Revisiting polynomial hybrid inflation: Planck and ACT compatibility via radiative corrections

We investigate the impact of one-loop radiative corrections in a nonsupersymmetric model of hybrid inflation with a chaotic (polynomial-like) potential, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>V</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>ϕ</a:mi> <a:mo stretchy="false">)</a:mo> <a:mo>=</a:mo> <a:msub> <a:mrow> <a:mi>V</a:mi> </a:mrow> <a:mrow> <a:mn>0</a:mn> </a:mrow> </a:msub> <a:mo>+</a:mo> <a:msub> <a:mrow> <a:mi>λ</a:mi> </a:mrow> <a:mrow> <a:mi>p</a:mi> </a:mrow> </a:msub> <a:msup> <a:mrow> <a:mi>ϕ</a:mi> </a:mrow> <a:mrow> <a:mi>p</a:mi> </a:mrow> </a:msup> </a:mrow> </a:math> , in the light of the latest constraints from and Atacama Cosmology Telescope (ACT) observations. Here, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>V</e:mi> <e:mn>0</e:mn> </e:msub> </e:math> denotes the energy scale of inflation, and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>λ</g:mi> <g:mi>p</g:mi> </g:msub> </g:math> is a coupling associated with the polynomial term of power <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>p</i:mi> </i:math> . These corrections can naturally arise from couplings of the inflaton to other matter fields, which also facilitate the reheating process. At the tree level, the predictions of such models for the scalar spectral index <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:math> and the tensor-to-scalar ratio <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>r</m:mi> </m:math> typically lie outside the current observational bounds. However, incorporating one-loop radiative corrections modifies the potential to <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mrow> <o:mi>V</o:mi> <o:mo stretchy="false">(</o:mo> <o:mi>ϕ</o:mi> <o:mo stretchy="false">)</o:mo> <o:mo>=</o:mo> <o:msub> <o:mrow> <o:mi>V</o:mi> </o:mrow> <o:mrow> <o:mn>0</o:mn> </o:mrow> </o:msub> <o:mo>+</o:mo> <o:msub> <o:mrow> <o:mi>λ</o:mi> </o:mrow> <o:mrow> <o:mi>p</o:mi> </o:mrow> </o:msub> <o:msup> <o:mrow> <o:mi>ϕ</o:mi> </o:mrow> <o:mrow> <o:mi>p</o:mi> </o:mrow> </o:msup> <o:mo>+</o:mo> <o:mi>A</o:mi> <o:msup> <o:mrow> <o:mi>ϕ</o:mi> </o:mrow> <o:mrow> <o:mn>4</o:mn> </o:mrow> </o:msup> <o:mi>ln</o:mi> <o:mo stretchy="false">(</o:mo> <o:mi>ϕ</o:mi> <o:mo>/</o:mo> <o:mi>μ</o:mi> <o:mo stretchy="false">)</o:mo> </o:mrow> </o:math> , where <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>A</u:mi> </u:math> characterizes the strength of the inflaton’s coupling to other fields, and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi>μ</w:mi> </w:math> is an appropriate renormalization scale. This radiatively corrected potential can reconcile the model with the combined <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mrow> <y:mi>Planck</y:mi> <y:mo>+</y:mo> <y:mi>ACT</y:mi> </y:mrow> </y:math> data over a suitable range of parameter space explored in this work. In particular, radiative corrections from fermionic loops ( <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mi>A</ab:mi> <ab:mo>&lt;</ab:mo> <ab:mn>0</ab:mn> </ab:math> ) suppress the tensor-to-scalar ratio <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mi>r</cb:mi> </cb:math> , while simultaneously yielding a red-tilted spectrum with <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:mo>&lt;</eb:mo> <eb:mn>1</eb:mn> </eb:math> , even for sub-Planckian field excursions. This brings the prediction in line with current observations, while still allowing for potentially detectable signatures of primordial gravitational waves. Furthermore, the inflaton’s couplings enable successful reheating and naturally accommodate nonthermal leptogenesis, providing a unified framework for inflation and baryogenesis.