Dissipative cosmology with $Λ$ from the first law of thermodynamics

TL;DR

The paper develops a dissipative cosmology by deriving a curvature-coupled dissipative term from the first law of thermodynamics, combining a constant $\Lambda/3$ with a dissipative rate $h_{\textrm{B}}(t)=\beta(2H^{2}+\dot{H})$ and horizon entropy $S_{\rm H}=S_{\rm BH}(1-\beta)$. The background evolution is solved exactly, revealing a transition from deceleration to acceleration for $\beta<0.5$ and a late-time approach to a de-Sitter-like state with effective density $\Omega_{\Lambda,\gamma}=\Omega_{\Lambda}/(1-\gamma)$. Horizon thermodynamics satisfy the second law ($\dot{S}_{\rm BH}\ge0$) and entropy maximization ($\ddot{S}_{\rm BH}<0$) in the final regime, linking dissipative dynamics to thermodynamic constraints. Observational fits to $H(z)$ data favor a weakly dissipative Universe with a nonzero $\Lambda$, consistent with ΛCDM while allowing for small dissipation as a bridge to standard cosmology. The work provides a thermodynamic underpinning for dissipative cosmologies and motivates further exploration of perturbations and alternative entropy forms.

Abstract

We phenomenologically derive a cosmological model that includes both a cosmological constant term $Λ/3$ and a dissipative driving term $β(2 H^{2} + \dot{H})$ by applying the first law of thermodynamics to matter creation cosmology. Here $H$, $\dot{H}$, and $β$ are the Hubble parameter, the time derivative of $H$, and a non-negative dimensionless coefficient, respectively. The dissipative term is proportional to the Ricci scalar curvature, suggesting that the dynamic creation pressure has the same dependence. We examine the model's background evolution in the late universe and its horizon thermodynamics. The present model supports a transition from a decelerating universe to an accelerating universe when $β<0.5$. The second law of thermodynamics is always satisfied on the horizon, and maximization of entropy is satisfied in the final stage. We examine constraints on the present model using observed Hubble parameter data and the transitional and thermodynamic constraints and find that a weakly dissipative universe with $Λ$ is likely favored and consistent with our Universe. We also discuss irreversible entropy due to adiabatic particle creation, assuming a holographic-like matter creation cosmology.

Figures (6)

• Figure 1: (Color online). Evolution of the universe for the present model for $\Omega_{\Lambda,\gamma} =0.685$. (a) Normalized Hubble parameter $H/H_{0}$. (b) Deceleration parameter $q$. In (a), the open circles with error bars are observed points (57 recently compiled data points) taken from Ref. 57dataOdin. To normalize the data points, $H_{0}$ is set to $67.4$ km/s/Mpc based on Ref. Planck2018. In (b), the horizontal break line represents $q=0$. A positive and negative $q$ represent deceleration and acceleration, respectively
• Figure 2: Boundary of $q= 0$ in the $(\Omega_{\Lambda,\gamma}, \beta)$ plane for various values of $\tilde{a}=a/a_{0}$. The arrow attached to each boundary indicates an accelerating-universe region that satisfies $q< 0$. Each numerical value (from $0.25$ to $1.25$) near each boundary represents the value of $\tilde{a}$. The region in gray (namely $\beta >0.5$) represents an always-accelerating-universe region. This region and $\beta=0.5$ do not satisfy a decelerating and accelerating universe. The closed circle represents $(\Omega_{\Lambda,\gamma}, \beta) = (0.685, 0)$ for the $\Lambda$CDM model. We can convert $\beta$ into $\gamma = 4 \beta/3$, using Eq. (\ref{['eq:gamma']}) and $w=0$.
• Figure 3: Evolution of the normalized $S_{mc}$ in the comoving volume and the normalized $S_{mH}$ in the Hubble volume for the present model for $\Omega_{\Lambda,\gamma} =0.685$. (a) $S_{mc} / S_{mc,0}$ in the comoving volume. (b) $S_{mH} / S_{mH,0}$ in the Hubble volume. The evolution for $\beta =0$ corresponds to that for the $\Lambda$CDM model in a non-dissipative universe.
• Figure 4: Evolution of the normalized $S_{\rm{BH}}$, $\dot{S}_{\rm{BH}}$, and $\ddot{S}_{\rm{BH}}$ for the present model for $\Omega_{\Lambda,\gamma} =0.685$. (a) $S_{\rm{BH}} / S_{\rm{BH},0}$. (b) $\dot{S}_{\rm{BH}}/ (S_{\rm{BH},0} H_{0})$. (c) $\ddot{S}_{\rm{BH}}/ (S_{\rm{BH},0} H_{0}^{2})$.
• Figure 5: Boundary of $\ddot{S}_{\rm{BH}} = 0$ in the $(\Omega_{\Lambda,\gamma}, \beta)$ plane for various values of $\tilde{a}=a/a_{0}$. The solid lines represent the boundary of $\ddot{S}_{\rm{BH}} = 0$. The arrow attached to each solid-line boundary indicates a region that satisfies $\ddot{S}_{\rm{BH}} < 0$. The dashed lines represent the boundary of $q = 0$, plotted from Fig. \ref{['Fig-q_plane']}. The arrow attached to each dashed-line boundary indicates an accelerating-universe region that satisfies $q< 0$. The region for $\beta < 0.5$ satisfies a decelerating and accelerating universe. The closed circle represents $(\Omega_{\Lambda,\gamma}, \beta) = (0.685, 0)$ for the $\Lambda$CDM model. See also the caption of Fig. \ref{['Fig-q_plane']}.