  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 ($16 \le N \le 8192$), $\RN\sim N^{1/2}$ the typical chain size,
$\TN\sim N^2$ 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.
