Quantum-corrected $$\phi ^{4}$$ inflation in light of ACT observations

Abstract Recent measurements from the Atacama Cosmology Telescope (ACT), combined with Planck and DESI data, suggest a 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> higher than the Planck 2018 baseline, thereby placing conventional attractor-type inflationary models such as Starobinsky $$R^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> and Higgs inflation under increasing tension at the $$\gtrsim 2\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>≳</mml:mo> <mml:mn>2</mml:mn> <mml:mi>σ</mml:mi> </mml:mrow> </mml:math> level. In this work, we examine quantum-corrected $$\phi ^4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>ϕ</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:math> inflation with a non-minimal coupling to gravity. Introducing an anomalous scaling parameter $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> to capture quantum corrections to the effective potential, we derive analytic expressions for the inflationary observables $$n_s$$ <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> and r . Confronting these predictions with ACT, Planck, and BAO+lensing constraints, we demonstrate that modest values of $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> can raise $$n_s$$ <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> into the ACT-preferred range while maintaining a strongly suppressed tensor-to-scalar ratio. For instance, with $$N=60$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>60</mml:mn> </mml:mrow> </mml:math> and $$\gamma \simeq 0.006$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mo>≃</mml:mo> <mml:mn>0.006</mml:mn> </mml:mrow> </mml:math> , the model predicts $$n_s\simeq 0.974$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>≃</mml:mo> <mml:mn>0.974</mml:mn> </mml:mrow> </mml:math> and $$r\simeq 0.007$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>≃</mml:mo> <mml:mn>0.007</mml:mn> </mml:mrow> </mml:math> , in excellent agreement with current bounds. We further investigate preheating dynamics, focusing on particle production via parametric resonance in quantum-corrected $$\phi ^4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>ϕ</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:math> inflation with a non-minimal coupling to gravity. In this scenario, the inflaton $$\phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> couples to an additional scalar $$\chi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>χ</mml:mi> </mml:math> through an interaction $$g^{2}\phi ^{2}\chi ^{2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>g</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:msup> <mml:mi>ϕ</mml:mi> <mml:mn>2</mml:mn> </mml:msup>