Flipped rotating axion: Baryogenesis and Dark Matter

Technical Summary: Flipped Rotating Axion: Baryogenesis and Dark Matter

Problem Statement
The paper addresses two fundamental cosmological puzzles: the origin of the baryon asymmetry of the Universe (BAU) and the nature of Dark Matter (DM). Standard baryogenesis mechanisms often require explicit $U(1)$ symmetry breaking operators, while axion dark matter models typically rely on the misalignment mechanism. The authors propose a unified scenario where a single spectator axion-like particle (ALP) generates both the BAU and constitutes the DM, without introducing explicit $U(1)$ breaking terms. The mechanism relies on a "flipped" vacuum manifold orientation at the end of inflation, driven by a non-minimal coupling to gravity.

Methodology and Model Construction
The authors construct a model based on an axion field $\phi$ with a periodic potential $V(\phi) = M^4[1 - \cos(\phi/f)]$, where $f$ is the decay constant and $M$ is the symmetry breaking scale. The axion is non-minimally coupled to gravity via the term $\gamma^2(\phi) = 1 + \xi[1 - \cos(\phi/f)]$ in the Lagrangian, preserving the discrete shift symmetry $\phi \to \phi + 2\pi f$.

The cosmological evolution is analyzed within a non-oscillatory inflationary scenario (specifically "quintessential inflation" with a runaway inflaton potential), characterized by:

1. Inflation: A period with equation of state $w = -1$.
2. Kination: A post-inflationary phase dominated by the kinetic energy of the inflaton, with $w = 1$.
3. Reheating: The transition to the radiation-dominated era.

The effective potential of the axion is derived by considering the Ricci scalar $R = 3(1-3w)H^2$. Crucially, the sign of the non-minimal coupling contribution to the effective potential flips between the inflationary phase ($w=-1$) and the kination phase ($w=1$).

Key Mechanisms and Results

1. Vacuum Flipping and Axion Rotation:
   During inflation, the effective potential is tilted such that the axion is driven to the minimum at $\phi = \pi f$. Upon the transition to kination, the sign of the curvature coupling term reverses, flipping the vacuum manifold. The axion, initially at the minimum, finds itself at the maximum of the new effective potential and begins to roll. This initiates a coherent rotation in field space ($\theta = \phi/f$).

2. Spontaneous Baryogenesis:
   The rotation of the axion field ($\dot{\theta} \neq 0$) spontaneously breaks CPT symmetry in the expanding universe. Through derivative couplings to fermion currents ($x_\psi \bar{\psi}\gamma^\mu\psi \partial_\mu \phi / f$), this rotation generates a chemical potential $\mu \sim \dot{\phi}/f$ for baryons and/or leptons. In the presence of baryon-number violating interactions in thermal equilibrium, this leads to a net baryon asymmetry. The resulting asymmetry $Y_B$ is proportional to the coupling $\xi$, the decay constant $f$, and the reheating temperature $T_{\text{reh}}$.

3. Dark Matter Production:
   The axion continues to rotate during the kination and radiation eras. Its energy density scales as $\rho_\phi \propto a^{-6}$ during kination (maintaining a constant ratio with the background) and eventually freezes when the kinetic energy becomes comparable to the bare mass potential $M^4$. Once the Hubble scale drops below the axion mass ($m_\phi \sim M^2/f$), the field begins to oscillate around the minimum ($\phi=0$), behaving as cold dark matter with $\rho_\phi \propto a^{-3}$.

4. Constraints and Stability:

   • Fragmentation: The authors analyze the risk of axion condensate fragmentation via parametric resonance. They derive a conservative bound on the non-minimal coupling $\xi \lesssim 5.3 (f/m_P)^2$ to prevent significant kinetic energy loss. Numerical investigations suggest this bound can be relaxed, allowing $\xi \sim (f/m_P)^2$.
   • Kibble Issue: To avoid the randomization of the rotation direction (clockwise vs. anticlockwise) which would lead to domain walls, the authors invoke a slight misalignment of the initial vacuum expectation value. This requires the axion mass to be small ($m_\phi \lesssim H$) during inflation, further constraining the parameter space.
   • Gravitational Waves (GW): The kination era modifies the primordial GW spectrum, enhancing high-frequency modes. The authors use Big Bang Nucleosynthesis (BBN) constraints on extra relativistic degrees of freedom ($\Delta N_{\text{eff}}$) to place a lower bound on the reheating temperature, $T_{\text{reh}} \gtrsim 2.2 \times 10^7$ GeV.

Key Findings and Parameter Space
The paper identifies a specific region of parameter space where the scenario is viable:

• Coupling: The non-minimal coupling must satisfy $\xi \sim (f/m_P)^2$.
• Mass Scale: For GUT-scale inflation ($H \sim 10^{-5} m_P$) and a decay constant $f \sim 10^{-2} m_P$, the symmetry breaking scale is $M \sim \text{keV}$, resulting in an axion mass $m_\phi \sim 10^{-20}$ eV.
• Temperatures: Successful baryogenesis and DM production are achieved with a reheating temperature $T_{\text{reh}} \sim 10^7$ GeV and a decoupling temperature for baryon-violating interactions $T_{B-L} \sim 8 \times 10^7$ GeV.

Significance and Claims
The authors claim to demonstrate a unified mechanism where the rotation of a spectator axion, induced solely by a gravitational "flip" in the vacuum manifold, simultaneously accounts for the baryon asymmetry and dark matter. The model is notable for:

• Preserving the discrete shift symmetry of the axion without explicit $U(1)$ breaking operators.
• Providing a predictive relationship between the non-minimal coupling $\xi$, the decay constant $f$, and the cosmological observables.
• Offering testable predictions via the primordial gravitational wave spectrum, which could be probed by future experiments such as BBO, U-DECIGO, and resonant cavity detectors.

The paper concludes that the condition $\xi \sim (f/m_P)^2$ is the critical requirement for the success of this "flipped rotating axion" scenario, linking the microphysics of the axion-gravity coupling to macroscopic cosmological outcomes.