  A class of exact solutions of the geodesic equations in (anti-)de Sitter
AdS$_4$ and dS$_4$ spacetimes is presented. The geodesics for test particles in
AdS$_4$ and dS$_4$ spacetimes are respectively sinusoidal and hyperbolic sine
world lines. The world line for light rays is straight lines as known. In
particular, the world lines of test particles are not dependent on their
energy. Spontaneous symmetry breaking of AdS$_4$ spacetime provides a physical
explanation for arising of the virtual particle and antiparticle pairs in
vacuum. Interestingly, the energy of a pair and the time its particles moving
along their geodesics can be related by a relation similar to Heisenberg
uncertainty one pertaining quantum vacuum fluctuations. The sinusoidal
geodesics of AdS$_4$ spacetime can describe the world lines of the virtual
particles and antiparticles. The hyperbolic sine geodesics of dS$_4$ spacetime
can explain why galaxies move apart with positive accelerations.

General Relativity and Quantum Cosmology