Boson mixing and flavor oscillations in curved spacetime

We develop a quantum field theory of boson mixing in curved space. We derive new general oscillation probabilities and prove that the formalism correctly reproduces the flat space limit. We explicitly compute the oscillation formulas for two cosmologically relevant Friedmann-Lemaitre-Robertson-Walker metrics.

Figure 1

Plots of the oscillation formula for a Universe with de Sitter expansion, as a function of conformal time $\eta$. Masses and momenta are expressed in units of $H_0$ and $\eta ,{\eta }_0$ in units of $H_0^{-1}$. The blue solid line corresponds to $m_1=10$, $m_2=20$, $k=1$, the orange dashed line to $m_1=5$, $m_2=10$, $k=1$ and the green dot-dashed line to $m_1=3$, $m_2=6$ and $k=1$. The mixing angle is chosen as ${\sin }^{2}2\theta =0.861$ and the reference time as ${\eta }_0=-20.1$.

Figure 2

Plots of the oscillation formula for a Universe dominated by radiation, as a function of conformal time $\eta$. Masses and momenta are expressed in units of $a_0^2$ and $\eta ,{\eta }_0$ in units of $a_0^{-2}$. The blue solid line corresponds to $m_1=2$, $m_2=4$, $k=4$, the green dashed line to $m_1=5$, $m_2=10$, $k=2$ and the red dot-dashed line to $m_1=1$, $m_2=2$ and $k=1$. The mixing angle is chosen as ${\sin }^{2}2\theta =0.861$ and the reference time as ${\eta }_0=0.1$.