Constraints on attractor models of inflation and reheating from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>P</mml:mi> <mml:mi>l</mml:mi> <mml:mi>a</mml:mi> <mml:mi>n</mml:mi> <mml:mi>c</mml:mi> <mml:mi>k</mml:mi> </mml:math> , BICEP/Keck, ACT DR6, and SPT-3G data
John Ellis, Marcos A. G. García, Keith A. Olive, Sarunas Verner
Abstract
We analyze the latest cosmic microwave background (CMB) constraints on the scalar spectral index <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>n</a:mi> <a:mi>s</a:mi> </a:msub> </a:math> and tensor-to-scalar ratio <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>r</c:mi> </c:math> from 2018, BICEP/Keck 2018, the Atacama Cosmology Telescope Data Release 6 (ACT DR6), and the South Pole Telescope (SPT-3G) data, focusing on their implications for attractor models of inflation. We compare systematically observational bounds with theoretical predictions for both E-model ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>α</e:mi> </e:math> -Starobinsky) and T-model potentials. The observational constraints accommodate E-models with <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>α</g:mi> <g:mo>≲</g:mo> <g:mn>25</g:mn> </g:math> , with the canonical Starobinsky model ( <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>α</i:mi> <i:mo>=</i:mo> <i:mn>1</i:mn> </i:math> ) predicting <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>n</k:mi> <k:mi>s</k:mi> </k:msub> <k:mo>=</k:mo> <k:mn>0.958</k:mn> <k:mi>–</k:mi> <k:mn>0.963</k:mn> </k:math> for reheating temperatures between <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mn>100</m:mn> <m:mo>−</m:mo> <m:msup> <m:mn>10</m:mn> <m:mn>10</m:mn> </m:msup> <m:mtext> </m:mtext> <m:mtext> </m:mtext> <m:mi>GeV</m:mi> </m:math> , in good agreement with 2018 data and within the 95% CL region determined by the -ACT-SPT combination, but below the 95% confidence region of the -ACT-DESI combination. Higher reheating temperatures from near-instantaneous reheating improve the compatibility. T-models predict slightly lower <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>n</o:mi> <o:mi>s</o:mi> </o:msub> </o:math> values (0.956–0.961), in some tension with 2018 data, and we find an upper limit of <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>α</q:mi> <q:mo>≲</q:mo> <q:mn>11</q:mn> </q:math> in these models. We extend our analysis to generalized <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>α</s:mi> </s:math> -attractors with monomial potentials <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>V</u:mi> <u:mo stretchy="false">(</u:mo> <u:mi>φ</u:mi> <u:mo stretchy="false">)</u:mo> <u:mo>∝</u:mo> <u:msup> <u:mi>φ</u:mi> <u:mi>k</u:mi> </u:msup> </u:math> near the minimum, demonstrating that models with <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mi>k</y:mi> <y:mo>≥</y:mo> <y:mn>6</y:mn> </y:math> naturally predict <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msub> <ab:mi>n</ab:mi> <ab:mi>s</ab:mi> </ab:msub> <ab:mo>≃</ab:mo> <ab:mn>0.965</ab:mn> <ab:mi>–</ab:mi> <ab:mn>0.968</ab:mn> </ab:math> for typical number of <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mi>e</cb:mi> </cb:math> -folds, in better agreement with the ACT DR6 data. We also consider deformed E- and T-models, which allow significantly higher values of <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:msub> <eb:mi>n</eb:mi> <eb:mi>s</eb:mi> </eb:msub> </eb:math> for low values of <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:mi>α</gb:mi> <gb:mo>≃</gb:mo> <gb:mn>1</gb:mn> </gb:math> .