $H(z)$5, with $H(z)$6 (Garny et al., 2024).

The latent heat released at the transition is

$H(z)$7

and the transition is fast relative to Hubble, with

$H(z)$8

The same construction argues that the non-thermal scalar condensate decays efficiently into massless dark gauge bosons for $H(z)$9, while non-Abelian self-interactions ensure ultra-fast thermalization of the post-transition dark plasma (Garny et al., 2024). This microphysics is the basis for the “hot” character of Hot NEDE: the decay products are thermal and relativistic.

3. Background evolution, perturbations, and the sound horizon

At the effective-fluid level, Hot NEDE inherits the NEDE background parameterization. Before the transition the component behaves like vacuum energy, $r_s$0, and after the transition it becomes a decaying fluid with $r_s$1 (Niedermann et al., 2019). The fractional energy density at the transition is denoted $r_s$2, and the reduction of the sound horizon follows from the standard relation

$r_s$3

A localized increase in $r_s$4 before recombination reduces $r_s$5, so fits to the observed acoustic scale require a larger $r_s$6.

The perturbations are fixed by matching across the transition surface. In the thermal version the trigger variable is the dark-sector temperature, so spatial variations in the transition time obey $r_s$7, and the matching conditions give

$r_s$8

followed by the standard synchronous-gauge fluid evolution with $r_s$9 (Niedermann et al., 2023). This differs from baseline NEDE, where the transition surface is tied to the trigger-field fluctuation $1/3 \le w_{\rm NEDE} \le 1$0.

Two rather different timing regimes appear in the literature. In the original NEDE-like phenomenology the transition sits near matter–radiation equality, typically $1/3 \le w_{\rm NEDE} \le 1$1–$1/3 \le w_{\rm NEDE} \le 1$2, and the released energy is modeled as a transient fluid (Niedermann et al., 2021). In the later supercooled $1/3 \le w_{\rm NEDE} \le 1$3 completion, the phase transition occurs after BBN but before recombination, broadly within $1/3 \le w_{\rm NEDE} \le 1$4, and reheats the dark sector into strongly interacting dark radiation; the analysis finds the lower bound $1/3 \le w_{\rm NEDE} \le 1$5 at $1/3 \le w_{\rm NEDE} \le 1$6 C.L. (Garny et al., 2024). The latter model realizes a two-step evolution in the effective number of relativistic degrees of freedom,

$1/3 \le w_{\rm NEDE} \le 1$7

with a benchmark $1/3 \le w_{\rm NEDE} \le 1$8, $1/3 \le w_{\rm NEDE} \le 1$9, and $w_{\rm NEDE}=1/3$0 for $w_{\rm NEDE}=1/3$1, $w_{\rm NEDE}=1/3$2, and $w_{\rm NEDE}=1/3$3 (Garny et al., 2024). This post-BBN injection is central to the Hot NEDE claim of reconciling early-time sound-horizon reduction with BBN consistency.

4. Dark radiation, anisotropic stress, and comparison to related early-time models

A defining issue for Hot NEDE is the nature of its hot decay products. In the 2024 $w_{\rm NEDE}=1/3$4 completion, the post-transition radiation is strongly interacting dark radiation (SIDR): the remaining massless $w_{\rm NEDE}=1/3$5 gauge bosons self-interact efficiently, so the dark radiation is tightly coupled and has vanishing shear to a good approximation (Garny et al., 2024). In Boltzmann treatments this is implemented as a fluid with $w_{\rm NEDE}=1/3$6 and zero shear. This distinguishes it from free-streaming dark radiation, which produces different phase shifts and damping-tail signatures.

The literature also uses Hot NEDE as a comparison point in perturbation-sector studies. A phenomenological analysis of Early Dark Energy microphysics notes that Hot NEDE can be viewed as a phase transition that injects energy into a transient EDE condensate and a “hot” relativistic component with significant free-streaming anisotropic stress, effectively a $w_{\rm NEDE}=1/3$7-like piece (Sabla et al., 2022). That same work shows that anisotropic-sound-speed EDE can mimic some of Hot NEDE’s perturbative signatures—peak-shape modulation, phase shifts, and lensing impacts—without adding a true dark-radiation background. The background difference is explicit: the anisotropic-fluid model redshifts as $w_{\rm NEDE}=1/3$8 after activation, not $w_{\rm NEDE}=1/3$9, so there is no lasting $c_s^2=w_{\rm NEDE}$0 shift and no associated BBN or damping-tail constraints (Sabla et al., 2022).

