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Disformal interactions in the Dark Sector: From driving Early Dark Energy to confronting cosmological tensions

Pulkit Bansal, Joseph P. Johnson, S. Shankaranarayanan

TL;DR

This work develops a field-theoretic framework for dark energy–dark matter interactions based on general disformal couplings, unifying conformal, disformal, and pure-momentum interactions. A general action is mapped to the Einstein frame via disformal transformations, yielding explicit DE–DM couplings that can drive an interacting Early Dark Sector without fine-tuned potentials. The authors classify seven models (M1–M7), showing that pure disformal couplings (notably M3/M4) naturally produce an EDE-like phase with three-stage DE evolution, potentially reconciling the H0 tension and explaining large-angle CMB power suppression, while pure momentum models (M6/M7) imprint distinctive perturbation signatures. The framework makes testable predictions for background expansion, structure growth, and CMB spectra, with implications for upcoming surveys and gravitational-wave memory probes to distinguish these scenarios from ΛCDM. Overall, the disformal DE–DM framework offers a robust, first-principles path beyond ΛCDM for addressing key cosmological tensions and connecting late-time acceleration to the dark sector’s microphysics.

Abstract

The $Λ$CDM model faces significant challenges, including an incomplete understanding of the dark sector and persistent tensions in the Hubble constant and the clustering amplitude. To address these issues, we propose a general disformal coupling between dark energy (DE) and dark matter from a field-theoretic action which can generate a rich variety of interactions including conformal and pure-momentum coupling scenarios. Our analysis reveals that a pure disformal coupling naturally produces a unique interacting Early Dark Sector, wherein the interactions with dark matter suppress the Hubble friction on the DE scalar field leading to a kinetic-driven cosmological constant-like behavior at early times followed by its dilution as $a^{-6}$ and eventually leading to a potential-driven epoch characteristic of late-time dark energy. In contrast to existing Early Dark Energy (EDE) models that rely on finely-tuned potentials, the EDE-like behavior, in our framework, is purely a consequence of the disformal coupling paired with the dilution of dark matter, offering a more fundamental and less ad hoc solution to cosmological tensions. This framework also predicts a suppression of power in the CMB temperature spectrum on large angular scales, offering a potential physical explanation for the observed low-$\ell$ anomaly. By deriving these effects from a fundamental action, our work provides a unified, testable alternative to $Λ$CDM that can be constrained by next-generation cosmological surveys and gravitational wave observations.

Disformal interactions in the Dark Sector: From driving Early Dark Energy to confronting cosmological tensions

TL;DR

This work develops a field-theoretic framework for dark energy–dark matter interactions based on general disformal couplings, unifying conformal, disformal, and pure-momentum interactions. A general action is mapped to the Einstein frame via disformal transformations, yielding explicit DE–DM couplings that can drive an interacting Early Dark Sector without fine-tuned potentials. The authors classify seven models (M1–M7), showing that pure disformal couplings (notably M3/M4) naturally produce an EDE-like phase with three-stage DE evolution, potentially reconciling the H0 tension and explaining large-angle CMB power suppression, while pure momentum models (M6/M7) imprint distinctive perturbation signatures. The framework makes testable predictions for background expansion, structure growth, and CMB spectra, with implications for upcoming surveys and gravitational-wave memory probes to distinguish these scenarios from ΛCDM. Overall, the disformal DE–DM framework offers a robust, first-principles path beyond ΛCDM for addressing key cosmological tensions and connecting late-time acceleration to the dark sector’s microphysics.

Abstract

The CDM model faces significant challenges, including an incomplete understanding of the dark sector and persistent tensions in the Hubble constant and the clustering amplitude. To address these issues, we propose a general disformal coupling between dark energy (DE) and dark matter from a field-theoretic action which can generate a rich variety of interactions including conformal and pure-momentum coupling scenarios. Our analysis reveals that a pure disformal coupling naturally produces a unique interacting Early Dark Sector, wherein the interactions with dark matter suppress the Hubble friction on the DE scalar field leading to a kinetic-driven cosmological constant-like behavior at early times followed by its dilution as and eventually leading to a potential-driven epoch characteristic of late-time dark energy. In contrast to existing Early Dark Energy (EDE) models that rely on finely-tuned potentials, the EDE-like behavior, in our framework, is purely a consequence of the disformal coupling paired with the dilution of dark matter, offering a more fundamental and less ad hoc solution to cosmological tensions. This framework also predicts a suppression of power in the CMB temperature spectrum on large angular scales, offering a potential physical explanation for the observed low- anomaly. By deriving these effects from a fundamental action, our work provides a unified, testable alternative to CDM that can be constrained by next-generation cosmological surveys and gravitational wave observations.

Paper Structure

This paper contains 32 sections, 73 equations, 13 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Field-theoretic description and fluid mapping of a disformally interacting dark sector
  3. Scalar field interactions from a disformal origin
  4. Dark sector interactions with a generalized disformal coupling
  5. Field-Fluid mapping of dark matter for the generalized disformal coupling
  6. Cosmology of the disformally interacting dark sector
  7. Cosmological Implications of the disformal dark sector
  8. Pure-Momentum Coupling between DE and DM fluids
  9. Cosmological evolution within Model M6
  10. Cosmological evolution within Model M7
  11. Pure disformal coupling, and a unified Early and late dark energy
  12. Impact on linear perturbations
  13. Approximate analytical derivation of DE density scaling for Models M1-M7
  14. Model M1: Scalar Field-Dependent Conformal Coupling ($C(\phi), D=0$)
  15. Model M3: Pure & Constant Disformal Coupling ($C=c_0, D=d_0$)
  16. ...and 17 more sections

Figures (13)

  • Figure 1: Modified evolution of the energy densities of different components (top), DE equation of state (center) and the Hubble parameter (bottom) due to pure-momentum DE-DM interactions. Left: Model M6 and Right: Model M7 from Table \ref{['Table:iDEDM']} .
  • Figure 2: Flow chart detailing the evolution of DE scalar field $\phi$ and its energy density $\rho_{\mathrm{DE}}$ from early till late times due to Model M6-like pure-momentum coupling between DE and DM fluids. Note that one obtains a functionally identical evolution of the DE field for kinetic-energy (K.E.) dependent conformal and disformal coupling models M2 and M5 from Table \ref{['Table:iDEDM']} .
  • Figure 3: Modified linear matter power spectrum (left), CMB temperature power spectrum (right) and relative deviation from their uncoupled counterparts due to pure-momentum exchange, corresponding to Model M6 from Table \ref{['Table:iDEDM']} , between the DE and DM fluids.
  • Figure 4: Modified linear matter power spectrum (left), CMB temperature power spectrum (right) and relative deviation from their uncoupled counterparts due to pure-momentum exchange, corresponding to Model M7 from Table \ref{['Table:iDEDM']} , between the DE and DM fluids.
  • Figure 5: Modified cosmological background evolution of the DE energy density (top left), DM energy density relative to the non-interacting case (top right), DE effective equation of state (bottom left) and the relative change in Hubble parameter compared to the non-interacting case (bottom right), for different coupling strengths of disformal DE-DM interactions (Model M3 in Table \ref{['Table:iDEDM']}).
  • ...and 8 more figures