The main muscle of normal quiet breathing is the diaphragmDuring Inspiration, it contracts which causes it to flatten. This increases the volume of the thoracic cavity and so the pressure decreases. This allows air to move in along a diffusion gradient.During expiration, the diaphragm relaxes which causes it to flatten. As a result the volume of the thoracic cavity decreases and so by convention pressure increases, this causes air to move out of the lungs.However, during exercise and when coughing additional muscles are required in order to carry out the work of breathing for example, the intercostal muscles.