Big-Bang Nucleosynthesis and WIMP dark matter in modified gravity

In the present work the primordial Big-Bang Nucleosynthesis (BBN) and weakly interacting massive particle (WIMP) dark matter are discussed in a certain class of modified gravitational theories, namely $f(R) \sim R^n$ gravity. The new gravitational model is characterized by a single parameter $n$. First we determine the conditions under which the theoretical predictions for the $^{4}$He abundance are in agreement with the observations. More precisely, during BBN the physics is known and all the parameters are known. The only free parameter to be constrained is the power $n$ related to the new gravitational model. After that, for cold dark matter we use the value of $n$ determined from the BBN considerations and determine how the mass of the dark matter particle is related to the annihilation cross section in order for the cold dark matter constraint to be satisfied.