  In this article, we discuss some well-known theoretical models where an
observer-independent energy scale or a length scale is present. The presence of
this invariant scale necessarily deforms the Lorentz symmetry. We study
different aspects and features of such theories about how modifications arise
due to this cutoff scale. First we study the formulation of energy-momentum
tensor for a perfect fluid in doubly special relativity (DSR), where an energy
scale is present. Then we go on to study modifications in thermodynamic
properties of photon gas in DSR. Finally we discuss some models with
generalized uncertainty principle (GUP).
