Trace-anomaly driven inflation in f(T)f(T) gravity and in minimal massive bigravity

We explore trace-anomaly driven inflation in modified gravity. It is explicitly shown that in T2T2 teleparallel gravity, the de Sitter inflation can occur, although quasi de Sitter inflation happens in R2R2 gravity. Furthermore, we investigate the influence of the trace anomaly on inflation. It is found that in f(T)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 owing to the trace anomaly for smaller parameter regions in comparison with those in teleparallelism. The instability of the de Sitter inflation in T2T2 gravity and R2R2 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.