Constraints on scalar-induced gravitational waves up to third order from a joint analysis of BBN, CMB, and PTA data

Recently, strong evidence for a gravitational-wave background has been reported by collaborations of pulsar timing arrays (PTAs). In the framework of scalar-induced gravitational waves, we concurrently investigate the second- and third-order gravitational waves by jointly analyzing PTA data alongside big-bang nucleosynthesis and cosmic microwave background datasets. We determine the primordial curvature spectral amplitude as <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mn>0.021</a:mn><a:mo><</a:mo><a:msub><a:mi>A</a:mi><a:mi>ζ</a:mi></a:msub><a:mo><</a:mo><a:mn>0.085</a:mn></a:mrow></a:math> and the spectral peak frequency as <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:msup><b:mn>10</b:mn><b:mrow><b:mo>−</b:mo><b:mn>7.3</b:mn></b:mrow></b:msup><b:mspace width="4pt"/><b:mi>Hz</b:mi><b:mo><</b:mo><b:msub><b:mi>f</b:mi><b:mo>*</b:mo></b:msub><b:mo><</b:mo><b:msup><b:mn>10</b:mn><b:mrow><b:mo>−</b:mo><b:mn>6.3</b:mn></b:mrow></b:msup><b:mspace width="4pt"/><b:mi>Hz</b:mi></b:mrow></b:math> at a 95% confidence interval, pointing towards a mass range for primordial black holes of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:msup><e:mn>10</e:mn><e:mrow><e:mo>−</e:mo><e:mn>4.5</e:mn></e:mrow></e:msup><e:msub><e:mi>M</e:mi><e:mo>⊙</e:mo></e:msub><e:mo><</e:mo><e:msub><e:mi>m</e:mi><e:mi>PBH</e:mi></e:msub><e:mo><</e:mo><e:msup><e:mn>10</e:mn><e:mrow><e:mo>−</e:mo><e:mn>2.5</e:mn></e:mrow></e:msup><e:msub><e:mi>M</e:mi><e:mo>⊙</e:mo></e:msub></e:mrow></e:math>. Our findings suggest that third-order gravitational waves contribute more significantly to the integrated energy density than the second-order ones when <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:msub><f:mi>A</f:mi><f:mi>ζ</f:mi></f:msub><f:mo>≳</f:mo><f:mn>0.06</f:mn></f:mrow></f:math>. Furthermore, we expect future PTA projects to validate these findings and provide robust means to investigate the genesis and evolution of the universe, especially inflation. Published by the American Physical Society 2024