By Monte Carlo simulations of a variant of the bond-fluctuation model without topological constraints we examine the center-of-mass (COM) dynamics of polymer melts in $d=3$ dimensions. Our analysis focuses on the COM displacement correlation function
$CN(t) approx partial_t^2 MSDcmN(t)/2$, measuring the curvature of the COM mean-square displacement $MSDcmN(t)$. We demonstrate that $CN(t) approx -(RN/TN)^2 (rhostar/rho) f(x=t/TN)$ with $N$ being the chain length ($16 le N le 8192$), $RNsim N^{1/2}$ the typical chain size, $TNsim N^2$ the longest chain relaxation time, $rho$ the monomer density, $rhostar approx N/RN^d$ the self-density and $f(x)$ a universal function decaying asymptotically as $f(x) sim x^{-omega}$ with $omega = (d+2) times alpha$ where $alpha = 1/4$ for $x ll 1$ and $alpha = 1/2$ for $x gg 1$. We argue that the algebraic decay $N CN(t) sim - t^{-5/4}$ for $t ll TN$ results from an interplay of chain connectivity and melt incompressibility giving rise to the correlated motion of chains and subchains.
