An unexpectedly tiny cosmological constant (i.e. the vacuum energy density) Λ = 10^-122 M_P⁴ has been observed since the 1990s. This thesis examine the statistical interpretation of the cosmological constant problem in supergravity models. The racetrack model in Type IIB string theory is studied in the presence of leading α-correction in flux compactification. We show that a class of de-Sitter vacua is generic under the approximation of large volume compactification. The absence of constraint on the compactified volume for the meta-stable de-Sitter vacua in this model leads to a controllable α' correction. We find that the median Λ_50% is exponentially suppressed by the compactified volume and the probability distribution function of Λ diverges as Λ approaches 0⁺. We then study th...[ Read more ]

An unexpectedly tiny cosmological constant (i.e. the vacuum energy density) Λ = 10^-122 M_P⁴ has been observed since the 1990s. This thesis examine the statistical interpretation of the cosmological constant problem in supergravity models. The racetrack model in Type IIB string theory is studied in the presence of leading α-correction in flux compactification. We show that a class of de-Sitter vacua is generic under the approximation of large volume compactification. The absence of constraint on the compactified volume for the meta-stable de-Sitter vacua in this model leads to a controllable α' correction. We find that the median Λ_50% is exponentially suppressed by the compactified volume and the probability distribution function of Λ diverges as Λ approaches 0⁺. We then study the large volume scenario model and show that the scale of gravitino mass can be splitted from that of the cosmological constant. The probability distribution of Λ in this model where SUSY can be broken or remain unbroken peaks at Λ = 0^- but anti de-Sitter vacua is generic in this model in the absence of fine tuned uplifting.