Unified Origin of Curvature Perturbation and Baryon Asymmetry of the Universe

TL;DR

This work presents a unified scenario in which the radial component of a complex Affleck-Dine field acts as the curvaton to produce the observed curvature perturbations, while the angular component drives baryogenesis through small baryon-number violation. A novel δN-based analytical method is developed to compute the scalar power spectrum and bispectrum for polynomial curvaton potentials, including transitions between quartic and quadratic regimes. The study shows that the model can reproduce the Planck-normalized power spectrum with a negative non-Gaussianity parameter $f_{NL}$ (e.g., $f_{NL}\approx-1.5$ to $-1.6$ in benchmarks) and can generate the observed baryon asymmetry when the curvaton dominates prior to decay, with z ~ 0 isocurvature perturbations. These results offer testable predictions for future CMB and large-scale structure surveys and connect inflationary perturbations, baryogenesis, and dark matter within a single framework.

Abstract

We propose a unified framework that describes both the curvaton mechanism for generating primordial density fluctuations and the Affleck-Dine (AD) mechanism for baryogenesis. By introducing a complex scalar field (AD field) carrying a baryon/lepton number and its potential consisting of quadratic and quartic terms with a small baryon/lepton-number-violating mass term, we investigate the evolution of the scalar field during the radiation-dominated era following inflation. We set the initial conditions such that the quartic term dominates the scalar potential, and the angular component of the AD field is non-zero. We focus on a scenario where the AD field sufficiently dominates the energy density of the universe before its decay. We show that the radial component of the AD field can be identified with the curvaton to solely produce the Planck normalized scalar power spectrum while the evolution of the angular component is crucial for generating the observed baryon asymmetry of the universe. Additionally, we find that the amplitude of scalar bispectrum $f_{NL}$ is negative, which is consistent with the current Planck data and testable in future observations such as CMB-S4, LiteBIRD, LSS, and 21-cm experiments. In our estimation of the scalar power spectrum and bispectrum, we develop a novel analytical scheme for computing scalar fluctuations based on the $δN$ formalism, which allows us to deal with the evolution of curvaton with polynomial potential more accurately in comparison to the existing analytical methods.

Figures (7)

• Figure 1: Comparison between scalar power spectrum estimated by our method and analytic approach. Here we have set the parameters as: $H=10^{-5},~m=10^{-6},~t_f=10^{30}$. The choice of $t_f = 10^{30}$ corresponds to $r_d \gg 1$, such that the curvaton energy density dominates the radiation energy density at the time of decay. Our result matches with the analytic estimation (solid and dashed lines are overlapping). All dimensionful quantities are expressed in the units of $M_P = 1$.
• Figure 2: Comparison between scalar bispectrum estimated by our method and analytic approach. Our result matches with analytic estimation (solid and dashed lines are overlapping). The field values are expressed in the units of $M_P = 1$.
• Figure 3: Plot for the power spectrum's dependence on $\phi_I$ with different choices of mass while $H_I= 10^{-5}$, $\lambda = 10^{-11}$. The horizontal dotted black line denotes the Planck normalization for power spectrum, and the vertical dotted lines denotes the $\phi_I$ values required to meet this value for different choices of mass. In these plots curvaton dominates the energy density before decay. The dimensionful parameters are expressed in the units of $M_P = 1$.
• Figure 4: Plot for the bispectrum's dependence on $\phi_I$ with different choices of mass while $H_I= 10^{-5}$, $\lambda = 10^{-11}$. The vertical dotted lines denotes the required value of $\phi_I$ to match Planck normalization of power spectrum. In these plots curvaton dominates the energy density before decay. The dimensionful parameters are expressed in the units of $M_P = 1$.
• Figure 5: Plot for the power spectrum's dependence on $r_d$ while $m = 10^{-3}$, $\lambda = 10^{-11}$, $\phi_I = 3.5 \times 10^{-2}$. The dimensionful parameters are expressed in the units of $M_P = 1$. The power spectrum $P_{\zeta} = 2.1\times 10^{-9}$ can be achieved at $r_d = 40$.