Updating GUT-Scale Pole Higgs Inflation After ACT DR6

TL;DR

The study develops a GUT-scale pole Higgs inflation model (pHI) built from a uniquely fixed superpotential and two fractional shift-symmetric Kähler potentials with parameters $p$ and $N$, tuned to fit ACT DR6 data while allowing sub-Planckian inflaton values and potentially detectable tensor modes with $r$ of order $10^{-3}$–$10^{-2}$. It derives the inflationary potential $V_{ m HI}$, canonical normalization, and analytic expressions for $n_s$, $a_s$, and $r$, identifying an allowed region in the $(p,N)$ plane (roughly $1.355 ext{–}6.7$ for $p$ and $6 imes10^{-5} ext{–}0.7$ for $N$) that reproduces the data with $N_* o ext{54.7--56.8}$. The work embeds pHI into a $B-L$ MSSM framework, producing a post-inflationary sector that resolves the MSSM $ extmu$ problem via a generated $ extmu$ term and enables baryogenesis through non-thermal leptogenesis while respecting gravitino constraints. It provides a concrete, testable link between high-scale inflationary dynamics and low-energy SUSY phenomenology, with predictions for future CMB polarization experiments and gravitational-wave searches to probe the tensor-to-scalar ratio. The analysis also delineates the reheating dynamics and their impact on the baryon asymmetry and gravitino abundance, yielding a self-consistent cosmological history within the proposed GUT context.

Abstract

We consider models of chaotic inflation driven by the real parts of a conjugate pair of Higgs superfields involved in the spontaneous breaking of a grand unification symmetry at a scale assuming its value within MSSM. We combine a superpotential, which is uniquely determined by applying a continuous R symmetry, with two fractional shift-symmetric Kaehler potentials introducing two free parameters (p,N). The inflationary observables provide an excellent match to the recent ACT data for 1.355<=p<=6.7 and 6x10^-5<= N<=0.7. The attainment of inflation allows for subplanckian inflaton values and possibly detectable primordial gravitational waves with (p,N) values of order unity. A solution to the mu problem of MSSM and baryogenesis via non-thermal leptogenesis can be also accommodated by embedding the model into a B-L extension of MSSM.

Figures (4)

• Figure 1: Allowed curves in the $n_{\rm s}-r$ plane for various $p$'s shown in the legend and varying $N$ as shown along the curves. The marginalized joint $68\%$ [$95\%$] regions from P-ACT-LB-BK18 data are depicted by the dark [light] shaded contours.
• Figure 2: Allowed (shaded) region as determined by Eqs. (\ref{['data']}), (\ref{['prob']}) and (\ref{['Nmin']}) in the $p-N$ plane. Along the solid line we fix $n_{\rm s}=0.974$. The conventions adopted for the various lines are also shown.
• Figure 3: Contours yielding the central $Y_B$ in Eq. (\ref{['ybdat']}) consistently with Eqs. (\ref{['data']}), (\ref{['prob']}), (\ref{['lmb']}), (\ref{['kin']}) and (\ref{['ygdat']}) in the $N-M_{1N^c}$ and $N-T_{\rm rh}$ planes for $p=2$, $N_{\rm st}=1/3$ and various $\mu/m_{3/2}$ values indicated on the curves -- recall that $1~{\hbox{\rm EeV}}=10^{9}~{\hbox{\rm GeV}}$. The gray [light gray] segments of the lines are allowed by Eq. (\ref{['ygdat']}) for $m_{3/2}=10.6~{\hbox{\rm TeV}}$ [$m_{3/2}=13.6~{\hbox{\rm TeV}}$].
• Figure 4: The evolution of the quantities $\log\rho$ (gray dashed line), $\log\rho_{\rm R}$ (gray line), $\log |Y_L|$ (black solid line), and $\log Y_{3/2}$ (black dashed line) as functions of $\log T$ for the inputs in Eq. (\ref{['inp']}). The values of the resulting parameters found by employing our numerical or analytic formulae presented in Sec. \ref{['num']} and \ref{['an']} respectively are listed in the Table.