Precision cosmology and the stiff-amplified gravitational-wave background from inflation: NANOGrav, Advanced LIGO-Virgo and the Hubble tension

The recent NANOGrav finding of a common-spectrum process has invited interpretations as possible evidence of a primordial stochastic gravitational-wave background (SGWB) stronger than predicted by standard inflation + Lambda CDM. Such an SGWB would contribute an extra radiation component to the background Universe which may affect its expansion history. As such, it may help alleviate the current Hubble tension, a novel connection between gravitational waves and cosmology. We demonstrate this by considering a cosmological model, the standard inflation + stiff amplification scenario, with two components added to the base-Lambda CDM model: a stiff component (w equivalent to p/rho = 1) and the primordial SGWB. Previously, we showed that even for standard inflation, the SGWB may be detectable at the high frequencies probed by laser interferometers, if it is amplified by a possible early stiff era after reheating. Models that boost the SGWB enough to cause significant backreaction, however, must still preserve the well-measured radiation-matter equality, respecting the demands of precision cosmology. For that, we calculate the fully-coupled evolution of the SGWB and expansion history, sampling parameter space (tensor-to-scalar ratio, reheating temperature and temperature at stiff-to-radiation equality). We then perform a joint analysis of the NANOGrav results and latest upper bounds from Planck, big bang nucleosynthesis and Advanced LIGO-Virgo, to constrain the model. The resulting blue-tilted, stiff-amplified SGWB is still too small to explain the NANOGrav results. However, if someday, Advanced LIGO-Virgo detects the SGWB, our model can explain it within standard inflation (without requiring an initial spectral tilt). Meanwhile, this model may bring current high-z measurements of the Hubble constant within 3.4 sigma of the low- z measurements by SH0ES (from 4.4 sigma) and within 2.6 sigma of those by H0LiCOW (from 3.1 sigma), reducing the tension.

Automated summary

The study suggests that the SGWB may influence the expansion history of the Universe and possibly alleviate the current Hubble tension, but models amplifying the SGWB must consider the demands of precision cosmology. The resulting blue-tilted, stiff-amplified SGWB is still too small to explain the NANOGrav results, but if Advanced LIGO-Virgo detects the SGWB, the model may be able to explain it.