In this dissertation, four different topics are investigated in high energy physics beyond the standard model. In the first chapter, diffeomorphism invariance breaking in gravity is studied in the concept of emergent symmetry, which has not been studied before in this concept. In the second chapter, this investigation is extended by studying the cosmological evolution of the scale factor in our diffeomorphism violating model. In the third chapter, a higher derivative model of four-form fields is considered. The model presents a counter-example for several accepted no-goes in the literature. Finally, in the last chapter, another commonly accepted conjecture is questioned, which assumes that the tree unitarity violation in an effective field theory determines the domain of validity of the theory and predicts the onset of new physics. It is argued that this is parametrically incorrect in the case of chiral perturbation theory and is probably theoretically incorrect in general.