Evolution of thermodynamic quantities on cosmological horizon in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>model
Nobuyoshi KOMATSU
Abstract
The horizon of a flat Friedmann-Robertson-Walker (FRW) universe is considered to be dynamic when the Hubble parameter $H$ and the Hubble radius ${r}_{H}$ vary with time, unlike for de Sitter universes. To clarify the thermodynamics on a dynamic horizon, the evolution of a dynamical Kodama-Hayward temperature and Bekenstein-Hawking entropy on the horizon of a flat FRW universe is examined in a $\mathrm{\ensuremath{\Lambda}}(t)$ model similar to time-varying $\mathrm{\ensuremath{\Lambda}}(t)$ cosmologies. The $\mathrm{\ensuremath{\Lambda}}(t)$ model includes both a power-law term proportional to ${H}^{\ensuremath{\alpha}}$ (where $\ensuremath{\alpha}$ is a free variable) and the equation of state parameter $w$, extending a previous analysis [N. Komatsu, Phys. Rev. D 100, 123545 (2019)]. Using the present model, a matter-dominated universe ($w=0$) and a radiation-dominated universe ($w=1/3$) are examined, setting $\ensuremath{\alpha}<2$. Both universes tend to approach de Sitter universes and satisfy the maximization of entropy in the last stage. The evolution of several parameters (such as the Bekenstein-Hawking entropy) is similar for both $w=0$ and $w=1/3$, though the dynamical temperature ${T}_{H}$ is different. In particular, ${T}_{H}$ is found to be constant when $w=1/3$ with $\ensuremath{\alpha}=1$, although $H$ and ${r}_{H}$ vary with time. To discuss this case, the specific conditions required for constant ${T}_{H}$ are examined. Applying the specific condition to the present model gives a cosmological model that can describe a universe at constant ${T}_{H}$, as if the dynamic horizon is in contact with a heat bath. The relaxation processes for the universe are also discussed.