Signatures of Extended Dark Energy Parametrisations in Structure Formation under Background Constraints

Abstract

We study structure formation in alternative cosmological models constrained by background observations, including $Λ$CDM, wCDM, the Chevallier-Polarski-Linder parametrisation and a flexible Chebyshev expansion of the dark energy equation of state. The models are constrained using baryon acoustic oscillations, cosmic microwave background, cosmic chronometers and strong lensing measurements. Using the best-fitting parameters, we generate cosmology-dependent initial conditions and perform N-body simulations to analyse the matter power spectrum, halo mass function and halo density profiles. Although all models remain broadly consistent with $Λ$CDM at the background level, differences in the physical matter density $Ω_{0m}h^2$ and in the expansion history $H(z)$ lead to distinct growth histories that are amplified by non-linear evolution. We find a clear hierarchy in the power spectrum amplitude and in $σ_8$, with the Chebyshev and CPL models exhibiting enhanced small-scale power, earlier halo formation at $z\gtrsim2$ and a migration of excess toward higher masses at late times. The wCDM model displays milder and partially compensating effects driven by its different expansion history. When expressed in terms of the scaled radius $r/R_{200c}$, halo density profiles show a high degree of universality across cosmologies, indicating that internal halo structure is largely governed by the same gravitational dynamics. These results demonstrate that even modest background-level variations in $w(z)$ can translate into coherent non-linear signatures, highlighting the constraining power of large-scale structure observables in extended dark energy models.

Figures (10)

• Figure 1: 1D marginalised posterior distributions and the 2D 68% and 95% confidence levels for the parameters of the four models considered in this work.
• Figure 2: 1D marginalised posterior distributions and the 2D 68% and 95% confidence levels for the Chebyshev coefficients.
• Figure 3: A panel of three plots showing the redshift evolution of the Hubble parameter normalised by the Planck reference, $H(z)/H_{\rm Planck}(z)$ (left column), the dark energy equation of state $w(z)$ (middle column) and the deceleration parameter $q(z) = (1+z) \frac{1}{E(z)} \frac{dE(z)}{dz} - 1$ (right column), for the cosmological models under consideration. The shaded regions represent the $1\sigma$ confidence intervals derived from error propagation of the chains. The results are based on the parameter constraints obtained from a joint fit to all observational data sets considered in this work.
• Figure 4: Projected density map along the $z$-axis for a $100~\mathrm{Mpc}/h$ region simulated under the $\Lambda$CDM cosmology at $z=0$. A $20~\mathrm{Mpc}/h$ scale bar is shown in the bottom-right corner. The red square highlights the zoomed-in region, which is displayed in the adjacent panel. The colourbar represents particle number.
• Figure 5: Left column: matter power spectrum measured from the simulations, shown as the combination $kP(k)$, which visually enhances the difference between models. The green, red, purple and orange colours correspond to the $\Lambda$CDM, $w$CDM, CPL and Chebyshev cosmologies, respectively. Each power spectrum is shown up to the Nyquist frequency, $k_N=8.04$$h$/Mpc. Right column: relative difference between the power spectra and the Planck-$\Lambda$CDM reference spectrum, ${P(k)}/{P(k)}_{\mathrm{\rm Planck}} - 1$. The various rows show the results at redshifts $z = 21.5,\ 3.7,\ 3.3,\ 2.0,\ 1,\ 0.5,$ and $0$, from top to bottom.