Probing the bounce energy scale in bouncing cosmologies with pulsar timing arrays

Abstract In this work, we constrain the bounce energy scale $$\rho _{s\downarrow }^{1/4}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>ρ</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>↓</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> in a generic bouncing-cosmology framework using the probable nanohertz stochastic gravitational-wave signal from NANOGrav 15-year, EPTA DR2, PPTA DR3, and IPTA DR2. A full Bayesian fit to the analytic stochastic-GW spectrum, for the first time, reveals two distinct posterior branches in $$\bigl (\rho _{s\downarrow }^{1/4},\,w_{1}\bigr )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> </mml:mrow> <mml:msubsup> <mml:mi>ρ</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>↓</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>,</mml:mo> <mml:mspace/> <mml:msub> <mml:mi>w</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> : one near $$w_{1}\approx 0.3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>w</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>≈</mml:mo> <mml:mn>0.3</mml:mn> </mml:mrow> </mml:math> and another at $$w_{1}\gg 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>w</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>≫</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , where $$w_{1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>w</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> is the contraction-phase equation of state. We find that current PTA data strongly favor the bounce hypothesis over six conventional SGWB sources, while yielding smaller Bayes factors than its parent dual inflation–bounce scenario as the bounce scale is explicit. Both branches imply $$\rho _{s\downarrow }^{1/4}&gt;M_\textrm{pl}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>ρ</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>↓</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>&gt;</mml:mo> <mml:msub> <mml:mi>M</mml:mi> <mml:mtext>pl</mml:mtext> </mml:msub> </mml:mrow> </mml:math> , indicating a trans-Planckian probe. In particular, the $$w_{1}\gg 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>w</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>≫</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> branch violates the dominant energy condition, motivating novel early-Universe physics. These results, confirmed by an accelerated machine learning approach, offer a rare observational window into UV completions of cosmology.