Perturbation growth and cosmic microwave background anisotropies in the string-like matter dominated universe

It is well known that the $\Lambda$-term is a very good candidate for the smooth component of the universe since it resolves the so-called ``$\Omega$-problem'' giving, at the same time, sufficiently large age of the universe. However, the constant $\Lambda$-term is not the only possibility. Some people consider the $\Lambda$-term varying in time according to the law $\Lambda\approx R^{-2}$. Moreover the global texture in a closed universe and the network of cosmic strings obeying the same law of variation ($\rho\approx R^{-2}$) seem to be good candidates as well. We call the ``exotic'' form of matter scaling according to this law -- string-like matter. In the paper we discuss perturbation growth and anisotropies of the CMB in the string-like dominated universe. One can show that the perturbations cannot grow in the curvature dominated universe. Since the energy density of the string-like matter scales with the expansion in the same way as the curvature term one asserts that the perturbations cannot grow in the string-like matter dominated universe either. We find this generally accepted statement not quite correct and one of the purposes of the paper is to clear up this point. The second purpose of the paper is to check whether the eventual existence of the string-like matter may have an impact on the large-angular-scale anisotropies of the CMB. We show that such exotic matter has no effect on the value of the anisotropy amplitude $\delta T/T(theta).$