Focus issue: Planck and fundamentals of cosmology

Despite the wealth of Planck results, there are difficulties in disentangling the primordial non-Gaussianity of the Cosmic Microwave Background (CMB) from the secondary and the foreground non-Gaussianity (NG). For each of these forms of NG the lack of complete data introduces model-dependences. Aiming at detecting the NGs of the CMB temperature anisotropy $\delta T$, while paying particular attention to a model-independent quantification of NGs, our analysis is based upon statistical and morphological univariate descriptors, respectively: the probability density function $P(\delta T)$, related to v₀, the first Minkowski Functional (MF), and the two other MFs, v₁ and v₂. From their analytical Gaussian predictions we build the discrepancy functions ${{ \Delta }_{k}}$ (k  =  P, 0, 1, 2) which are applied to an ensemble of 10⁵ CMB realization maps of the $\Lambda$CDM model and to the Planck CMB maps. In our analysis we use general Hermite expansions of the ${{ \Delta }_{k}}$ up to the 12th order, where the coefficients are explicitly given in terms of cumulants. Assuming hierarchical ordering of the cumulants, we obtain the perturbative expansions generalizing the second order expansions of Matsubara to arbitrary order in the standard deviation ${{\sigma}_{0}}$ for $P(\delta T)$ and v₀, where the perturbative expansion coefficients are explicitly given in terms of complete Bell polynomials. The comparison of the Hermite expansions and the perturbative expansions is performed for the $\Lambda$CDM map sample and the Planck data. We confirm the weak level of non-Gaussianity (1–2)σ of the foreground corrected masked Planck 2015 maps.

Several unexpected features have been observed in the microwave sky at large angular scales, both by WMAP and by Planck. Among those features is a lack of both variance and correlation on the largest angular scales, alignment of the lowest multipole moments with one another and with the motion and geometry of the solar system, a hemispherical power asymmetry or dipolar power modulation, a preference for odd parity modes and an unexpectedly large cold spot in the Southern hemisphere. The individual p-values of the significance of these features are in the per mille to per cent level, when compared to the expectations of the best-fit inflationary ΛCDM model. Some pairs of those features are demonstrably uncorrelated, increasing their combined statistical significance and indicating a significant detection of CMB features at angular scales larger than a few degrees on top of the standard model. Despite numerous detailed investigations, we still lack a clear understanding of these large-scale features, which seem to imply a violation of statistical isotropy and scale invariance of inflationary perturbations. In this contribution we present a critical analysis of our current understanding and discuss several ideas of how to make further progress.

Supersymmetry is the most natural framework for physics above the TeV scale, and the corresponding framework for early-Universe cosmology, including inflation, is supergravity. No-scale supergravity emerges from generic string compactifications and yields a non-negative potential, and is therefore a plausible framework for constructing models of inflation. No-scale inflation yields naturally predictions similar to those of the Starobinsky model based on $R+{R}^{2}$ gravity, with a tilted spectrum of scalar perturbations: ${n}_{s}\sim 0.96$, and small values of the tensor-to-scalar perturbation ratio $r\lt 0.1$, as favoured by Planck and other data on the cosmic microwave background (CMB). Detailed measurements of the CMB may provide insights into the embedding of inflation within string theory as well as its links to collider physics.

The results from Planck2015, when combined with earlier observations from the Wilkinson Microwave Anisotropy Probe, Atacama Cosmology Telescope, South Pole Telescope and other experiments, were the first observations to disfavor the 'classic' inflationary paradigm. To satisfy the observational constraints, inflationary theorists have been forced to consider plateau-like inflaton potentials that introduce more parameters and more fine-tuning, problematic initial conditions, multiverse-unpredictability issues, and a new 'unlikeliness problem'. Some propose turning instead to a 'postmodern' inflationary paradigm in which the cosmological properties in our observable Universe are only locally valid and set randomly, with completely different properties (and perhaps even different physical laws) existing in most regions outside our horizon. By contrast, the new results are consistent with the simplest versions of ekpyrotic cyclic models in which the Universe is smoothed and flattened during a period of slow contraction followed by a bounce, and another promising bouncing theory, anamorphic cosmology, has been proposed that can produce distinctive predictions.

We discuss the implications of the recently released Planck data for inflation. We show that they favor the simplest category of inflationary models, namely single-field slow-roll inflation, with a plateau-like potential, a typical representative of this class of scenarios being the Starobinsky model. We also investigate the constraints on the inflationary reheating. Finally, we briefly address the question of which observables should be measured as a matter of priority in order to further improve our knowledge of inflation.

The Planck collaboration has provided us rich information about the early Universe, and a host of new observational missions will soon shed further light on the 'anomalies' that appear to exist on the largest angular scales. From a quantum gravity perspective, it is natural to inquire if one can trace back the origin of such puzzling features to Planck scale physics. Loop quantum cosmology provides a promising avenue to explore this issue because of its natural resolution of the big bang singularity. Thanks to advances over the last decade, the theory has matured sufficiently to allow concrete calculations of the phenomenological consequences of its pre-inflationary dynamics. In this article we summarize the current status of the ensuing two-way dialog between quantum gravity and observations.

We review the status of string gas cosmology (SGC) after the 2015 Planck data release. SGC predicts an almost scale-invariant spectrum of cosmological perturbations with a slight red tilt, like the simplest inflationary models. It also predicts a scale-invariant spectrum of gravitational waves with a slight blue tilt, unlike inflationary models which predict a red tilt of the gravitational wave spectrum. SGC yields two consistency relations which determine the tensor to scalar ratio and the slope of the gravitational wave spectrum given the amplitude and tilt of the scalar spectrum. We show that these consistency relations are in good agreement with the Planck data. We discuss future observations which will be able to differentiate between the predictions of inflation and those of SGC.