Negentropy as Diagnostic of Cosmic Density Fields and Dynamical Dark Energy Models

TL;DR

This work introduces negentropy as an information-theoretic scalar to quantify non-Gaussianity in the cosmic density field and to probe dynamical dark energy models. By linking differential entropy of Gaussian and log-normal density fields, and by extending to discrete galaxy distributions with nonlinear bias, the authors define $J(a)$ and its derivatives $\Gamma_1(a)$ and $\Gamma_2(a)$ to track structure formation across cosmic time. They identify characteristic epochs $z_{NG}$ and $z_{TA}$, showing ΛCDM values of $z_{NG}\approx0.81$ and $z_{TA}\approx0.18$, and demonstrate thatnegentropy discriminates between thawing, freezing, and phantom dark-energy scenarios, with BA parametrisation providing particularly tight constraints. The paper also develops a Fisher-matrix framework to forecast DE parameter constraints from negentropy, highlighting that $\Gamma_2(a)$ yields the strongest, least-correlated constraints and pinpointing pivot redshifts around $z_p\sim0.1$–$0.2$, suggesting practical pathways for applying this approach to upcoming surveys and simulations.

Abstract

We employ negentropy ($J$), defined as the difference between the information content of a non-Gaussian probability distribution and a Gaussian with identical variance, as an information-theoretic probe of non-Gaussianity in the cosmic density field. We quantify its sensitivity to dynamical dark energy by studying the evolution of $J(a)$ and its derivatives $Γ_1(a)$ and $Γ_2(a)$ across three parameterisation schemes: CPL, JBP, and BA. We determine the characteristic redshift $z_{NG}$, marking the epoch of maximal non-Gaussian structure formation, and the turnaround redshift $z_{TA}$, when information production transitions due to dark-energy domination, finding $z_{NG}\sim0.81$ and $z_{TA}\sim0.18$ for $Λ$CDM. Our diagnostics clearly discriminate between thawing and freezing quintessence models and phantom dark energy at low redshifts. Thawing models show small departures from $Λ$CDM, freezing models display higher $z_{TA}$, while phantom models exhibit lower $z_{TA}$, reflecting late-time evolution. We provide a practical prescription for measuring negentropy from discrete galaxy distributions, establishing a framework that can be applied to simulations and observations. This information-theoretic approach offers a robust and complementary tool for probing dark energy dynamics, enabling sensitive discrimination between evolving and cosmological-constant scenarios.

Figures (5)

• Figure 1: This figure shows the growth of perturbations in the matter density field and the evolution of differential entropy and negentropy associated with it.
• Figure 2: The evolution of negentropy estimated for the 3 different parametrisation schemes, for different dark energy models with chosen values of ($w_0$,$w_a$) from Set I (\ref{['tab:w0wa_grid']}). The solid curved lines with different colours represent different physical models of dark energy. The colour coding is done as: {Black:$\Lambda$CDM; Red:Quintessence; Blue:Thawing; Purple:Freezing; Gold:Phantom }
• Figure 3: Same as \ref{['fig:evol_J_dde_set1']} but for the choice of parameters from Set II, having larger departure from $\Lambda$CDM compared to Set I.
• Figure 4: Same as \ref{['fig:evol_J_dde_set1']} and \ref{['fig:evol_J_dde_set2']} but for the choice of parameters from Set III, having larger departure from $\Lambda$CDM compared to both Set I and Set II.
• Figure 5: The contour plots display the Fisher forecast constraints in the ($w_0$,$w_a$) plane, illustrating the sensitivity of $J(a)$, $\Gamma_1(a)$ and $\Gamma_2 (a)$ to the dark energy parameters. Different colours correspond to different dark energy parametrisations. The confidence regions around the fiducial model ($w_0=-1$,$w_a=0$) are shown at $1\sigma$, $2\sigma$ and $3\sigma$ confidence levels, with decreasing opacity.