Early Dark Energy (EDE): Cosmological Implications

• EDE is a transient early-universe energy component that temporarily increases expansion rates and decreases the comoving sound horizon before recombination.
• Models employ scalar fields, effective fluid descriptions, or phase transitions to address the Hubble tension, each offering distinct microphysical insights.
• Upcoming CMB and 21-cm cosmology observations aim to decisively test EDE’s microphysics, helping to resolve discrepancies in current H0 and S8 measurements.

Early Dark Energy (EDE) refers to a cosmological component that contributes a non-negligible fraction of the total energy density at early times—typically just prior to recombination near matter–radiation equality—then rapidly dilutes and becomes insignificant before the epoch of structure formation and cosmic acceleration. The principal motivation for EDE models is to relieve the well-quantified ∼5σ “Hubble tension” between the Hubble constant $H_0$ inferred from early-Universe data (such as Planck CMB) and direct late-time distance-ladder measurements. EDE temporarily raises the pre-recombination expansion rate, decreasing the comoving sound horizon, which in turn allows a fit to a larger $H_0$ from CMB angular scales while preserving the observed acoustic features. The dominant realization of EDE is via a scalar field, but broader phenomenological classes—including microphysics beyond canonical scalars—are relevant for both theoretical consistency and phenomenological viability.

1. Theoretical Realizations and Parameterizations

Canonical EDE models utilize a minimally coupled scalar field, $\phi$, with a potential such as $V(\phi) = m^2 f^2 [1-\cos(\phi/f)]^n$ (with $n\geq2$), or similar plateau/axion-like or $\alpha$-attractor forms. At early times, Hubble friction freezes $\phi$ in a false vacuum ($w\approx-1$); close to the critical redshift $z_c$ (typically $z_c\sim 3000-5000$), $H_0$0 drops to the effective mass of the field, $H_0$1, and the field "thaws," rolling or oscillating around its minimum, with the energy density then redshifting faster than matter $H_0$2 and quickly diluting before recombination (Hill et al., 2021, Braglia et al., 2020, Sabla et al., 2022). The fraction of total energy density in EDE at its peak, $H_0$3, determines the model's impact.

More general parameterizations replace the scalar field with an effective fluid, with a time-dependent equation of state $H_0$4 and additional microphysical parameters: the effective sound speed $H_0$5 and anisotropic stress/shear viscosity $H_0$6 (Sabla et al., 2022). This framework encompasses both canonical models and extensions allowing, for example, non-scalar EDE or dark sector interactions.

Alternative construction includes phase transitions, e.g., hot NEDE, where finite-temperature effects in a dark sector trigger a first-order transition that injects vacuum energy near $H_0$7 (Niedermann et al., 2021). Chain EDE models posit a long sequence of metastable vacua, producing a temporally localized EDE injection via rapid tunneling events (Freese et al., 2021). Models inspired by extra dimensions or string theory identify the EDE scalar with moduli or axions, with explicit calculations of the non-perturbative potentials embedding the EDE sector in UV-complete frameworks (Cicoli et al., 2023, McDonough et al., 2022, Kojima et al., 2022).

2. Microphysical Effects and Perturbation Dynamics

The microphysics controlling EDE perturbations plays a pivotal role in observable consequences. For a scalar field, linear perturbations are characterized by $H_0$8 (sound speed of light) and vanishing anisotropic stress $H_0$9, ensuring pressure support and highly damped density perturbations on sub-horizon scales. In more general fluid or non-scalar models, both $\phi$0 and $\phi$1 are free parameters.

The linearized Einstein–Boltzmann system is modified by the EDE sector, with synchronous-gauge equations for density contrast $\phi$2 and velocity divergence $\phi$3: $\phi$4

$\phi$5

where $\phi$6 is shear stress and $\phi$7 is the adiabatic sound speed. Anisotropic sound speed models (“Shear II”) with $\phi$8 can suppress the EDE-induced enhancement of the Weyl potential and first CMB peak, enabling simultaneous relaxation of both $\phi$9 and $V(\phi) = m^2 f^2 [1-\cos(\phi/f)]^n$0 tensions that are exacerbated in canonical EDE (Sabla et al., 2022).

