The fate of Quasi-Exponential inflation in the light of ACT-DR6

TL;DR

The paper assesses quasi-exponential inflation (QEI) within a Mukhanov parametrization and Hamilton-Jacobi framework, confronting it with ACT-DR6, Planck BK18, and DESI-Y1 data. It derives analytic expressions for observables in terms of a single parameter $\alpha$ and the number of e-folds $N$, showing QEI can fit $n_S$ and its running while keeping $r$ below current bounds, though it generically predicts $r\gtrsim 0.01$. Confrontations with Planck and ACT-DR6 data yield viable $\alpha$ ranges (e.g., $\alpha$ up to about 3.5 for certain $N$) and demonstrate excellent agreement with joint analyses, while forecasts for LiteBIRD, SO, and CMB-S4 reveal that a future non-detection of primordial gravitational waves could rule out QEI. Overall, QEI remains a viable inflationary scenario under present data and will be decisively tested by upcoming CMB missions that probe $r$ down to $\sim 10^{-3}$–$10^{-2}$.

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, $r<0.032$. 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 $r\geq0.003$. 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 $r\geq10^{-2}$. However, non-detection of primordial gravitational waves by LiteBIRD, Simons Observatory and CMB-S4 will potentially rule out quasi-exponential model.

Figures (21)

• Figure 1: The variation of $\Delta \phi$ in the unit of Planck mass, $m_P$, with the model parameter $\alpha$ for three different values of $N$.
• Figure 2: Variation of $H_0$ in the unit of reduced Planck mass, $M_P$, with the model parameter $\alpha$ for two different values e-foldings, $N=50,\ 60$.
• Figure 3: Variation of $r$ with the model parameter $\alpha$ for two different values e-foldings, $N=50,\ 60$. The shaded area corresponds to the region where $r<0.032$.
• Figure 4: Variation of lower bound of $r$ with the number of e-folding.
• Figure 5: Variation of scalar spectral index, $n_{_S}$, with the model parameter $\alpha$ for two different values e-foldings, $N=50,\ 55, \ 60$. The yellow shaded region corresponds to the 1-$\sigma$ constraint on spectral index from Planck-2018 result ade2021improved.