Confronting Mukhanov Parametrization of Inflationary Equation-of-State with ACT-DR6

TL;DR

The paper tests Mukhanov's equation-of-state parametrization for inflation, $1+ω=\frac{β}{(N+1)^α}$, against the latest ACT-DR6 data using a Hamilton-Jacobi approach and assesses its compatibility with Planck-2018, DESI-Y1, and BK18 constraints. By relating the EOS to the scalar-field potential and deriving observables such as $n_s$ and $r$, the authors constrain the two parameters $α$ and $β$ and examine how future tensor-mode detections (LiteBIRD, CMB-S4) would sharpen these bounds. They find that the EOS framework provides a wide, data-compatible parameter space, with $α$ primarily tied to $n_s$ and $β$ to the tensor amplitude $r$, and that non-detections of primordial gravity waves would significantly narrow the viable $β$ range while leaving $α$ comparatively stable. The joint ACT-DR6+Planck+DESI-Y1 data tend to favor $α$ in the ~1–2 range (Starobinsky/α-attractors) and disfavor very large $α$ (hilltop) models, though monomial $α\approx1$ can re-enter viability for small $β$ under the joint constraints. Overall, Mukhanov's EOS remains compatible with current data and future CMB missions, with gravity-wave non-detections playing a crucial role in tightening the parameter space.

Abstract

We provide a simple yet effective semi-analytical approach to confront Mukhanov Parametrization of inflationary equation-of-state, $1+ω=\fracβ{({N}+1)^α}$, with the latest ACT-DR6 data employing Hamilton-Jacobi formulation. We find that equation-of-state formalism comes up with excellent fit to the latest data. In the process we are also able to put stringent constraint on the two model parameters. In order to get the bounds of $α$ and $β$ we have also made use of the recent finding $r<0.032$. We have further utilized results from the joint analysis of ACT-DR6, Planck-2018 and DESI-Y1 data to find the observationally viable region for $α$ and $β$. We have also employed the predictions on primordial gravity waves from forthcoming CMB missions in the likes of CMB-S4 and LiteBIRD along with results from the combination of ACT-DR6, Planck-2018 and DESI-Y1 data to further restrict the model parameters. We find that detection of gravity waves would help us narrow the viable parameter space for Mukhanov parametrization. But in the absence of detection of primordial gravity waves signal by those CMB missions parameter space is reduced significantly for $β$, while the range for $α$ is slightly increased. In addition we observe that, $α$ is primarily dependent on the observationally viable range for scalar spectral index while other model parameter $β$ is resting heavily on the restriction upon the amplitude of primordial gravity waves. We find that equation-of-state formalism has a wide range of parameter values consistent with recent observational data set along with futuristic CMB missions in the likes of CMB-S4 and LiteBIRD.

Figures (16)

• Figure 1: Constraints on the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ from Planck 2018. The cyan and magenta shaded regions denote the $68\%$ and $95\%$ confidence contours from Planck+Lensing+BAO and Planck+Lensing+BAO+BK18, respectively. The dashed curves correspond to predictions of the EOS inflation model for different values of the parameter $\alpha$ and fixed $N=50, \ 60$. For each fixed value of $\alpha$, there exists a corresponding range of $\beta$ values for which the observational predictions of the EOS model remain consistent with the Planck 2018 data.
• Figure 2: Variation of $\beta_{\rm Max}$ with the model parameter $\alpha$ for $N=50$ (solid red line) and $N=60$ (dashed blue curve). For the plot we have considered the constraint on scalar spectral index (2-$\sigma$ upper/lower bound) from Planck-2018 result along with $r<0.032$.
• Figure 3: Constraints on the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ from Planck-2018 analysis in combination with Lensing, BAO and BK18. The cyan and magenta shaded regions denote the $68\%$ and $95\%$ confidence contours from Planck+Lensing+BAO and Planck+Lensing+BAO+BK18, respectively. The dashed curves correspond to predictions of the EOS inflation model for different fixed values of the parameter $\alpha$ and fixed $N=50, \ 60$, while varying $\beta$ within its allowed range $0.003\leq0.032$ as predicted by LiteBIRD. For each fixed value of $\alpha$, there exists a corresponding range of $\beta$ values for which the observational predictions of the EOS model remain consistent with the Planck 2018 data and LiteBIRD sensitivity for a detection of primordial gravitational waves.
• Figure 4: Variation of $\beta$ with the model parameter $\alpha$ for $N=50$ and $N=60$. For the plot we have considered the constraint on primordial gravity waves $0.003<r<0.032$ from the sensitivity of futuristic space mission LiteBIRD and along with the recent bound from Planck+Lensing+BAO+BK18 results. Shaded region corresponds to the observationally viable range for $\beta$.
• Figure 5: The cyan and magenta shaded regions as before denote the $68\%$ and $95\%$ confidence contours from Planck+Lensing+BAO and Planck+Lensing+BAO+BK18, respectively. The dashed curves correspond to predictions of the EOS inflation model for different values of the parameter $\alpha$ and fixed $N=50, \ 60$ (Left and Right Panel respectively). The Lower limit of $\beta$ has been set from the LiteBIRD sensitivity for non-detection of primordial gravitational waves $r<0.002$.