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+LCDM. 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 LCDM model: a stiff component (w=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, as precision cosmology demands. 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 blue 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.