  We investigate cosmological evolution and implications of cosmic strings with
time-dependent tension. We derive basic equations of time development of the
correlation length and the velocity of such strings, based on the one scale
model. Then, we find that, in the case where the tension depends on some power
of the cosmic time, cosmic strings with time-dependent tension goes into the
scaling solution if the power is lower than a critical value. We also discuss
cosmic microwave background anisotropy and matter power spectra produced by
these strings. The constraints on their tensions from the Wilkinson microwave
anisotropy probe (WMAP) three year data and Sloan digital sky survey (SDSS)
data are also given.