This comparison clarifies a common misconception. Hot NEDE is not equivalent to “just extra radiation.” In explicit realizations it combines a sharply timed first-order phase transition, latent-heat release after BBN, and nontrivial perturbation physics whose detailed signatures depend on whether the hot component is free-streaming or strongly interacting. The strongly interacting case alters the usual relation between extra radiation and CMB anisotropic stress, which is precisely why Hot NEDE is discussed alongside SIDR and stepped-dark-radiation scenarios (Garny et al., 2024).

5. Neutrino masses, ultraviolet embeddings, and interacting dark matter

Hot NEDE has been used as a bridge between early-Universe cosmology and inverse-seesaw neutrino mass generation. In one formulation, a Yukawa coupling between the NEDE field $c_s^2=w_{\rm NEDE}$1 and a sterile fermion generates a sterile Majorana mass when $c_s^2=w_{\rm NEDE}$2 acquires a vacuum expectation value,

$c_s^2=w_{\rm NEDE}$3

and the one-generation inverse-seesaw mass matrix is

$c_s^2=w_{\rm NEDE}$4

(Niedermann et al., 2023). A related analysis argues that the Hot NEDE framework strengthens cosmological bounds on the heaviest neutrino mass and predicts a constrained dark-sector temperature window,

$c_s^2=w_{\rm NEDE}$5

together with an upper bound on the heaviest active mass eigenstate of approximately $c_s^2=w_{\rm NEDE}$6 in the relevant parameter range (Niedermann et al., 2021).

The inverse-seesaw connection was then extended to two correlated phase transitions. An eV-scale infrared transition generates the small sterile Majorana mass $c_s^2=w_{\rm NEDE}$7 and provides the Hot NEDE energy injection, while a ultraviolet transition at MeV–TeV scales generates the heavy Dirac mass entry $c_s^2=w_{\rm NEDE}$8 through a dark Higgs $c_s^2=w_{\rm NEDE}$9 (Cruz et al., 2023). In that framework, the UV transition can occur at the GeV scale and source a stochastic gravitational-wave background in the nHz band. The paper quotes the NANOGrav-preferred window

$\Psi$0

and emphasizes that Hot NEDE’s supercooled regime naturally supports large $\Psi$1 and bubble-runaway dynamics (Cruz et al., 2023).

A further extension adds a fermion multiplet charged under the dark $\Psi$2 gauge symmetry and thereby produces a naturally stable dark-matter component. In this 2025 construction, spontaneous symmetry breaking induces a loop-level mass splitting

$\Psi$3

so the charged component that couples to dark radiation becomes Boltzmann suppressed when $\Psi$4, leading to dark-radiation matter decoupling (DRMD) near matter–radiation equality (Garny et al., 5 Aug 2025). The mechanism is designed to preserve the Hot NEDE reduction of $\Psi$5 while altering potential evolution and small-scale growth through time-dependent DM–DR drag.

6. Observational status, forecasts, and open issues

The observational status of Hot NEDE depends on which realization is tested. In the supercooled $\Psi$6 model fitted to Planck+BAO+Pantheon+BBN, Hot NEDE prefers $\Psi$7 when including SH0ES and yields $\Psi$8; without SH0ES it gives $\Psi$9, reducing the DMAP tension to $\psi \equiv \sqrt{2}|\Psi|$0 (Garny et al., 2024). The same model predicts dark acoustic oscillations in the matter power spectrum at

$\psi \equiv \sqrt{2}|\Psi|$1

making the range $\psi \equiv \sqrt{2}|\Psi|$2 relevant for Lyman-$\psi \equiv \sqrt{2}|\Psi|$3 forest searches.

