Confronting Inflation and Reheating with Observations: Improved Predictions

TL;DR

This work confronts inflation and reheating by solving the full inflaton dynamics numerically, going beyond slow-roll to yield precise predictions for the observables $n_s$ and $r$ and for the reheating parameters $N_{ ext{re}}$ and $T_{ ext{re}}$. By applying the method to $oldsymbol{ ext{alpha-attractor}}$ models and power-law potentials, the authors demonstrate that numerical evolution breaks degeneracies inherent in slow-roll analyses and can shift model viability under current data from ACT, Planck, BICEP/Keck, and DESI. The study also shows that numerical reheating predictions tighten constraints on the inflaton decay rate $oldsymbol{\Gamma}$ through tighter $T_{ ext{re}}$ bounds, and it differentiates reheating histories that appear degenerate in the slow-roll framework. Overall, the numerical approach provides a more robust connection between inflationary dynamics and the subsequent thermal history, with direct implications for early-universe phenomenology and observational viability of specific models.

Abstract

Using the latest observational data, we constrain the inflationary dynamics and the subsequent reheating epoch. Predictions for both phases can be significantly improved by employing numerically computed results compared to the slow-roll approximations. These results enable a more accurate reassessment of the observational viability of inflationary models, provide tighter constraints on the reheating history, and help lift the degeneracies in the predictions of inflation and reheating dynamics. Given current observational bounds, this enables a more accurate understanding of the early universe physics.

Figures (6)

• Figure 1: Evolution of the comoving Hubble radius from $a_k$ to $a_0$, illustrating the phases of inflation, reheating, and standard expansion. The dotted line corresponds to instantaneous reheating with an effective equation-of-state parameter $w_{\phi} = 1/3$. The post-inflationary evolution of the universe influences the present-day horizon scale, necessitating that viable reheating histories be consistent with current observations Liddle2003.
• Figure 2: Predictions for reheating from the E-model ($\alpha=10$), T-model ($\alpha=10$), and power-law inflation model (top to bottom) are shown, where within each panel the solid line denotes the slow-roll approximation, with red and blue curves corresponding to inflation endpoints defined by $\epsilon_V=1$ and $\epsilon_1=1$, respectively, and dashed lines represent the numerical results. The dark blue band is the 1$\sigma$ constraint on $n_s$ from the P-ACT-LB-BK18 data, while the light blue band shows the 2$\sigma$ constraint. The black dashed line denotes the upper bound on $T_{\mathrm{re}}$, corresponding to instantaneous reheating with $N_{\mathrm{re}}=0$. The dark yellow and light yellow regions correspond to the lower bounds of $T_{\mathrm{re}}$ from BBN Hasegawa:2019jsaHannestad:2004pxDeBernardis:2008zzdeSalas:2015glj and the electroweak (EW) scale, respectively. The region shaded in red are the parameter space of $N_{\mathrm{re}}$ that excluded by Big Bang nucleosynthesis (BBN) requirements by using Eq. (\ref{['eq.19']}).
• Figure 3: Predictions for the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$ in $\alpha$-attractor inflation models, comparing the slow-roll approximation (solid lines) and numerical results (dashed lines). The left panel shows E- and T-models with $n=1$ and varying $\alpha$, while the right panel shows E,T-models with $\alpha=10$ for varying $n$. The shaded regions denote the 2$\sigma$ (light blue) and 1$\sigma$ (dark blue) confidence contours from the combined P-ACT-LB-BK18 dataset.
• Figure 4: Predictions for reheating in $\alpha$-attractor inflation models at $n=1$ ($w_{\phi}=0$), as $\alpha$ varies. The left panel shows results for the E-model, while the right panel shows those for the T-model. In both figures, solid curves represent results under the slow-roll approximation, and dashed curves denote numerical results. The values $\alpha=1$, $10$, and $100$ correspond to red, orange, and blue, respectively.
• Figure 5: The inflationary potentials for the E-model with $\alpha=2$, $n=1$ (blue) and Fibre Inflation (brown).