Trace-anomaly driven inflation in $f(T)$ gravity and in minimal massive
  bigravity
  We explore trace-anomaly driven inflation in modified gravity. It is
explicitly shown that in $T^2$ teleparallel gravity, the de Sitter inflation
can occur, although quasi de Sitter inflation happens in $R^2$ gravity.
Furthermore, we investigate the influence of the trace anomaly on inflation. It
is found that in $f(T)$ gravity, the de Sitter inflation can end because it
becomes unstable due to the trace anomaly, whereas also in higher derivative
gravity, the de Sitter inflation can be realized and it will be over thanks to
the trace anomaly for smaller parameter regions in comparison with those in
teleparallelism. The instability of the de Sitter inflation in $T^2$ gravity
and $R^2$ gravity (both with taking account of the trace anomaly) is examined.
In addition, we study trace-anomaly driven inflation in minimal massive
bigravity, where the contribution from the massive graviton acts as negative
cosmological constant. It is demonstrated that the de Sitter inflation can
occur and continue for long enough duration.
