Emergence and correction of cosmological inflation from deformed relativistic kinematics on curved spacetime

The acceleration of gravitational redshift observed by E. Hubble (1929) has led to the development of cosmological inflation and dark energy theories. However, there are some tensions between the theory and some recent interpretations of JWST observations. As an alternative theory, in this paper, it is shown that there is the acceleration of gravitational redshift observed by the accelerated frame judging by the decrease of the frequency of the photon over time seen from the resulted dispersion relation obtained by employing deformed relativistic kinematics on curved spacetime [Pfeifer et al. (2022)], while the Minkowskian observers see a state of static space for the same scenario. The resulted dispersion relation is calculated by employing the metric in momentum space instead of position space. Ultimately, it can be shown that it gives a new perspective on the theory of inflation.