Brian Greene Sean Carroll -

[ S_{\text{CG}}(t_{\text{initial}}) = S_{\text{min}} ] where ( S_{\text{min}} ) is the entropy of a smooth, homogeneous initial patch — consistent with a low-entropy beginning.

[ \rho_{\text{DE}} = \frac{\Lambda}{8\pi G}, \quad \dot{S}_{\text{horizon}} = \frac{2\pi}{G} \dot{r}_h^2 \geq 0 ] brian greene sean carroll

[ \frac{d S_{\text{CG}}}{dt} = \sigma(t) \geq 0 ] with ( \sigma(t) ) the entropy production rate from stringy UV modes falling across the horizon. We postulate a boundary condition at ( t = t_{\text{initial}} ): brian greene sean carroll

The entropy of the cosmological horizon is [ S_{\text{dS}} = \frac{A}{4G} = \frac{3\pi}{G\Lambda} ] where ( \Lambda > 0 ) is the cosmological constant. brian greene sean carroll

Brian Greene (Columbia University) & Sean Carroll (Caltech / Santa Fe Institute)