Inflationary models with Gauss–Bonnet coupling in light of ACT observations
Yigan Zhu, Qing Gao, Yungui Gong, Zhu Yi
Abstract
Abstract Recent analyses combining Atacama Cosmology Telescope (ACT) data with other cosmological datasets report a higher scalar spectral index $$n_s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> , creating tension with a wide range of inflationary models. Since a Gauss–Bonnet term with a coupling function $$\xi (\phi ) = 3\lambda /[4V(\phi )]$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ξ</mml:mi> <mml:mo>(</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mi>λ</mml:mi> <mml:mo>/</mml:mo> <mml:mo>[</mml:mo> <mml:mn>4</mml:mn> <mml:mi>V</mml:mi> <mml:mo>(</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo>)</mml:mo> <mml:mo>]</mml:mo> </mml:mrow> </mml:math> leaves $$n_s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> nearly unchanged (up to a field rescaling) while reducing the tensor-to-scalar ratio r by a factor $$(1-\lambda )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:mi>λ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , so choosing $$(1-\lambda )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:mi>λ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> sufficiently small effectively removes r as a limiting observable, making it easier for inflationary models to satisfy the latest observational constraints and alleviating this tension. Applying this mechanism to chaotic inflation, E-models, T-models, and hilltop inflation, we find that broad regions of parameter space become consistent with the latest ACT-based cosmic microwave background (CMB) constraints. These results demonstrate that Gauss–Bonnet couplings can help bring a broad class of inflationary models into agreement with current CMB measurements.