Recent observations show that apart from the gravitational attraction, there is another force due to "dark energy" at large scales in the universe. This can be modelled in Newtonian physics by modifying the gravitational potential energy of a system of mass $M$ and $m$ separated by a distance $r$ to include a universal repulsive force
$V=-\frac{G M m}{r}-\frac{\Lambda m r^2}{6}$.
Here $\Lambda$ is a positive constant called the cosmological constant. A particle is slightly displaced away from the equilibrium point. Select the correct option.

• Correct answer
  A

  Acceleration is equal to $\Lambda$ times the displacement from the equilibrium point and away from the equilibrium point.
• B

  Particle oscillates about the equilibrium point with angular frequency $\omega=\sqrt{\Lambda / 3}$.
• C

  Equilibrium point is at $r=(6 G M / \Lambda)^{1 / 3}$.
• D

  Acceleration is equal to $\Lambda / 3$ times the displacement from the equilibrium point and towards the equilibrium point.

Hence, the correct answer is option: 'A'.