Fermions localization on de Sitter branes

Spin $1/2$ fields localization on an asymmetric ${\mathrm{dS}}_4$ scenario, where the brane interpolates between two spacetimes ${\mathrm{dS}}_5$ and ${\mathrm{AdS}}_5$, is determined. The bulk spinor is coupled to scalar field of the brane by a nonminimal Yukawa term compatible with the scenario’s geometry. We show that, independently of wall’s thickness, only one massless chiral mode is localized on the wall. The massive chiral modes follow a Schrödinger equation, whose potential has a mass gap determined by Yukawa constant, which is a generic property of this system. The fermions spectrum is defined bellow the gap, by bound states of both chiralities with the same mass, and above the gap, by a continuous spectrum with local and global resonant modes of both chiralities and different mass.

Figure 1

Plots of potentials $V_{\mathrm{L}}$ (top panel) and $V_{\mathrm{R}}$ (bottom panel) in the dS thick wall, for $\alpha =0$ (gray line), $\alpha =3$ (dashed line), and $\alpha =6$ (black line).

Figure 2

Plots of potentials $V_{\mathrm{L}}$ (solid line) and $V_{\mathrm{R}}$ (dashed line) in the ${\mathrm{dS}}_4$ thin wall.

Figure 3

A graphical solution of equations $y_{1\mathrm{L}}=y_{2\mathrm{L}}$ (black) and $y_{1\mathrm{R}}=y_{2\mathrm{R}}$ (gray) for the mass of seven bound states of chiral fermion in a dS spacetime with parameters $\beta =\alpha =5$ and Yukawa constant $\lambda =15\beta$.

Figure 4

Plots of left resonant modes for different asymmetric scenarios for fixed Yukawa constant and $|{\mathrm{\Lambda }}_{-}/{\mathrm{\Lambda }}_{+}|=1$ (gray line), $|{\mathrm{\Lambda }}_{-}/{\mathrm{\Lambda }}_{+}|=1/2$ (gray dashed line), $|{\mathrm{\Lambda }}_{-}/{\mathrm{\Lambda }}_{+}|=2/5$ (black dashed line), $3/10$ (black line).

Figure 5

Plots of right resonant modes for different asymmetric scenarios for fixed Yukawa constant and $|{\mathrm{\Lambda }}_{-}/{\mathrm{\Lambda }}_{+}|=1$ (gray line), $|{\mathrm{\Lambda }}_{-}/{\mathrm{\Lambda }}_{+}|=1/5$ (dashed line), and $|{\mathrm{\Lambda }}_{-}/{\mathrm{\Lambda }}_{+}|\sim 0$ (black line).