O(D,D) Duality In String Cosmology And Correlation-Duality Or Holographic Effect On Black Hole Background

Abstract: In this thesis, based on string theory and general relativity, O(d,d) duality and quantum properties in cosmology were studied, the effects of dark energy in mater fluctuation and black hole’s absorption were analyzed. Moreover, the correlation-duality and holographic effect of Fermi condensation on black hole background were studied by using the method of functional integral in quantum field theory. The development histories of string theory and cosmology were introduced briefly in chapter1; The equations of string cosmology with O(d,d) duality symmetry were derived in chapter2; The new cosmological solutions with matter coupling were obtained according to trial method and renormalization group equation, the quantum probability in dual cosmology was also calculated in chapter3; The effects of quintessence and phantom dark energy on matter fluctuation was analyzed in chapter4; The absorbtion of dark energy in black hole and on the influence of it’s mass change in the acceleration stage was discussed in chapter5; The correlation-temperature duality of Fermi condensation on two-dimension black hole background was studied according to perturbative functional integral method in chapter6; The holographic effect of Fermi condensation on the Ads3/CFT2black hole background was studied based on non-perturbative functional integral method in chapter7.The new works of this thesis are as follows1. The power and inflaton cosmological solutions with O(d,d) dual symmetry and matter coupling were obtained by using the trial method and renormalization group equation;2. The fluctuation equation of matter under the effect of quintessence and phantom dark energy was derived and the fluctuation function of matter was calculated by means of numerical method;3. The absorption effect of black hole on dark energy was calculated in the acceleration stage of universe;4. The correlation function and temperature duality of Fermi condensation on two-dimension black hole background was studied according to perturbative functional integral method;5. The absorption to Hawking radiation and holographic fluctuation effect of Fermi condensation on Ads3/CFT2black hole background was studied based on non-perturbative functional integral method.