Reconstruction of $f(R)$ gravity models for an accelerated universe using Raychaudhuri equation

Understand

A new strategy for the reconstruction of $f(R)$ gravity models have been attempted using Raychaudhuri equation.

• Two examples, one for an eternally accelerating universe and the other for one that mimics a ${\Lambda}$CDM expansion history have been worked out.
• For both the cases, the relevant $f=f(R)$ could be found out analytically.
• In the first case, $f(R)$ is found to be a combination of power-law terms and in the expression for the second case involves hypergeometric functions.