Spontaneous Symmetry Breaking as a Late-Time Trigger for Interacting Dark Energy

TL;DR

The paper investigates a late-time, density-triggered interacting dark energy model in which a scalar field with a $\\\mathbb{Z}_2$-symmetric quartic potential couples to dark matter after spontaneous symmetry breaking (SSB). The SSB induces a time-dependent vacuum expectation value $v(a)$ and an epoch-dependent coupling $\\beta(a)$, activating energy exchange that suppresses linear structure growth while leaving the background expansion close to $\\Lambda$CDM. By comparing a fixed $\\Lambda$CDM background with a self-consistent coupled-scalar evolution against diverse data (RSD, BAO, cosmic chronometers, Pantheon+SH0ES, and Planck distance priors), the study finds that late-time coupling can reduce $S_8$ without significantly shifting the inferred $H_0$, with joint analyses favoring a mild nonzero coupling and a transition near $z_c \\sim 1$. The framework provides a microphysical mechanism that decouples growth from expansion and offers a distinct origin for the $H_0$ and $S_8$ tensions, highlighting the potential of epoch-dependent IDE to address cosmological anomalies. Foreseeable advances include incorporating the full CMB likelihood and nonlinear structure formation to sharpen constraints on the parameter set $\\{\\Omega_m, H_0, \\sigma_{8,0}, \\beta_0, a_c, n\\}$ and testing the model with upcoming surveys such as DESI, Euclid, and LSST.

Abstract

Persistent tensions in the Hubble constant (H0) and the matter clustering parameter (S8) motivate late-time new physics that suppresses structure growth without significantly altering the background expansion history of the LambdaCDM model. We study a class of dark-sector dynamics in which a scalar dark energy field, governed by a Z2-symmetric quartic potential, interacts with dark matter through Yukawa and portal couplings. When the matter density drops below a critical threshold, a cosmological spontaneous symmetry breaking mechanism generates a time-dependent vacuum expectation value v(a) and activates an effective coupling eta(a). This creates a symmetric phase (a <= ac) identical to LambdaCDM at early times, and a broken phase (a > ac) in which eta(a) > 0 transfers energy from dark matter to dark energy, suppressing linear structure growth. Using RSD, BAO, cosmic chronometers, Pantheon+SH0ES supernovae, and compressed Planck distance priors, we compare a fixed LambdaCDM background with a self-consistent coupled-scalar evolution. The RSD-only analysis shows a strong shift: the dynamical background gives Omega_m ~ 0.31 +/- 0.10 and sigma8,0 ~ 0.59 +/- 0.01, while the fixed-background case gives Omega_m ~ 0.20 +/- 0.09 and sigma8,0 ~ 0.75 +/- 0.05. In the full joint fit, we obtain Omega_m = 0.29 +/- 0.01, H0 = 69.7 +/- 0.6 km s^-1 Mpc^-1, and sigma8,0 = 0.78 +/- 0.01. A late-time interaction triggered by spontaneous symmetry breaking can therefore damp structure growth and ease the S8 tension while leaving the expansion history and the inferred H0 essentially unchanged, suggesting distinct physical origins for the two tensions.

Figures (8)

• Figure 1: Panel (A) shows the normalized order parameter $v(a)/v_\infty$, which rises smoothly from the symmetric phase ($v=0$) to its asymptotic value as the effective mass term changes sign. Panel (B) displays the corresponding coupling $\beta(a)=\beta_0\,f(a)$, whose evolution directly follows that of $v(a)$ through Eq. \ref{['eq:v_dot']}. Panel (C) shows the normalized kernel $Q(a)$, peaking shortly after the transition epoch when the field’s relaxation rate $\dot v$ is maximal. The inset highlights the background Hubble scaling factor in Eq. \ref{['eq:Q_compact']}, showing that the overall amplitude of $Q(a)$ is dominated by the late-time acceleration regime.
• Figure 2: Linear matter power spectra $P(k)$ for the fiducial $\Lambda$CDM model (blue solid line) and IDE models (black lines). Rows correspond to different steepness parameters $n = 1, 2, 3$, while columns correspond to coupling epochs $a_c = 10^{-4}$ (early radiation era), $0.01$ (mid-matter era), and $0.71$ (late-time). Different line styles correspond to varying present-day coupling strengths $\beta_0$. Early-time couplings ($a_c \ll 1$) strongly amplify small- and intermediate-scale power, conflicting with Planck and BAO constraints, whereas mid-to-late couplings lead to moderate growth enhancements. Late-onset of couplings ($a_c \gtrsim 0.7$) leaves the matter power spectrum nearly indistinguishable from the $\Lambda$CDM prediction. The curves represent linear-theory predictions based on CAMB transfer functions rescaled by the corresponding growth factors, intended as illustrative trends rather than fully self-consistent Boltzmann solutions.
• Figure 3: Posterior constraints on $\Omega_m$, $H_0$, $\sigma_{8,0}$, $\beta_0$, and $a_c$ from the RSD-only MCMC analysis of the epoch-dependent coupling model with fixed $n=1$. The blue contours correspond to the analysis performed with a fixed $\Lambda$CDM background, while the red contours show the results obtained when the background expansion is evolved self-consistently with the scalar–matter coupling. The dynamical background leads to a higher matter density ($\Omega_m \simeq 0.31$) and a lower growth amplitude ($\sigma_{8,0} \simeq 0.59$) compared to the fixed-background case ($\sigma_{8,0} \simeq 0.75$), indicating suppressed late-time structure formation.
• Figure 4: Two-dimensional marginalized posteriors with fixed $\Lambda$CDM background comparing the full joint analysis (BOSS RSD + Planck priors + BAO + SN; blue, filled) with the reduced dataset (BOSS RSD + Planck priors + BAO; red, dashed). Contours show the 68% and 95% credible regions. The inclusion of SN sharpens the constraints, reducing degeneracies between $\Omega_m$ and $H_0$, and slightly shifts the preferred region for $\sigma_{8,0}$ toward lower values.
• Figure 5: Posterior predictive distributions for the linear growth rate observable $f\sigma_8(z)$ derived from the RSD-only MCMC analysis of the model with fixed $n=1$. The solid curves represent the posterior median predictions, while the shaded regions denote the 68% credible intervals obtained from 400 posterior samples. The blue and orange curves correspond to analyses performed with a fixed $\Lambda$CDM background and a self-consistently evolved dynamical background, respectively. The data points with $1\sigma$ error bars are RSD measurements compiled in Ref. kazantzidis2018evolution. The underlying microphysical parameters are fixed to $\lambda = 10^{-2}$, $v_0 = 1.0\,M_{\mathrm{Pl}}$, and $\xi_{\mathrm{density}} = 10^{-3}$. The dynamical background predicts a systematically suppressed late-time growth amplitude relative to the fixed background, a strong case of the scalar--matter coupling on the background expansion, and the corresponding modification to structure formation.