Effects and Detectability of Quasi-Single Field Inflation in the Large-Scale Structure and Cosmic Microwave Background

Abstract

Quasi-single field inflation predicts a peculiar momentum dependence in the squeezed limit of the primordial bispectrum which smoothly interpolates between the local and equilateral models. This dependence is directly related to the mass of the isocurvatons in the theory which is determined by the supersymmetry. Therefore, in the event of detection of a non-zero primordial bispectrum, additional constraints on the parameter controlling the momentum-dependence in the squeezed limit becomes an important question. We explore the effects of these non-Gaussian initial conditions on large-scale structure and the cosmic microwave background, with particular attention to the galaxy power spectrum at large scales and scale-dependence corrections to galaxy bias. We determine the simultaneous constraints on the two parameters describing the QSF bispectrum that we can expect from upcoming large-scale structure and cosmic microwave background observations. We find that for relatively large values of the non-Gaussian amplitude parameters, but still well within current uncertainties, galaxy power spectrum measurements will be able to distinguish the QSF scenario from the predictions of the local model. A CMB likelihood analysis, as well as Fisher matrix analysis, shows that there is also a range of parameter values for which Planck data may be able distinguish between QSF models and the related local and equilateral shapes. Given the different observational weightings of the CMB and LSS results, degeneracies can be significantly reduced in a joint analysis.

Figures (14)

• Figure 1: Upper panels: comparison of the bispectrum $B_\Phi$ as described by the template, Eq. (\ref{['eq:tempQsA']}), with the numerical evaluation for flattened triangles, $B(k_s,k,k_s-k)$ as a function of $k$ with constant $k_s=1\, h \, {\rm Mpc}^{-1}$, for $\nu=1$, $0.5$, $0.3$ and $0$ ( left to right). Lower panels: same comparison for squeezed isosceles triangles, $B(k,k_s,k_s)$ as a function of $k$ with $k_s=1\, h \, {\rm Mpc}^{-1}$. Notice that a lesser number of points has been evaluated in the $\nu=1$ case.
• Figure 2: Upper panels: comparison of the QSF template for $\nu=1.5$ with the local shape for flattened squeezed, $B(k_s,k,k_s-k)$ ( left panel) and isosceles, squeezed configurations, $B(k,k_s,k_s)$ ( right panel) assuming $k_s=1\, h \, {\rm Mpc}^{-1}$. Lower panels: comparison of the QSF template for $\nu=0.5$ with the orthogonal shape for the same triangular configurations.
• Figure 3: Left panel: comparison of the primordial component to the matter bispectrum due to QSF models ( red, dashed curves) to the component due to the local ( black, dot-dashed curve) and equilateral ( black, dotted curve) non-Gaussian models as well as to the one due to gravitational instability ( gray, continuous curve) for squeezed triangular configurations, i.e. $B(k,k_s,k_s)$ as function of $k$ for fixed $k_s=1\, h \, {\rm Mpc}^{-1}$. We consider the cases given by $\nu=0$, $0.5$, $1$ and $1.5$ corresponding to the increasingly long-dashed curves from bottom to top. Right panel: similar comparison for the reduced matter bispectrum with fixed $k_1=0.01\, h \, {\rm Mpc}^{-1}$ and $k_2=1.1\, h \, {\rm Mpc}^{-1}$ as a function of the angle $\theta$ between ${\bf k}_1$ and ${\bf k}_2$: now the different curves correspond to the same models, but including the gravity contribution.
• Figure 4: Reduced skewness $s_3$, defined in Eq. (\ref{['eq:skew']}), as a function of the halo mass for local ( black, dot-dashed curve), equilateral ( black, dotted curve) and QSF non-Gaussianity with $\nu=0$, $0.5$, $1$ and $1.5$ ( red, increasingly long-dashed curves). Assumes $f_{\rm NL}=100$, for all models.
• Figure 5: Left panel: non-Gaussian correction to the halo mass function at $z=0$. Different models are denoted as in the left panel. Right panel: Relative, scale-independent bias correction, $\Delta b_{1,si}/b_{1,G}$, as a function of linear bias $b_{1,G}$.