Detecting a Gravitational-Wave Background from Inflation with Null Energy Condition Violation: Prospects for Taiji

The null energy condition (NEC) is a fundamental principle in general relativity, and its violation could leave discernible signatures in gravitational waves (GWs). A violation of the NEC during the primordial era would imprint a blue-tilted spectrum on the stochastic gravitational wave background (SGWB) at nanohertz frequencies, potentially accounting for the recently detected signal by pulsar timing arrays. Remarkably, models of NEC violation during inflation also predict a nearly scale-invariant GW spectrum in the millihertz frequency range, which could be detectable by upcoming space-based GW detectors such as Taiji. The observation of this distinctive spectrum would provide compelling evidence for new physics beyond the standard cosmological paradigm. In this study, we explore Taiji's ability to detect an SGWB arising from NEC violation during inflation, considering various foregrounds and noise sources, including an extragalactic foreground from binary black hole mergers throughout the universe, a galactic foreground from white dwarf binaries, and the intrinsic noise of the Taiji detector. Employing comprehensive Bayesian parameter estimation techniques to analyze simulated Taiji data, we demonstrate a remarkable precision improvement of three orders of magnitude compared to the NANOGrav 15-year data set for measuring the tensor power spectrum amplitude, $P_{T,2}$, during the second inflationary stage. This substantial enhancement in measurement capabilities underscores Taiji's potential as a powerful probe for investigating the NEC violation in the early Universe.