**Core Concept**
The question is testing the knowledge of laryngeal muscles involved in vocal cord movement. The abductor muscles are responsible for opening the glottis, allowing air to enter the lungs during inspiration. In the context of this question, the specific muscle to identify is the one responsible for abducting (moving apart) the vocal cords.

**Why the Correct Answer is Right**
The correct answer is the posterior cricoarytenoid muscle, which is the only abductor of the vocal cords. This muscle is innervated by the recurrent laryngeal nerve, a branch of the vagus nerve (cranial nerve X). The posterior cricoarytenoid muscle acts on the arytenoid cartilages, causing them to rotate and move the vocal cords apart, thereby opening the glottis. This action is crucial for inspiration, as it allows air to enter the lungs.

**Why Each Wrong Option is Incorrect**
* **Option A:** The thyroarytenoid muscle is primarily an adductor of the vocal cords, not an abductor. It also helps to relax the vocal cords.
* **Option B:** The cricothyroid muscle is an adductor of the vocal cords, but it also helps to stretch and elongate the vocal cords, changing their tension.
* **Option D:** The lateral cricoarytenoid muscle is an adductor of the vocal cords, not an abductor. It helps to rotate the arytenoid cartilages and move the vocal cords together.

**Clinical Pearl / High-Yield Fact**
The posterior cricoarytenoid muscle is the only abductor of the vocal cords and is responsible for opening the glottis during inspiration. This muscle is also the only muscle innervated by the recurrent laryngeal nerve.

**Correct Answer:** C. Posterior cricoarytenoid muscle