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According to the Large Extra Dimensions (LED) model of Arkani-Hamed, Dimopoulos, and Dvali (ADD), in addition to the (3+1) observed space-time dimensions, there exist n gravity-only spatial dimensions. Due to the presence of the additional dimensions, the Planck scale of gravity should be brought down from 10 TeV to the TeV scale, near the electroweak scale, and thus solve the hierarchy problem. Based on the ADD theory, Kaluza-Klein (KK) gravitons, having masses of the order 100 MeV and lifetimes of the order of billions of years, are expected to be produced within supernova cores by nucleon-nucleon gravi-bremsstrahlung in the LED model. Once produced, they are predicted to be trapped by the gravitational potential of subsequently formed neutron stars (NS), and their decay is predicted to contribute to a measurable gamma-ray flux from NS. In this dissertation, refinements to past theoretical models are made, including modifications for the expected spectral energy distribution based on orbital motion of the KK gravitons, and magnetic fields and age. n = 2, 3, . . . , 7 extra dimensions are considered. A sample of 6 gamma-ray faint NS sources not reported in the first Fermi gamma-ray source catalog that are good candidates are selected for this analysis, based on age, surface magnetic field, distance, and galactic latitude. Based on 11 months of data from Fermi-LAT, 95% CL upper limits on the size of extra dimensions R from each source are obtained, as well as 95% CL lower limits on the (n+4)dimensional Planck scale MD. In addition, the limits from all of the analyzed NSs have been combined statistically using two likelihood-based methods. The results indicate more stringent limits on LED than quoted previously from individual neutron star sources in gamma-rays. In addition, the results are more stringent than current v collider limits, from the LHC, for n 3, the toroidal topology is still allowed.

Search for Large Extra Dimensions Based on Observations of Neutron Stars with the Fermi-LAT