Planck 2018 results. X. Constraints on inflation

Abstract: We report on the implications for cosmic inflation of the 2018 Release of the Planck CMB anisotropy measurements. The results are fully consistent with the two previous Planck cosmological releases, but have smaller uncertainties thanks to improvements in the characterization of polarization at low and high multipoles. Planck temperature, polarization, and lensing data determine the spectral index of scalar perturbations to be $n_\mathrm{s}=0.9649\pm 0.0042$ at 68% CL and show no evidence for a scale dependence of $n_\mathrm{s}.$ Spatial flatness is confirmed at a precision of 0.4% at 95% CL with the combination with BAO data. The Planck 95% CL upper limit on the tensor-to-scalar ratio, $r_{0.002}<0.10$, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtain $r_{0.002}<0.056$. In the framework of single-field inflationary models with Einstein gravity, these results imply that: (a) slow-roll models with a concave potential, $V" (\phi) < 0,$ are increasingly favoured by the data; and (b) two different methods for reconstructing the inflaton potential find no evidence for dynamics beyond slow roll. Non-parametric reconstructions of the primordial power spectrum consistently confirm a pure power law. A complementary analysis also finds no evidence for theoretically motivated parameterized features in the Planck power spectrum, a result further strengthened for certain oscillatory models by a new combined analysis that includes Planck bispectrum data. The new Planck polarization data provide a stringent test of the adiabaticity of the initial conditions. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadrupolar modulation of the primordial fluctuations. However, the polarization data do not confirm physical models for a scale-dependent dipolar modulation.

• The paper establishes tight constraints on single-field slow-roll inflation models by confirming a near scale-invariant primordial spectrum.
• The paper reconstructs the primordial power spectrum and refines the tensor-to-scalar ratio limits, challenging models with high gravitational wave predictions.
• The paper reinforces the ΛCDM framework by ruling out marked isocurvature fluctuations and unexpected primordial features.

Constraints on Inflation from the Planck 2018 Results

The Planck Collaboration's 2018 paper titled "Constraints on Inflation" explores the implications and constraints of inflationary models in the context of Planck satellite observations. The analysis relies on the data collected by the Planck satellite, which measures the Cosmic Microwave Background (CMB) radiation with high precision. This paper is part of a series of Planck 2018 results and focuses specifically on understanding the inflationary period of the early universe.

The main thrust of the paper is to derive constraints on different inflationary models using data on CMB anisotropies. The paper employs several sections of detailed analysis, including a thorough review of Planck 2018 results on the main inflationary observables, implications for single-field slow-roll inflation models, reconstruction of the inflaton potential, and exploration of the primordial power spectrum.

Key Findings

1. Single-Field Inflationary Models: The study finds significant constraints on single-field slow-roll inflation models. The data supports the predictions of inflationary scenarios characterized by a nearly scale-invariant power spectrum, with the spectral index $n_s$ constrained to be less than 1. This effectively rules out models that predict a large deviation from a flat spectrum.
2. Primordial Power Spectrum: The paper details the reconstruction of the primordial power spectrum, implying that the spectrum is close to a power law, with no strong evidence of deviations or features at scales observed by Planck. This result is important as it corroborates the standard inflationary predictions without significant unexpected features.
3. Constraints on Tensor-to-Scalar Ratio: The analysis explores the limits on the tensor-to-scalar ratio $r$, a critical parameter in distinguishing among inflationary models. Planck's data set tightens constraints on $r$, placing an upper limit, which challenges models that predict significant levels of primordial gravitational waves.
4. Isocurvature Fluctuations and Anisotropic Models: The paper also investigates constraints on isocurvature fluctuations and anisotropic models of inflation. The results present stringent limits on these alternative models, reinforcing the predominance of adiabatic initial conditions as predicted by inflation.
5. Search for Primordial Features: Planck data was examined for evidence of primordial features or oscillatory patterns but found no compelling evidence to support these scenarios in the range of scales observable with Planck.

Implications and Future Prospects

The implications of these results are profound for theoretical cosmology. By confirming many predictions of the conventional single-field inflationary models, the Planck data strengthens the standard cosmological model (ΛCDM). Moreover, the constraints on $n_s$ and $r$ are crucial for distinguishing between inflationary models and informing future theoretical developments.

From a practical standpoint, the high-precision data from Planck sets a benchmark for future CMB experiments aiming to probe the inflationary epoch with even greater sensitivity. Upcoming missions with enhanced capabilities are expected to further refine these constraints, especially those related to inflationary gravitational waves, potentially offering new insights into the fundamental physics of the early universe.

The analysis conducted in the Planck 2018 results paper provides a comprehensive assessment of inflationary models and sets a foundational precedent for future explorations into the very early cosmos. Researchers are now better equipped to build upon these findings with next-generation observational strategies and theoretical models to uncover the mysteries surrounding the origins and evolution of our universe.