Abstract:
The thesis mainly deals with the effect of the invariant ultraviolet scale on the
thermodynamics of the ideal gases such as photon and degenerate Fermi gas.
Incorporating another invariant scale say κ in the known relativistic theory gives us an ultraviolet cut-off on energy/momentum of the particle and a modified dispersion relation. When such an effective theory was used to study the equilibrium properties of the photon gas we found the various thermodynamic quantities to be lower than the usual SR value. We get the modified Stefan-Boltzmann law and the equation of state. We have also considered the most general modification in the phase-space at Planck scale where new exotic spacetime is expected to appear. This leads to the modified Planck’s energy density distribution and modified Wien’s law. As expected, from the correspondence principle, we get the usual results in the SR limit. Very peculiarly we noted that the results are nonperturbative in the SR limit, which seems to be the general feature of the theories with an ultraviolet cut-off.
As possible implications of the obtained results we have applied it near Big Bang and
found the modified age of the Universe. We have also suggested a table top experiment to
test the results at low energy scales. We looked into the low and high temperature limit of
all the results as well. Next we studied the thermodynamics of the degenerate Fermi gas
and obtained the modified degenerate pressure and energy. We have comparatively studied the mass and number density dependence of the degenerate pressure. Surprisingly, we found the results to be perturbative in the SR limit as opposed to the expectation. We have then studied the example of a white dwarf star and obtained the mass-radius relation and the modified Chandrasekhar limit, which gets a positive correction. The modified luminosity of the star has also been explored in detail using the radiative envelope and in both the relativistic and non-relativistic cases. We noted that since the correction in pressure is negative for a given mass and temperature and so is the correction in the luminosity as well. The correction to the luminosity of a white dwarf is nonperturbative in SR limit as expected because of the presence of an ultraviolet energy cut-off.
