Mutated hilltop inflation in light of Planck/ACT observations

TL;DR

The paper tests mutated hilltop inflation, with potential $V(\phi)=V_0[1-\mathrm{sech}(\alpha\phi)]$, against the latest $r$-$n_s$ data from Planck, BK18, and ACT, integrating reheating, the radiation-dominated era, and relic gravitational waves to constrain the model further. It derives and utilizes the relations for reheating parameters $N_{\rm re}$, $T_{\rm re}$, and $\omega_{\rm re}$, and links them to the end of inflation through $N$ and $\alpha$, including a model-dependent bound $\alpha\le 1.485$ from oscillation dynamics. The analysis finds that Planck+BK18 requires $44.4\le N\le 56$ and $0.161\le\alpha\le 0.890$ (95% CL), while including ACT tightens to $54\le N\le 56$ with $0.29\le\alpha\le 0.62$ (95% CL); the RD era does not significantly modify these bounds. Relic GW spectra are computed and shown to be potentially detectable for certain $(N,\alpha)$ combinations by future detectors (BBO/DECIGO/LISA/SKA/ET/CE), providing an independent observational test of the model and underscoring the value of combining CMB, reheating, RD, and GW constraints in precision cosmology.

Abstract

Here, a single field inflationary model driven by a mutated hilltop potential, a subclass of the hilltop models of inflation, is investigated. To constrain the parameter space, we employ the latest $r-n_{\rm s}$ constraints from Planck 2018, BICEP/Keck 2018, and the Atacama Cosmology Telescope (ACT) data, alongside reheating parameters $N_{\rm{re}}$, $T_{\rm{re}}$, and $ω_{\rm{re}}$, and the model independent bound on the radiation dominated (RD) era $N_{\rm{rd}}$. Furthermore, the relic gravitational wave (GW) spectrum within the sensitivity domains of future GW detectors are analyzed. By combining CMB, reheating, RD era, and GW constraints, we find for the Planck+BK18 data that the inflationary duration is confined to $46 \leq N \leq 56$ (95\% CL) and $48.1 \leq N \leq 56$ (68\% CL). Moreover, the model parameter $α$ is confined to $0.161 \leq α\leq 0.890$ (95\% CL) and $0.217 \leq α\leq 0.815$ (68\% CL). Inclusion of the ACT data further tighten the constraints to $54 \leq N \leq 56$ (95\% CL) and $0.29 \leq α\leq 0.62$ (95\% CL), thereby enhancing the precision and robustness of the model predictions.

Figures (8)

• Figure 1: Evolutions of (a) the scalar field $\phi$, (b) the Hubble parameter $H$, (b) the first slow-roll parameter $\epsilon_{\rm H}$, and (d) the second slow-roll parameter $\eta_{\rm H}$ for different values of $\alpha$. The green, brown, black, and red lines represent $\alpha = 0.1, 0.5, 1$ and $1.5$, respectively. Also the dashed curve in each panel corresponds to $\alpha_{\rm eq}=0.83$. The end of inflation is set at $N=0$.
• Figure 2: Tensor-to-scalar ratio $r$ versus the scalar spectral index $n_{\rm s}$ for different $\alpha$ and various numbers of $e$-folds $N$. The red, green, orange, blue, and yellow curves correspond to $N=45,~50,~55,~60$ and $65$, respectively. The dark (light) green area represents the 68% (95%) CL from the Planck 2018 TT, TE, EE + LowE + Lensing data, while the dark (light) blue regions show the 68% (95%) CL from the combined Planck 2018 + BK18 + BAO dataset. The dark (light) purple area in the background corresponds to the 68% (95%) CL constraints from the ACT data (Planck 2018 + BK18 +ACT). The parameter $\alpha$ varies from 0 at the top to 5 at the bottom along each curve.
• Figure 3: Variation of the equation of state parameter, $\omega_{\rm re}$, versus the model parameter, $\alpha$. The lower bound of $\omega_{\rm re}$ at $-1/3$ is shown as a horizontal dashed line, while the upper bound of $\alpha$ at $1.485$ is denoted by a vertical line. The shaded region represents disallowed values of $\omega_{\rm re}$.
• Figure 4: Variations of $N_{\rm re}$ vs (a, b) $n_{\rm s}$, (c, d) $\alpha$, and (e) $\omega_{\rm re}$. The dark (light) blue regions in panels (a) and (b) denote the 68% (95%) CL from the Planck 2018 + BK18 + BAO data and from the combined Planck 2018 + BK18 + BAO + ACT dataset, respectively. The light green shaded regions in panels (c)-(d) indicate the model independent bounds on $N_{\rm re}$ for $\omega_{\rm re}=0$ while the similar region in panel (e) corresponds to the model independent bound on $N_{\rm re}$ for $-1/3\leq\omega_{\rm re}<0$.
• Figure 5: Variations of the reheating temperature $T_{\rm re}$ versus (a, b) the scalar spectral index $n_{\rm s}$, and (c, d) the model parameter $\alpha$. The shaded blue regions in panels (a) and (b) are the same as in Fig. \ref{['Nre_ns']}. The light green region in panels (c) and (d) indicate the allowed range of $T_{\rm re}$ from the model independent constraint in Eq. (\ref{['eq:Tre MIB']}). The horizontal black dashed line represents the maximum allowed reheating temperature $T_{\rm re}^{\rm max}=5\times 10^{15}~\rm GeV$, while the bottom hatched area corresponds to the BBN constraint.