Primordial features as probes of baryogenesis from supersymmetric flat directions

TL;DR

The paper investigates baryogenesis via supersymmetric flat directions (Affleck–Dine mechanism) and updates the viable parameter space under current CMB baryon-density isocurvature constraints, treating inflationary fluctuations of the AD field as initial conditions. It then demonstrates that primordial features in the inflaton sector can act as a direct probe of baryogenesis models by inducing correlated sharp-feature and clock signals in both curvature and baryon-density isocurvature perturbations, revealing the presence of both light and heavy AD modes. The work analyzes two coupling scenarios—gravitational and direct/kinetic inflaton–AD interactions—and shows that primordial features can generate observable signatures, with clock signals particularly enhanced in the direct-coupling case. These results establish a framework where high-scale baryogenesis could be tested through precise measurements of the primordial perturbation spectra, linking UV physics of the early universe to accessible cosmological observables.

Abstract

The Affleck-Dine mechanism is a leading baryogenesis scenario in which scalar condensates form coherently during inflation along supersymmetric flat directions that are lifted by supersymmetry-breaking effects. We update the viable parameter space for baryogenesis using recent Cosmic Microwave Background constraints on baryon-density isocurvature perturbations, taking the quantum fluctuations of the scalar condensate generated during inflation as initial conditions. We then show that primordial features arising from the inflaton sector can serve as a unique probe of baryogenesis models, whose mechanisms are otherwise difficult to access directly due to their high energy scales. These primordial features leave correlated imprints, such as sharp feature signals and clock signals, on both the curvature and baryon-density isocurvature perturbations, providing direct evidence for the existence of both light and heavy modes involved in the Affleck-Dine mechanism.

Figures (16)

• Figure 1: The timeline of the baryogenesis scenario considered in this work. $N$ is the $e$-folding number of inflation up to a constant shift. $t$ is the physical time. We define $N_{\rm end} = t_{\rm end} = 0$ at the end of inflation where reheating of the universe starts due to the decay of inflaton $\phi$ into radiation. Reheating is assumed to be completed by the onset of the relaxation of the complex scalar $\sigma$ at $t = t_{\rm rex}$. $t =t_c \sim 1/m_\sigma$ is the time scale for which $\sigma$ enters the phase of harmonic oscillation with a constant angular velocity. $t=t_{3/2}\sim 1/m_{3/2}$ is the time scale for the $A$ term in the potential \ref{['def_UFD']} dominates over the $c_A$ term. $t_{\rm eq}$ denotes the time at matter-radiation equality around the temperature $T_{\rm eq} \approx 9.8\times 10^{-10}$ GeV. A primordial feature in the inflaton potential is present at $N = N_\ast$.
• Figure 2: [Left Panel] Snapshots of the flat-direction potential $U_{\rm FD}$ at $t=0$, $t = t_{\rm rex}$ and $t = t_c$. [Right Panel] A bird-eye view of the potential at $t = 0$. Parameters with $n = 4$, $\xi = 2$, $m_\sigma/H_I = 10^{-3}$, $\lambda = c_A = A = 1$, $\Lambda/H_I = 100$, $m_{3/2}/H_I = 10^{-6}$ and $\delta = \pi/2$ are used in these plots.
• Figure 3: The evolution of $R_0$ (left panel) and $\dot{\theta}_0$ (right panel) with $n = 4$, $\Lambda/H_I = 100$, $m_\sigma/H_I = 0.01$, $\xi = \lambda = A = 1$, $c_A = 0.1$, $\delta = \pi/2$ and $H_I = 10^{11}$ GeV. The radial mode relaxes to the conventional (unwanted) minimum at $R_0 = 0$ ($R_0 > 0$) in the case with $M_{3/2} \equiv m_{3/2}/H_I = 0.01$ ($M_{3/2} = 0.04$), respectively. The case with $M_{3/2} = 0.04$ violates the condition \ref{['condition_unwanted_VEV']}. In the left panel, the dotted line is given by \ref{['Xmin_unwanted_VEV']} and the vertical dashed line is $\tau = \tau_{\rm rex}$ given by \ref{['def_tau_rex']}.
• Figure 4: The corresponding baryon asymmetry $Y_B$ of Figure \ref{['fig.unwanted_minima']}. The case with $M_{3/2} = 0.04$ violates the condition \ref{['condition_unwanted_VEV']}.
• Figure 5: The baryon density isocurvature (BDI) perturbation with respect to the Hubble parameter of inflation $H_I$ based on the separated universe approach (Section \ref{['Sec_Separated_Universe']}) and the linear perturbation theory (Section \ref{['Sec_Linear_Perturbation']}). The dashed line is the upper bound of the BDI perturbation from the generally correlated adiabatic and isocurvature models in Planck:2018jri. The solid line for $\vert\delta\theta\vert$ is the initial value of the angular perturbation used in both methods, which differ from $I_{\rm BDI}$ by a constant ratio. The dot-dashed line is the estimation of BDI perturbation based on \ref{['Delta_theta_formalism']}. $\xi = \lambda = A = 1$ are used in the computations of these results. We use the dimensionless notations $M_\sigma\equiv m_\sigma/H_I$ and $M_{3/2} \equiv m_{3/2}/H_I$ in this plot. The corresponding angular mass is $m_\theta/H_I = 0.488$.