[Paper Review] Planck 2015. XX. Constraints on inflation

P. A. R. Ade, N. Aghanim+243 more|arXiv (Cornell University)|Feb 10, 2015

Relativity and Gravitational Theory10 citations

TL;DR

This paper presents constraints on cosmic inflation using Planck full-mission CMB data in temperature and polarization, finding a spectral index of $n_s = 0.968 \pm 0.006$ and a tight upper bound on the tensor-to-scalar ratio $r_{0.002} < 0.11$ (95% CL). These results disfavor $V(\phi) \propto \phi^2$ and natural inflation models in favor of those predicting smaller $r$, such as $R^2$ inflation.

ABSTRACT

We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be $n_\mathrm{s} = 0.968 \pm 0.006$ and tightly constrain its scale dependence to $d n_s/d \ln k =-0.003 \pm 0.007$ when combined with the Planck lensing likelihood. When the high-$\ell$ polarization data is included, the results are consistent and uncertainties are reduced. The upper bound on the tensor-to-scalar ratio is $r_{0.002} < 0.11$ (95% CL), consistent with the B-mode polarization constraint $r< 0.12$ (95% CL) obtained from a joint BICEP2/Keck Array and Planck analysis. These results imply that $V(\phi) \propto \phi^2$ and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as $R^2$ inflation. Three independent methods reconstructing the primordial power spectrum are investigated. The Planck data are consistent with adiabatic primordial perturbations. We investigate inflationary models producing an anisotropic modulation of the primordial curvature power spectrum as well as generalized models of inflation not governed by a scalar field with a canonical kinetic term. The 2015 results are consistent with the 2013 analysis based on the nominal mission data.

Motivation & Objective

• To test cosmic inflation models using high-precision Planck CMB temperature and polarization data.
• To constrain the spectral index of curvature perturbations and its scale dependence.
• To place limits on the tensor-to-scalar ratio $r$ using both temperature and B-mode polarization data.
• To evaluate the viability of specific inflationary models, including $V(\phi) \propto \phi^2$, natural inflation, and $R^2$ inflation.
• To investigate primordial power spectrum reconstruction and deviations from adiabatic perturbations.

Proposed method

• Analysis of Planck full-mission temperature anisotropy data and first release of large-scale polarization data.
• Combination with the Planck lensing likelihood to improve constraints on $n_s$ and $dn_s/d\ln k$.
• Joint analysis with BICEP2/Keck Array data to constrain the tensor-to-scalar ratio $r_{0.002}$ using B-mode polarization.
• Application of three independent methods to reconstruct the primordial power spectrum from CMB data.
• Investigation of models with anisotropic modulation and non-canonical kinetic terms in the inflationary action.
• Use of likelihood-based inference to compare model predictions with observed CMB power spectra.

Experimental results

Research questions

• RQ1 What are the constraints on the spectral index of curvature perturbations and its scale dependence from Planck full-mission data?
• RQ2 What upper bound does Planck place on the tensor-to-scalar ratio $r_{0.002}$ at 95% confidence?
• RQ3 How do the Planck results compare with previous analyses based on the nominal mission data?
• RQ4 Which inflationary models—such as $V(\phi) \propto \phi^2$, natural inflation, or $R^2$ inflation—are favored or disfavored by the data?
• RQ5 To what extent is the primordial power spectrum consistent with adiabatic perturbations and standard inflationary models?

Key findings

• The spectral index of curvature perturbations is measured as $n_s = 0.968 \pm 0.006$ from temperature and lensing data.
• The scale dependence of the spectral index is tightly constrained to $dn_s/d\ln k = -0.003 \pm 0.007$ when combined with lensing.
• The upper bound on the tensor-to-scalar ratio is $r_{0.002} < 0.11$ at 95% confidence, consistent with the B-mode constraint $r < 0.12$.
• Models such as $V(\phi) \propto \phi^2$ and natural inflation are now disfavored compared to models predicting smaller $r$, such as $R^2$ inflation.
• Three independent reconstruction methods of the primordial power spectrum yield consistent results, supporting adiabatic primordial perturbations.
• The data are consistent with the 2013 Planck results based on the nominal mission, confirming stability of the constraints.