Measurement of the power spectrum turnover scale from the cross-correlation between CMB lensing and Quaia

We use the projected clustering of quasars in the Gaia-unWISE quasar catalog, Quaia, and its cross-correlation with CMB lensing data from Planck, to measure the large-scale turnover of the matter power spectrum, associated with the size of the horizon at the epoch of matter-radiation equality. The turnover is detected with a significance of between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mn>2.3</mml:mn> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>3.1</mml:mn> <mml:mi>σ</mml:mi> </mml:mrow> </mml:math> , depending on the method used to quantify it. From this measurement, the equality scale is determined at the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>20</mml:mn> <mml:mi>%</mml:mi> </mml:mrow> </mml:math> level. Using the turnover scale as a standard ruler alone (suppressing information from the large-scale curvature of the power spectrum), in combination with supernova data through an inverse distance ladder approach, we measure the current expansion rate to be . The addition of information coming from the power spectrum curvature approximately halves the standard ruler uncertainty. Our measurement in combination with calibrated supernovae from Pantheon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mo>+</mml:mo> </mml:math> and SH0ES constrains the CMB temperature to be , independently of CMB data. Alternatively, assuming the value of from COBE-FIRAS, we can constrain the effective number of relativistic species in the early Universe to be .