  The pulsar timing array (PTA) collaborations have recently suggested the
presence of a gravitational wave background at nano-Hertz frequencies. In this
paper, we explore potential inflationary interpretation of this signal within
the context of a simple and health parity-violating gravity model termed the
Nieh-Yan modified Teleparallel Gravity. Through this model, two inflationary
scenarios are evaluated, both yielding significant polarized primordial
gravitational waves (PGWs) that align well with the results from PTA
observations. Furthermore, the resulting PGWs can display strong circular
polarization and significant anisotropies in the PTA frequency band, which are
distinct features to be verified by observations of both PTA and the cosmic
microwave background.The detection of such a distinctive background of PGWs is
expected to provide strong evidence supporting our scenarios and insights into
inflationary dynamics and gravity theory.
