[Paper Review] Suppression of scalar power on large scales and associated bispectra

H. V. Ragavendra, Debika Chowdhury+1 more|arXiv (Cornell University)|Mar 2, 2020

Cosmology and Gravitation Theories67 references4 citations

TL;DR

This paper investigates inflationary models that suppress scalar power on large cosmological scales, comparing scenarios with kinetically dominated initial conditions, punctuated inflation, and Starobinsky-type models. It finds that while these models produce similar large-scale power spectra, their scalar bispectra and non-Gaussianity parameters ($f_{\mathrm{NL}}$) differ significantly, particularly in the violation of the consistency relation for large-scale modes in kinetically dominated models, offering a potential observational discriminator between them.

ABSTRACT

[Abridged] A sharp cut-off in the primordial scalar power spectrum on large scales has been known to improve the fit to the cosmic microwave background (CMB) data when compared to the more standard, nearly scale invariant power spectrum that arises in slow roll inflation. In an earlier work, we had numerically investigated the characteristics of the scalar bispectrum generated in models with kinetically dominated initial conditions. In this work, we compare the scenario with two other competing scenarios (viz. punctuated inflation and a model due to Starobinsky) which also suppress the scalar power in a roughly similar fashion on large scales. We further consider two other scenarios involving inflation of a finite duration, one wherein the scalar field begins on the inflationary attractor and another wherein the field starts with a smaller velocity and evolves towards the attractor. These scenarios too exhibit a sharp drop in power on large scales if the initial conditions on the perturbations for a range of modes are imposed on super-Hubble scales as in the kinetically dominated model. We compare the performance of all the models against the Planck CMB data at the level of power spectra. We also compare the amplitudes and shapes of the scalar non-Gaussianity parameter $f_{_{ m NL}}$ in all these cases which lead to scalar power spectra of similar form. Interestingly, we find that, in the models wherein the initial conditions on the perturbations are imposed on super-Hubble scales, the consistency relation governing the scalar bispectrum is violated for the large scale modes, whereas the relation is satisfied for all the modes in the other scenarios. These differences in the behavior of the scalar bispectra can conceivably help us observationally discriminate between the various models which lead to scalar power spectra of roughly similar shape.

Motivation & Objective

• To investigate whether models with kinetically dominated initial conditions can suppress scalar power on large scales while fitting CMB data.
• To compare the performance of such models against alternative scenarios like punctuated inflation and Starobinsky-type models in fitting Planck CMB data.
• To analyze the scalar bispectrum and non-Gaussianity parameter $f_{\mathrm{NL}}$ in these models, especially in the squeezed limit.
• To determine whether differences in bispectrum behavior—particularly consistency relation violation—can distinguish between models with similar power spectra.
• To assess the impact of these models on cosmological parameters, especially $H_0$, and their implications for the Hubble tension.

Proposed method

• Numerical computation of scalar bispectra using third-order action for scalar perturbations, separating contributions from bulk and boundary terms.
• Implementation of initial conditions on super-Hubble scales for perturbations in kinetically dominated models, contrasting with sub-Hubble Bunch-Davies conditions in other models.
• Comparison of scalar power spectra and $f_{\mathrm{NL}}$ across multiple models: kinetically dominated, punctuated inflation, Starobinsky, and finite-duration inflation with attractor or non-attractor initial conditions.
• Use of marginalized posterior distributions to constrain inflationary parameters ($\Lambda$, $m$, $N_*$) and cosmological parameters ($\Omega_b h^2$, $\Omega_c h^2$, $\theta$, $\tau$, $H_0$) via Planck CMB data.
• Analysis of the consistency relation for the scalar bispectrum in the squeezed limit across models, identifying violations in kinetically dominated cases.
• Use of specific potentials: $V(\phi) = \mu^3[\phi + b\phi_0 \cos(\phi/\phi_0)]$ and linear potentials with abrupt slope changes to model different inflationary dynamics.

Experimental results

Research questions

• RQ1 Do models with kinetically dominated initial conditions produce scalar power spectra that suppress large-scale modes and improve fit to Planck CMB data compared to standard slow-roll inflation?
• RQ2 How do the scalar bispectra and non-Gaussianity parameters ($f_{\mathrm{NL}}$) differ between kinetically dominated models and competing scenarios like punctuated inflation and Starobinsky models?
• RQ3 Is the consistency relation for the scalar bispectrum violated in kinetically dominated models on large scales, and if so, why?
• RQ4 Can the shape and amplitude of $f_{\mathrm{NL}}$ in the squeezed limit distinguish between models with similar large-scale power spectra?
• RQ5 What are the implications of these models for the Hubble parameter $H_0$, and do they alleviate or exacerbate the Hubble tension?

Key findings

• Models with kinetically dominated initial conditions produce a sharp suppression of scalar power on large scales, improving the fit to low-multipole CMB anisotropies compared to nearly scale-invariant spectra.
• Despite similar large-scale power spectrum shapes, the scalar bispectra and $f_{\mathrm{NL}}$ values differ significantly across models, especially in the squeezed limit.
• In kinetically dominated models, the consistency relation for the scalar bispectrum is violated for large-scale modes due to boundary term dominance in the third-order action, whereas it holds in other scenarios.
• The non-Gaussianity parameter $f_{\mathrm{NL}}$ in kinetically dominated models shows a characteristic behavior where the consistency condition is violated at large scales but restored at small scales.
• The model with the scalar field always on the attractor allows analytical computation of both the power spectrum and bispectrum, providing a benchmark for comparison.
• The Hubble parameter $H_0$ estimated in the punctuated inflation model is slightly lower than in the standard Planck model, potentially worsening the Hubble tension, while other models align more closely with the standard value.