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Thermodynamics of the FRW Universe in Generalized Proca Theory

Aofei Sang

TL;DR

This work addresses extending FRW horizon thermodynamics to Generalized Proca (GP) theory and uses it to test two GP-based dark energy models. The authors derive modified Friedmann equations and the thermodynamic first law on the apparent horizon, obtaining the equation of state $P(T,R_A)$ for each model and analyzing $P$–$V$ behavior. They find that Model A exhibits a van der Waals–type phase transition with a well-defined critical point and universal exponents $(\tilde{\alpha},\tilde{\beta},\tilde{\gamma},\tilde{\delta})=(0,\tfrac{1}{2},0,3)$, while Model B shows no phase transition within observationally allowed parameter ranges. These results imply that horizon thermodynamics can serve as a diagnostic tool to distinguish viable dark energy models in GP theory and extend FRW thermodynamics to vector-tensor gravity.

Abstract

We investigate the thermodynamics of a spatially flat Friedmann-Robertson-Walker (FRW) universe within the framework of Generalized Proca (GP) theory, a comprehensive vector-tensor theory. By adopting two distinct dark energy models in GP, we derive the corresponding modified Friedmann equations, the thermodynamic first law for the apparent horizon, and the equation of state for these models. For the first model, characterized by power-law couplings and an ansatz linking the Proca field to the Hubble parameter, we analytically demonstrate the existence of a critical point in the pressure-volume$(P-V)$ diagram, indicating a $P-V$ phase transition. For the second model, defined by a Proca field marginal coupled to curvature, we show that there is no phase transition when the coupling constants are selected within the range permitted by observations. This investigation not only extends the FRW thermodynamics to vector-tensor theories but also demonstrates that cosmological phase transitions can serve as a powerful diagnostic tool for distinguishing viable dark energy models in GP theory.

Thermodynamics of the FRW Universe in Generalized Proca Theory

TL;DR

This work addresses extending FRW horizon thermodynamics to Generalized Proca (GP) theory and uses it to test two GP-based dark energy models. The authors derive modified Friedmann equations and the thermodynamic first law on the apparent horizon, obtaining the equation of state for each model and analyzing – behavior. They find that Model A exhibits a van der Waals–type phase transition with a well-defined critical point and universal exponents , while Model B shows no phase transition within observationally allowed parameter ranges. These results imply that horizon thermodynamics can serve as a diagnostic tool to distinguish viable dark energy models in GP theory and extend FRW thermodynamics to vector-tensor gravity.

Abstract

We investigate the thermodynamics of a spatially flat Friedmann-Robertson-Walker (FRW) universe within the framework of Generalized Proca (GP) theory, a comprehensive vector-tensor theory. By adopting two distinct dark energy models in GP, we derive the corresponding modified Friedmann equations, the thermodynamic first law for the apparent horizon, and the equation of state for these models. For the first model, characterized by power-law couplings and an ansatz linking the Proca field to the Hubble parameter, we analytically demonstrate the existence of a critical point in the pressure-volume diagram, indicating a phase transition. For the second model, defined by a Proca field marginal coupled to curvature, we show that there is no phase transition when the coupling constants are selected within the range permitted by observations. This investigation not only extends the FRW thermodynamics to vector-tensor theories but also demonstrates that cosmological phase transitions can serve as a powerful diagnostic tool for distinguishing viable dark energy models in GP theory.
Paper Structure (8 sections, 49 equations, 1 figure)

This paper contains 8 sections, 49 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Dynamics of the FRW Universe in Generalized Proca Theory
  3. Review of FRW Thermodynamics
  4. Thermodynamics of the FRW Universe in Generalized Proca Theory
  5. Model A
  6. Model B
  7. Conclusion
  8. Expressions of some parameter in the main text

Figures (1)

  • Figure 1: Isothermal curves of the dimensionless pressure $p$ versus dimensionless AH $r_A$ for Model A in GP cosmology. Different colors correspond to different dimensionless temperatures: $\tau=0.5$(Red), $\tau=0.8$(Orange), $\tau=1$(Black, critical isotherm), $\tau=1.2$(Blue), $\tau=1.5$(Green). The characteristic van der Waals–like loop appears for $\tau<1$, while the critical isotherm shows a clear inflection point at (1,1).