2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/4563The structure and origin of the Friedmann integrals are analyzed within the framework of large extra dimensions proposed by Arkani-Hamed et all. (1998). It is demonstrated that the integrals might emerge from extra-dimension physics and reveal its signature. In the case of two extra dimensions, the integrals are expressed via the product $M_* R$ of the only fundamental energy $M_*$ and the size $R $ of the extra dimensions. The cosmic vacuum density turns out to be $\sim R^4$, in this case. The effective cut-off in the spectrum of the quantum zero-point oscillations at the frequency $ω_V \sim 1/R$ is assumed to be associated with the epoch when the Hubble radius becomes larger than $R$. This occurs at temperatures $ \sim M_*$ in the first three picoseconds of the cosmic expansion.7 pages, LaTeX, no figure, for correspondence chernin@sai.msu.ruAstrophysicstext