Primordial Non-Gaussianity from LAMOST Surveys

The primordial non-Gaussianity (PNG) in matter density perturbation is a very powerful probe of the physics of the very early Universe. The local PNG can induce a distinct scale-dependent bias on the large scale structure distribution of galaxies and quasars, which could be used for constraining it. We study the detection limits on PNG from the surveys of the LAMOST telescope. The cases of the main galaxy survey, the luminous red galaxy (LRG) survey, and the quasar survey of different magnitude limits are considered. We find that the MAIN1 sample (i.e. the main galaxy survey with one magnitude deeper than the SDSS main galaxy survey, or r<18.8) could only provide very weak constraint on PNG. For the MAIN2 sample (r<19.8) and the LRG survey, the 2\sigma (95.5%) limit on the PNG parameter f_{NL} are |f_{NL}|<145 and |f_{NL}|<114 respectively, comparable to the current limit from cosmic microwave background (CMB) data. The quasar survey could provide much more stringent constraint, and we find that the 2\sigma limit for |f_{NL}| is between 50 and 103, depending on the magnitude limit of the survey. With Planck-like priors on cosmological parameters, the quasar survey with g<21.65 would improve the constraints to |f_{NL}|<43 (2\sigma). We also discuss the possibility of further tightening the constraint by using the relative bias method proposed by Seljak(2008).Comment: 8 pages, 2 figures, RAA accepte

A generalized exchange-correlation functional: the Neural-Networks approach

A Neural-Networks-based approach is proposed to construct a new type of exchange-correlation functional for density functional theory. It is applied to improve B3LYP functional by taking into account of high-order contributions to the exchange-correlation functional. The improved B3LYP functional is based on a neural network whose structure and synaptic weights are determined from 116 known experimental atomization energies, ionization potentials, proton affinities or total atomic energies which were used by Becke in his pioneer work on the hybrid functionals [J. Chem. Phys. ${\bf 98}$, 5648 (1993)]. It leads to better agreement between the first-principles calculation results and these 116 experimental data. The new B3LYP functional is further tested by applying it to calculate the ionization potentials of 24 molecules of the G2 test set. The 6-311+G(3{\it df},2{\it p}) basis set is employed in the calculation, and the resulting root-mean-square error is reduced to 2.2 kcal$\cdot$mol$^{-1}$ in comparison to 3.6 kcal$\cdot$mol$^{-1}$ of conventional B3LYP/6-311+G(3{\it df},2{\it p}) calculation.Comment: 10 pages, 1figur