R 2 -Higgs inflation: R 3 contribution and preheating after ACT and SPT data

The <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi>R</a:mi> <a:mn>2</a:mn> </a:msup> </a:math> -Higgs inflation is one of the simplest yet best-fit models consistent with Planck data. The higher spectral index <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>n</c:mi> <c:mi>s</c:mi> </c:msub> </c:math> recently reported by the combined cosmic microwave background (CMB) data from the Atacama Cosmology Telescope (ACT), South Pole Telescope (SPT), and Planck, along with baryonic acoustic oscillation data from the Dark Energy Spectroscopic Instrument (DESI), disfavors the single-field-like regime of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msup> <e:mi>R</e:mi> <e:mn>2</e:mn> </e:msup> </e:math> -Higgs inflation at approximately <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mn>2</g:mn> <g:mi>σ</g:mi> </g:math> . Following a doubly covariant formalism, we show that the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msup> <i:mi>R</i:mi> <i:mn>2</i:mn> </i:msup> </i:math> -Higgs inflation, when modified by a dimension-six <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msup> <k:mi>R</k:mi> <k:mn>3</k:mn> </k:msup> </k:math> term, can account for the high <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi>n</m:mi> <m:mi>s</m:mi> </m:msub> </m:math> reported by <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mrow> <o:mi>CMB</o:mi> <o:mo>+</o:mo> <o:mi>BAO</o:mi> </o:mrow> </o:math> . In this regard, we find that preheating may play a pivotal role. We also show that if the nonminimal coupling between the Ricci scalar <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>R</q:mi> </q:math> and the Higgs field is <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi mathvariant="script">O</s:mi> <s:mo stretchy="false">(</s:mo> <s:mn>10</s:mn> <s:mo stretchy="false">)</s:mo> </s:math> , then preheating via the production of Higgs quanta may help explain the reported observations.