[en] We study, both theoretically and experimentally, the dynamical polarizability $\mathrm{\alpha <!--\; ??\; -->}(\mathrm{\omega <!--\; ??\; -->})$ of ${\mathrm{R}\mathrm{b}}_2$ molecules in the rovibrational ground state of $a^3{\mathrm{\Sigma <!--\; ??\; -->}}_u^{+}$. Taking all relevant excited molecular bound states into account, we compute the complex-valued polarizability $\mathrm{\alpha <!--\; ??\; -->}(\mathrm{\omega <!--\; ??\; -->})$ for wave numbers up to 20 000 ${\mathrm{c}\mathrm{m}}^{-<!--\; ???\; -->1}$. Our calculations are compared to experimental results at $1064.5\mathrm{n}\mathrm{m}$ ($\sim <!--\; ???\; -->9400{\mathrm{c}\mathrm{m}}^{-<!--\; ???\; -->1}$) as well as at $830.4\mathrm{n}\mathrm{m}$ ($\sim <!--\; ???\; -->12000{\mathrm{c}\mathrm{m}}^{-<!--\; ???\; -->1}$). Here, we discuss the measurements at $1064.5\mathrm{n}\mathrm{m}$. The ultracold Rb₂ molecules are trapped in the lowest Bloch band of a 3D optical lattice. Their polarizability is determined by lattice modulation spectroscopy which measures the potential depth for a given light intensity. Moreover, we investigate the decay of molecules in the optical lattice, where lifetimes of more than $2\mathrm{s}$ are observed. In addition, the dynamical polarizability for the $X^1{\mathrm{\Sigma <!--\; ??\; -->}}_g^{+}$ state is calculated. We provide simple analytical expressions that reproduce the numerical results for $\mathrm{\alpha <!--\; ??\; -->}(\mathrm{\omega <!--\; ??\; -->})$ for all vibrational levels of $a^3{\mathrm{\Sigma <!--\; ??\; -->}}_u^{+}$ as well as $X^1{\mathrm{\Sigma <!--\; ??\; -->}}_g^{+}$. Precise knowledge of the molecular polarizability is essential for designing experiments with ultracold molecules as lifetimes and lattice depths are key parameters. Specifically the wavelength at $\sim <!--\; ???\; -->1064\mathrm{n}\mathrm{m}$ is of interest, since here, ultrastable high power lasers are available. (paper)