  The pulsar timing array (PTA) collaborations have recently reported
compelling evidence for the presence of a stochastic signal consistent with a
gravitational-wave background. In this letter, we combine the latest data sets
from NANOGrav, PPTA and EPTA collaborations to explore the cosmological
interpretations for the detected signal from first-order phase transitions,
domain walls and cosmic strings, separately. We find that the first-order phase
transitions and cosmic strings can give comparable interpretations compared to
supermassive black hole binaries (SMBHBs) characterized by a power-law
spectrum, but the domain wall model is strongly disfavored with the Bayes
factor compared to the SMBHB model being 0.009. Furthermore, the constraints on
the parameter spaces indicate that: 1) a strong phase transition at
temperatures below the electroweak scale is favored and the bubble collisions
make the dominant contribution to the energy density spectrum; 2) the cosmic
string tension is $G \mu \in [1.46, 15.3]\times 10^{-12}$ at $90\%$ confidence
interval and a small reconnection probability $p<6.68\times 10^{-2}$ is
preferred at $95\%$ confidence level, implying that the strings in
(super)string theory are strongly favored over the classical field strings.