Phenomenological CMB analyses are less favorable when full Planck high-$\psi \equiv \sqrt{2}|\Psi|$4 information is included. A Planck-free analysis based on WMAP+ACT+BAO+Pantheon finds non-zero NEDE and $\psi \equiv \sqrt{2}|\Psi|$5–$\psi \equiv \sqrt{2}|\Psi|$6 without late-time priors, and the parameter space explicitly includes the hot limit $\psi \equiv \sqrt{2}|\Psi|$7 (Poulin et al., 2021). However, Planck+ACT constrains NEDE more strongly than axion-like EDE, tightening $\psi \equiv \sqrt{2}|\Psi|$8 to $\psi \equiv \sqrt{2}|\Psi|$9–$$V(\psi; T_D)=D(T_D^2-T_0^2)\psi^2-E T_D\psi^3+\frac{\lambda}{4}\psi^4+V_0(T_D),$$0 at $$V(\psi; T_D)=D(T_D^2-T_0^2)\psi^2-E T_D\psi^3+\frac{\lambda}{4}\psi^4+V_0(T_D),$$1 C.L. and leaving a residual $$V(\psi; T_D)=D(T_D^2-T_0^2)\psi^2-E T_D\psi^3+\frac{\lambda}{4}\psi^4+V_0(T_D),$$2 tension with SH0ES. High-$$V(\psi; T_D)=D(T_D^2-T_0^2)\psi^2-E T_D\psi^3+\frac{\lambda}{4}\psi^4+V_0(T_D),$$3 TT and TEEE data provide the main leverage, indicating that perturbative structure, not only background evolution, is decisive.

The DRMD extension yields a different observational profile. Using Planck 2018, DESI DR2 BAO, and Pantheon+, it gives $$V(\psi; T_D)=D(T_D^2-T_0^2)\psi^2-E T_D\psi^3+\frac{\lambda}{4}\psi^4+V_0(T_D),$$4 without SH0ES and $$V(\psi; T_D)=D(T_D^2-T_0^2)\psi^2-E T_D\psi^3+\frac{\lambda}{4}\psi^4+V_0(T_D),$$5 with SH0ES, while reducing the DMAP tension to $$V(\psi; T_D)=D(T_D^2-T_0^2)\psi^2-E T_D\psi^3+\frac{\lambda}{4}\psi^4+V_0(T_D),$$6; the corresponding fit prefers $$V(\psi; T_D)=D(T_D^2-T_0^2)\psi^2-E T_D\psi^3+\frac{\lambda}{4}\psi^4+V_0(T_D),$$7, $$V(\psi; T_D)=D(T_D^2-T_0^2)\psi^2-E T_D\psi^3+\frac{\lambda}{4}\psi^4+V_0(T_D),$$8 at $$V(\psi; T_D)=D(T_D^2-T_0^2)\psi^2-E T_D\psi^3+\frac{\lambda}{4}\psi^4+V_0(T_D),$$9 C.L., and $w_{\rm NEDE}^*\in[1/3,1]$00 (Garny et al., 5 Aug 2025). This suggests that Hot NEDE combined with interacting dark matter is capable of improving the fit beyond a pure SIDR step in $w_{\rm NEDE}^*\in[1/3,1]$01.

Several open issues remain explicit in the literature. A full Boltzmann-code implementation of the original thermal-trigger Hot NEDE perturbations was left for future work in the foundational 2021 treatment (Niedermann et al., 2021). Later synthesis papers similarly note that the full Hot NEDE likelihood is still outstanding and that detailed source modeling—bubble dynamics, sound speed, viscosity, and the precise fate of the condensate—remains to be computed (Niedermann et al., 2023). Future tests are correspondingly well defined: CMB-S4 can sharpen constraints on $w_{\rm NEDE}^*\in[1/3,1]$02, high-$w_{\rm NEDE}^*\in[1/3,1]$03 signatures, and the SIDR versus free-streaming character of the hot component; DESI Lyman-$w_{\rm NEDE}^*\in[1/3,1]$04 forest data can search for dark acoustic oscillations; and pulsar timing arrays can probe gravitational waves from associated supercooled phase transitions (Garny et al., 2024, Cruz et al., 2023).

Hot NEDE therefore occupies a distinctive place in the early-Universe model space. It is simultaneously a thermal generalization of NEDE, a post-BBN mechanism for stepped dark radiation, a laboratory for anisotropic-stress effects in the CMB, and, in several ultraviolet completions, a candidate unification of early dark energy, neutrino mass generation, and dark-sector self-interactions.