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Dark energy from Geometrothermodynamics

Alessandro Bravetti, Orlando Luongo

TL;DR

This paper uses geometrothermodynamics to derive a dark energy fluid with constant thermodynamic curvature, yielding a fundamental equation of state that drives late-time acceleration while preserving ΛCDM behavior at small redshift. By enforcing R^natural_U = −2 and adopting a volume V that tracks the FRW scale factor, the authors obtain a fluid with P = −2 c2 V U and U(S,V) = U0 exp(c1 S + c2 V^2), leading to ρ_DE and ω_DE that evolve with redshift as ρ_DE = exp(c1 S0 + c2/(1+z)^6) (1+z)^3 and ω_DE = −2 c2/(1+z)^6. The model naturally reduces to ΛCDM in the z → 0 limit and to a matter-dominated regime at high z, while addressing the coincidence and fine-tuning issues by tying dark energy to geometric-thermodynamic interactions. The framework offers a testable, data-driven path to compare GTD-based predictions with observations and to explore alternative volume scalings within cosmology.

Abstract

Geometrothermodynamics is a geometric theory which combines thermodynamics with contact and Riemannian geometry. In this work we use the formalism of geometrothermodynamics to infer cosmological models which predict the observed speed up. As a relevant consequence, our simple model shows dynamical properties which seem to fairly well describe the late time universe dynamics. To do so, we use geometric considerations about constant thermodynamic curvature and derive the model of a fluid which is expected to \emph{naturally} reproduce the dark energy effects. In particular, our approach reduces to the $Λ$CDM model in the limiting case of small redshift, providing however significative departures from $Λ$CDM as the universe expands. The main goal consists in interpreting our \emph{geometrothermodynamic fluid} as an energetic source and to explain the dark energy effects as emerging from the interplay between geometry and thermodynamics, providing a new interpretation of the observed positive acceleration.

Dark energy from Geometrothermodynamics

TL;DR

This paper uses geometrothermodynamics to derive a dark energy fluid with constant thermodynamic curvature, yielding a fundamental equation of state that drives late-time acceleration while preserving ΛCDM behavior at small redshift. By enforcing R^natural_U = −2 and adopting a volume V that tracks the FRW scale factor, the authors obtain a fluid with P = −2 c2 V U and U(S,V) = U0 exp(c1 S + c2 V^2), leading to ρ_DE and ω_DE that evolve with redshift as ρ_DE = exp(c1 S0 + c2/(1+z)^6) (1+z)^3 and ω_DE = −2 c2/(1+z)^6. The model naturally reduces to ΛCDM in the z → 0 limit and to a matter-dominated regime at high z, while addressing the coincidence and fine-tuning issues by tying dark energy to geometric-thermodynamic interactions. The framework offers a testable, data-driven path to compare GTD-based predictions with observations and to explore alternative volume scalings within cosmology.

Abstract

Geometrothermodynamics is a geometric theory which combines thermodynamics with contact and Riemannian geometry. In this work we use the formalism of geometrothermodynamics to infer cosmological models which predict the observed speed up. As a relevant consequence, our simple model shows dynamical properties which seem to fairly well describe the late time universe dynamics. To do so, we use geometric considerations about constant thermodynamic curvature and derive the model of a fluid which is expected to \emph{naturally} reproduce the dark energy effects. In particular, our approach reduces to the CDM model in the limiting case of small redshift, providing however significative departures from CDM as the universe expands. The main goal consists in interpreting our \emph{geometrothermodynamic fluid} as an energetic source and to explain the dark energy effects as emerging from the interplay between geometry and thermodynamics, providing a new interpretation of the observed positive acceleration.

Paper Structure

This paper contains 9 sections, 39 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Geometrothermodynamics
  3. The phase manifold $(\mathcal{T},\Theta,G^\natural)$
  4. The equilibrium manifold $(\mathcal{E},g^\natural)$
  5. Dark energy fundamental equation from GTD
  6. Consequences in cosmology
  7. Energy conditions and adiabatic speed of sound
  8. Reproducing the $\Lambda$CDM model as a low redshift limiting case
  9. Conclusion and perspectives

Figures (2)

  • Figure 1: The plot shows the evolution of the ECs over time (parametrized by the redshift $z$) for the standard value of $\Omega_m=0.25$ and for $c_2=0.5$ and $c_1=1/S_0$. The red and blue lines indicate the WEC, the green line is the SEC and the cyan line represents the DEC.
  • Figure 2: The plot shows the evolution of the adiabatic speed of sound over the redshift $z$, with $\Omega_m=0.25$, $c_2=0.5$ and $c_1=1/S_0$.