Charges, conserved quantities and fluxes in de Sitter spacetime

We discuss the definition of conserved quantities in asymptotically locally de Sitter spacetimes. One may define an analogue of holographic charges at future and past infinity and at other Cauchy surfaces $I_t$ as integrals over the intersection of timelike surfaces $C$ and the Cauchy surface $I_t$. In general, the charges $Q^t$ defined on the Cauchy surface $I_t$ depend on $C$, but if gravitational flux is absent the charges are independent of $C$. The quantity $\Delta Q^t(C_1, C_2) = Q^t(C_1)-Q^t(C_2)$ is zero and thus independent of $I_t$ in the absence of flux, defining a conserved quantity in spacetime. On the other hand, if there is a net gravitational flux entering or leaving the spacetime region bounded by $C_1, C_2$ and two Cauchy surfaces then $\Delta Q^t(C_1, C_2)$ changes by the same amount