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Register a new userPrimordial non-Gaussianities from inflation
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Hael Collins
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These notes present a detailed introduction to Maldacenas calculation of the three-point function generated by the simplest class of inflationary models: those with a single inflaton field whose potential satisfies the slow-roll conditions and whose quantum fluctuations start in the asymptotic Bunch-Davies vacuum state. The three-point function should be the most readily observed evidence for non-Gaussianities amongst the primordial fluctuations produced by inflation. In these inflationary theories the non-Gaussianities are predicted to be extremely small, being naturally suppressed by the small slow-roll parameters.
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We investigate expected constraints on equilateral-type primordial non-Gaussianities from future/ongoing imaging surveys, making use of the fact that they enhance the halo/galaxy bispectrum on large scales. As model parameters to be constrained, in addition to $f_{rm NL}^{rm equil}$, which is related to the primordial bispectrum, we consider $g_{rm NL}^{(partial sigma)^4}$, which is related to the primordial trispectrum that appeared in the effective field theory of inflation. After calculating the angular bispectra of the halo/galaxy clustering and weak gravitational lensing based on the integrated perturbation theory, we perform Fisher matrix analysis for three representative surveys. We find that among the three surveys, the tightest constraints come from Large Synoptic Survey Telescope ; its expected $1sigma$ errors on $f_{rm NL}^{rm equil}$ and $g_{rm NL}^{(partial sigma)^4}$ are respectively given by $7.0 times 10^2$ and $4.9 times 10^7$. Although this constraint is somewhat looser than the one from the current cosmic microwave background observation, since we obtain it independently, we can use this constraint as a cross check. We also evaluate the uncertainty with our results caused by using several approximations and discuss the possibility to obtain tighter constraint on $f_{rm NL}^{rm equil}$ and $g_{rm NL}^{(partial sigma)^4}$.
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