Minimizing the tensor-to-scalar ratio in single-field inflation models
William J. Wolf
Abstract
We revisit a class of simple single-field inflation models and demonstrate that they can readily produce a negligible tensor/scalar ratio <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>r</a:mi> </a:math> . Motivated by recent work suggesting the need to introduce higher order operators to stabilize unregulated potentials, as well as by work indicating that such terms can have significant effects on observable predictions, we explicitly construct corrected versions of the quadratic hilltop potential that are motivated by an effective field theory expansion. We employ Markov Chain Monte Carlo methods and optimization techniques to sample viable models and minimize <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>r</c:mi> </c:math> . We find that such potentials can readily lower <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>r</e:mi> </e:math> values below projected CMB-S4 sensitivity, while still remaining within observable constraints on <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>n</g:mi> <g:mi>s</g:mi> </g:msub> </g:math> . Furthermore, we find that the minimum <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>r</i:mi> </i:math> reached for each order of the expansion considered is well described by a power law <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>r</k:mi> <k:mi>min</k:mi> </k:msub> <k:mo stretchy="false">(</k:mo> <k:mi>q</k:mi> <k:mo stretchy="false">)</k:mo> <k:mo>∝</k:mo> <k:msup> <k:mi>q</k:mi> <k:mrow> <k:mo>−</k:mo> <k:mi>B</k:mi> </k:mrow> </k:msup> </k:math> before asymptoting to a value of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>r</o:mi> <o:mi>min</o:mi> </o:msub> <o:mo>∼</o:mo> <o:msup> <o:mn>10</o:mn> <o:mrow> <o:mo>−</o:mo> <o:mn>11</o:mn> </o:mrow> </o:msup> </o:math> , where <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>q</q:mi> </q:math> is the order to which the expansion of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>V</s:mi> <s:mo stretchy="false">(</s:mo> <s:mi>ϕ</s:mi> <s:mo stretchy="false">)</s:mo> </s:math> is carried out. Published by the American Physical Society 2024