The fate of quasi-exponential inflation in the light of ACT-DR6

Abstract We have revisited quasi-exponential model of inflation in the light of recent ACT-DR6 and Planck data along with latest constraint on the amplitude of primordial gravitational waves. For our analysis we have followed Mukhanov approach for inflationary equation-of-state employing Hamilton–Jacobi formulation. We find that the model is capable of mimicking latest Planck results by providing excellent fit to scalar spectral index and its running. Not only that, amount of primordial gravitational waves is also within the present observational bound, $$r&lt;0.032$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>0.032</mml:mn> </mml:mrow> </mml:math> . In addition to that, when the combination of ACT-DR6 and Planck joint with BICEP/Keck 2018 data is taken into account inflationary predictions from quasi-exponential model are in excellent agreement. The model also yields sublime fit to the result of joint analysis of ACT-DR6, Planck joint with BICEP/Keck 2018 and DESI-Y1 data. The futuristic CMB missions LiteBIRD, Simons Observatory and CMB-S4 are promising to detect primordial gravitational waves if $$r\ge 0.003$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>0.003</mml:mn> </mml:mrow> </mml:math> . We have also forecasted inflationary predictions from quasi-exponential model of inflation assuming the sensitivities of LiteBIRD, Simons Observatory and CMB-S4 along with combination of LiteBIRD and CMB-S4. We found that in each case quasi-exponential inflation may render excellent fit provided $$r\ge 10^{-2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>≥</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . However, non-detection of primordial gravitational waves by LiteBIRD, Simons Observatory and CMB-S4 will potentially rule out quasi-exponential model.