3. Observational Consequences and Current Constraints

The decisive signature of EDE is a transient reduction in the comoving sound horizon at photon decoupling, $V(\phi) = m^2 f^2 [1-\cos(\phi/f)]^n$1, driven by increased $V(\phi) = m^2 f^2 [1-\cos(\phi/f)]^n$2 from the EDE injection. This smaller $V(\phi) = m^2 f^2 [1-\cos(\phi/f)]^n$3, at fixed angle $V(\phi) = m^2 f^2 [1-\cos(\phi/f)]^n$4, forces a fit with larger $V(\phi) = m^2 f^2 [1-\cos(\phi/f)]^n$5. Canonical EDE with $V(\phi) = m^2 f^2 [1-\cos(\phi/f)]^n$6 at $V(\phi) = m^2 f^2 [1-\cos(\phi/f)]^n$7–$V(\phi) = m^2 f^2 [1-\cos(\phi/f)]^n$8 leads to $V(\phi) = m^2 f^2 [1-\cos(\phi/f)]^n$9–$n\geq2$0 km/s/Mpc, alleviating the $n\geq2$1 tension with SH0ES, while Planck-only $n\geq2$2CDM yields $n\geq2$3 km/s/Mpc (Hill et al., 2021, Braglia et al., 2020, Poulin et al., 2023).

CMB temperature and polarization spectra are affected via: (i) shifting acoustic peaks (larger $n\geq2$4), (ii) enhanced early ISW effect, and (iii) subtle modifications to the relative heights and phases of the first several acoustic peaks. High-resolution polarization data (ACT DR4, SPT-3G, Planck) are particularly sensitive to these changes, yielding nontrivial model-selection results: ACT+PlanckTT+BAO+lensing favor EDE at %%%%43$V(\phi) = m^2 f^2 [1-\cos(\phi/f)]^n$44%%%% with $n\geq2$7 (Hill et al., 2021, Posta et al., 2021), whereas Planck alone yields stringent upper limits, $n\geq2$8 (95% CL). The tension between different CMB datasets is driven by distinct multipoles—Planck high-$n\geq2$9 TT disfavors EDE, while ACT TE/EE at $\alpha$0 prefer its inclusion.

The impact on late-universe structure is mixed: EDE slightly increases the parameter $\alpha$1, thus worsening the extant $\alpha$2 tension unless microphysical freedom (anisotropic stress, e.g. $\alpha$3) or dark sector interactions are invoked (Sabla et al., 2022, Rebouças et al., 2023).

4. Microphysical Model-Building and UV Embeddings

Scalar-field EDE models require ultra-light fields with $\alpha$4 eV and specific non-trivial potential forms. Construction in $\alpha$5-attractor frameworks enables a range of injection shapes and avoids super-Planckian decay constants, with the scale $\alpha$6 set in theoretically natural ranges (Braglia et al., 2020). Hot NEDE and Chain EDE leverage either finite-temperature first-order vacuum transitions or long tunneling chains through axion-like potentials to explain both EDE and (in Chain EDE) potentially today's dark energy (Niedermann et al., 2021, Freese et al., 2021).

Contemporary string and higher-dimensional embeddings focus on non-perturbative axion potentials. In Type IIB string compactifications, EDE can be realized via $\alpha$7 axions in Large Volume Scenarios with suitable gaugino condensate harmonics, naturally achieving $\alpha$8, $\alpha$9, and $\phi$0 eV without severe tuning if the axionic Weak Gravity Conjecture is violated (Cicoli et al., 2023, McDonough et al., 2022). Extra-dimensional models derive the EDE scalar from a Wilson line of a higher-dimensional gauge field, relating the effective decay constant and potential scale directly to ultraviolet gauge and compactification parameters (Kojima et al., 2022). Viable models generically require potentials with $\phi$1 (steep oscillatory dilution) and careful engineering of the effective microphysics.

