S. Mallik

QCD sum rules at finite temperature

We derive thermal QCD sum rules for the correlation function of two vector currents in the rho-meson channel. It takes into account the leading non-perturbative corrections from the additional operators, which appear due to the breakdown of Lorentz invariance at finite temperature. The mixing of the new operators has a drastic effect on their coefficients. The thermal average of all the operators can be related to that of the quark condensate and the energy density. The sum rules then yield the temperature dependence of the parameters of the \ensuremath{\rho} meson, namely its mass and coupling to the vector current. Our result is that these parameters are practically independent of temperature at least up to a temperature of 125 MeV.

Density perturbation in extended inflation

We examine the calculation of density perturbation at large scales in the inflationary scenario. The formula for its magnitude is reviewed from first principles and applied to the original model of extended inflation. Our estimate is an order of magnitude bigger than the earlier ones due to the difference in the time at which the primordial fluctuation is evaluated and to the inclusion of terms neglected earlier in the standard formula for density perturbation.

Calculation of density fluctuations in the inflationary epoch

Starting from an initial state of thermal equilibrium, we derive an expression for the quantum fluctuation in the energy density during the inflationary epoch in terms of the mode functions for the inflaton field. The effect of this particular initial state is not washed out in the final formula, contrary to what is usually believed. Numerically, however, the effect is completely negligible, validating the use of the two point function in the vacuum state. We also point out the requirement of conventional quantum field theory during inflation, that the quantum fluctuation in a wavelength must be evaluated, at the latest, when the wavelength crosses the Hubble length, in contrast to the usual practice in the literature.