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.