5. Challenges, Coincidences, and Tensions

EDE, regardless of microphysics, faces several interconnected challenges:

• Coincidence problem: The occurrence of the EDE injection precisely near matter–radiation equality is unexplained in scalar models with decoupled initial conditions. Embedded models attempt to address this via dark matter–EDE couplings (e.g. tEDS “trigger EDS”), in which a Planck-suppressed interaction with DM fixes $\phi$2 near equality independently of fine-tuning (Lin et al., 2022).
• $\phi$3 tension: Canonical EDE raises $\phi$4 and $\phi$5 to fit Planck power spectra, conflicting with large-scale structure data. Negative anisotropic stress or dark sector interactions (hot NEDE, dark matter–dark radiation drag) partially alleviate this (Niedermann et al., 2021, Sabla et al., 2022).
• CMB constraints and permissible $\phi$6: Robust constraints on $\phi$7 ($\phi$8) are set primarily by the CMB at $\phi$9, with the TE/EE spectra at intermediate multipoles providing the key discriminant (Hill et al., 2021, Posta et al., 2021). The allowed parameter region is strongly reduced when full-shape large-scale structure and lensing data are included (Rebouças et al., 2023).

6. Future Probes and Experimental Outlook

Forthcoming experiments can distinguish EDE microphysics at the $w\approx-1$0 level. Stage-IV ground-based CMB polarization arrays (CMB-S4, Simons Observatory) will probe the characteristic signatures of $w\approx-1$1 and $w\approx-1$2 in the first two acoustic peaks. The predicted 1$w\approx-1$3 uncertainties are $w\approx-1$4 and $w\approx-1$5 (CMB-S4-like), guaranteeing high significance if anisotropic or non-scalar microphysics are realized (Sabla et al., 2022).

21-cm cosmology, especially with HERA, will provide independent and improved sensitivity to $w\approx-1$6 at $w\approx-1$7–30, potentially distinguishing EDE from $w\approx-1$8CDM at $w\approx-1$9 after two years of observation for $z_c$0 (Adi et al., 2024). High-redshift cluster abundance and the full-shape (not just BAO) large-scale structure power spectrum ($z_c$1) also carry strong discrimination capability; deviations of order 10–15% near the turnover are distinctive EDE features (Shi et al., 2015, Alam et al., 2010).

7. Summary Table: Representative Constraints and Model Features

Scenario	$z_c$2 (best-fit/allowed)	$z_c$3 (km/s/Mpc)	Principal microphysics	CMB fit / $z_c$4 impact
Canonical scalar EDE	$z_c$5–$z_c$6	$z_c$7–$z_c$8	$z_c$9, $z_c\sim 3000-5000$0	Improves $z_c\sim 3000-5000$1, worsens $z_c\sim 3000-5000$2 (Sabla et al., 2022, Hill et al., 2021)
Anisotropic sound speed	$z_c\sim 3000-5000$3	$z_c\sim 3000-5000$4	$z_c\sim 3000-5000$5, $z_c\sim 3000-5000$6	Simultaneously mitigates $z_c\sim 3000-5000$7 and $z_c\sim 3000-5000$8 tensions (Sabla et al., 2022)
Hot/chain NEDE	$z_c\sim 3000-5000$9	$H_0$00–$H_0$01	1st order PT / tunneling chain	Early phase transition, DM drag relieves $H_0$02 (Niedermann et al., 2021, Freese et al., 2021)
$H_0$03-attractor-EDE	$H_0$04–$H_0$05	$H_0$06–$H_0$07	Plateau/kination/“rock’n’roll”	Varying shapes, natural $H_0$08 (Braglia et al., 2020)
tEDS (trigger EDS)	$H_0$09	$H_0$10	Planck-suppressed DM coupling	Removes $H_0$11 coincidence (Lin et al., 2022)
String/LVS C2-axion EDE	$H_0$12	$H_0$13–$H_0$14	$H_0$15 potential from fluxed D7	UV complete, no severe tuning (Cicoli et al., 2023, McDonough et al., 2022)

Key: PT = phase transition

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In summary, EDE provides a dynamically rich, theoretically motivated, and observationally discriminable solution to the Hubble tension and a laboratory for dark sector microphysics. Current data marginally accommodate $H_0$16; the character of the microphysics—canonical scalar, anisotropic, or dark sector-interacting—can be decisively distinguished by upcoming CMB polarization and 21-cm cosmology. Future work targeting the coincidence problem, the $H_0$17–$H_0$18 interplay, and UV embedding will further clarify EDE’s viability as a cornerstone of precision cosmology (Sabla et al., 2022, Hill et al., 2021, Poulin et al., 2023).