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New Constraints on inflation from the Cosmic Microwave Background

William H. Kinney, Alessandro Melchiorri, Antonio Riotto

TL;DR

Inflation is evaluated as the mechanism solving the flatness and horizon problems, with Boomerang and MAXIMA-1 providing precision CMB constraints. The study maps inflationary predictions to the observable pair $(n_S,r)$ via slow-roll relations $r=13.6\epsilon$, $n_S=1-4\epsilon+2\eta$, and $n_T=-2\epsilon$, incorporating a consistency relation, then performs a multi-parameter likelihood analysis across cosmological priors. Without BBN priors, a broad range of models remains viable, with a near-scale-invariant $n_S\simeq 1$ favored; with BBN priors and negligible reionization, the data prefer a red tilt $n_S\simeq 0.93$ and $r\lesssim 0.17$, disfavoring large-field models with $n_S<0.9$. The results demonstrate that CMB data begin to discriminate among simple inflationary scenarios and highlight the importance of priors on baryon density and reionization; future observations are expected to further tighten these constraints.

Abstract

The recent data from the Boomerang and MAXIMA-1 balloon flights have marked the beginning of the precision era of Cosmic Microwave Background anisotropy (CMB) measurements. We investigate the observational constraints from the current CMB anisotropy measurements on the simplest inflation models, characterized by a single scalar field $φ$, in the parameter space consisting of scalar spectral index $n_S$ and tensor/scalar ratio $r$. If we include constraints on the baryon density from big bang nucleosynthesis (BBN), we show that the favored inflationary models have negligible tensor amplitude and a ``red'' tilt, with a best fit of $n_S \simeq 0.93$, which is consistent with the simplest ``small-field'' inflation models, but rules out large-field models at the $1σ$ level. Without including BBN constraints, a broader range of models are consistent with the data. The best fit (assuming negligible reionization) is a scale-invariant spectrum, $n_S \simeq 1$, which includes large-field and hybrid scenarios. Large-field models (such as chaotic and power-law inflation) with tilt $n_S < 0.9$ are strongly disfavored in all cases.

New Constraints on inflation from the Cosmic Microwave Background

TL;DR

Inflation is evaluated as the mechanism solving the flatness and horizon problems, with Boomerang and MAXIMA-1 providing precision CMB constraints. The study maps inflationary predictions to the observable pair via slow-roll relations , , and , incorporating a consistency relation, then performs a multi-parameter likelihood analysis across cosmological priors. Without BBN priors, a broad range of models remains viable, with a near-scale-invariant favored; with BBN priors and negligible reionization, the data prefer a red tilt and , disfavoring large-field models with . The results demonstrate that CMB data begin to discriminate among simple inflationary scenarios and highlight the importance of priors on baryon density and reionization; future observations are expected to further tighten these constraints.

Abstract

The recent data from the Boomerang and MAXIMA-1 balloon flights have marked the beginning of the precision era of Cosmic Microwave Background anisotropy (CMB) measurements. We investigate the observational constraints from the current CMB anisotropy measurements on the simplest inflation models, characterized by a single scalar field , in the parameter space consisting of scalar spectral index and tensor/scalar ratio . If we include constraints on the baryon density from big bang nucleosynthesis (BBN), we show that the favored inflationary models have negligible tensor amplitude and a ``red'' tilt, with a best fit of , which is consistent with the simplest ``small-field'' inflation models, but rules out large-field models at the level. Without including BBN constraints, a broader range of models are consistent with the data. The best fit (assuming negligible reionization) is a scale-invariant spectrum, , which includes large-field and hybrid scenarios. Large-field models (such as chaotic and power-law inflation) with tilt are strongly disfavored in all cases.

Paper Structure

This paper contains 9 sections, 19 equations, 4 figures.

Table of Contents

  1. Introduction
  2. The inflationary model space
  3. Large-field models: $-\epsilon < \eta \leq \epsilon$
  4. Small-field models: $\eta < -\epsilon$
  5. Hybrid models: $0 < \epsilon < \eta$
  6. Linear models: $\eta = - \epsilon$
  7. CMB Analysis
  8. Results
  9. Conclusions

Figures (4)

  • Figure 1: The parameter space divided into regions for small-field, large-field and hybrid models. The linear case is the dividing line between large- and small-field.
  • Figure 2: CMB constraints and inflation models for $\tau_c = 0$ and no BBN prior. The allowed contours are quite large but still exclude a significant portion of the inflationary model space.
  • Figure 3: CMB constraints and inflation models for $\tau_c = 0$ and the low deuterium BBN prior, $0.016 \le \Omega_{\rm b} h^2 \le 0.021$. The contours are significantly tightened in the $r$ coordinate and now favor a tilted spectrum.
  • Figure 4: Contours for various values of $\tau_c$ and $\Omega_{\rm b} h^2$. In general, BBN constraints tighten the contours in the $r$ direction, and reionization shifts the favored range of $n_S$ to the right, favoring hybrid models for large $\tau_c$. Strongly tilted large-field models are excluded in all cases.