Theories trying to unify quantum mechanics with general relativity and many supersymmetry models predict indeed that Lorentz symmetry has to be modified at energies of the order of the Planck scale (1028 eV). If standard dispersion relations of elementary particles are modified, then the propagation and therefore also the energy spectrum of ultrahigh-energy cosmic rays can be considerably changed. We study in particular how it is possible to constrain Lorentz invariance violating terms for photons and electrons (suppressed both at first and second order of the Planck mass) improving current constraints by several orders of magnitude. The main results are summarized in the following papers: • F. Finelli and M. Galaverni, “Rotation of Linear Polarization Plane and Circular Polarization from Cosmological Pseudoscalar Fields,” arXiv:0802.4210 [astro-ph], submitted. • M. Galaverni, F. Finelli, “Systematics of Cosmic Microwave Background Polarization,” Internal Report IASF-BO 454/2007. • M. Galaverni and G. Sigl, “Lorentz Violation in the Photon Sector and Ultra-High Energy Cosmic Rays,” Phys. Rev. Lett. 100, 021102 (2008) [arXiv:0708.1737 [astro-ph]]. • M. Galaverni and G. Sigl, “Lorentz Violation and Ultrahigh-Energy Photons,” Phys. Rev. D 78, 063003 (2008) [arXiv:0807.1210 [astroph]].