Proving security of an encryption scheme I have an encryption scheme $Enc(pk, m)$ which outputs ciphertext of the form $c_1 = (pk)^r, c_2 = g^r \cdot m$; where $pk$ is the public key of the form $g^a$, $a$ being the corresponding secret key. 

Is this secure?
If you are working in an order $p$ prime order group which is generated by $g$, and $a$ as well as $r$ are drawn uniformly random from $\mathbb{Z}_p$, you can prove this secure under the decisional Diffie-Hellman (DDH) assumption (what you sketch here, is often referred to as modified ElGamal in the literature).

Informally speaking, under DDH you can show that $c_1$ looks like a random value. Now, once you have shown that $c_1$ looks random, you can view $g^r$ like a one-time pad on the message. 

See Section 3 of this paper for an excellent formal treatment.