Probing the inflationary background of gravitational waves from large to small scales

The detection of Primordial Gravitational Waves (PGWs) is one the most important goals modern cosmology since PGWs can both provide substantial evidence for primordial inflation and shed light on its physical nature. Small scale experiments gravitational waves such as LIGO/VIRGO and, in future, LISA Einstein Telescope (ET), being sensitive to stochastic background waves, be used together with CMB data constrain inflationary parameters. In performing these analyses tensor spectrum usually parametrized a power law that includes only amplitude independent tilt. this paper, we investigate robustness assuming tilt independent. We show due huge difference scales probed by GWs data, even small dependence remarkably affect shape possibly breaking power-law assumption. When non-linear corrections are considered final constraints significantly changed. also study two different models providing an example negligible non-negligible dependence.