Ultra slow-roll inflation has recently been used to challenge the non-Gaussianity consistency relation. We show that this inflationary scenario belongs to a one-parameter class of models, and we study its properties and observational predictions. We demonstrate that the power spectrum remains scale invariant and that the bispectrum is of the local type with ${f}_{\mathrm{NL}}=5(3-{n}_{\mathrm{s}})/4$, which indeed represents a modification of the consistency relation. However, we also show that the system is unstable and suffers from many physical problems among which is the difficulty in correctly WMAP normalizing the model. We conclude that ultra slow-roll inflation remains a very peculiar case, the physical relevance of which is probably not sufficient to call into question the validity of the consistency relation.

We present the first Bayesian constraints on the single field inflationary reheating era obtained from cosmic microwave background (CMB) data. After demonstrating that this epoch can be fully characterized by the so-called reheating parameter, we show that it is constrained by the seven years Wilkinson microwave anisotropies probe (WMAP7) data for all large and small field models. An interesting feature of our approach is that it yields lower bounds on the reheating temperature which can be combined with the upper bounds associated with gravitinos production. For large field models, we find the energy scale of reheating to be higher than those probed at the Large Hadron Collider, $\rho${}reh1/4>17.3\,\,TeV at 95% of the confidence limit. For small field models, we obtain the two-sigma lower limits $\rho${}reh1/4>890\,\,TeV for a mean equation of state during reheating w\ifmmode\bar\else\textasciimacron\fi{}reh=-0.3 and $\rho${}reh1/4>390\,\,GeV for w\ifmmode\bar\else\textasciimacron\fi{}reh=-0.2. The physical origin of these constraints is pedagogically explained by means of the slow-roll approximation. Finally, when marginalizing over all possible reheating history, the WMAP7 data push massive inflation under pressure (p<2.2 at 95% of the confidence limit where p is the power index of the large field potentials) while they slightly favor super-Planckian field expectation values in the small field models.

Reheating is the epoch which connects inflation to the subsequent hot big-bang phase. Conceptually very important, this era is, however, observationally poorly known. We show that the current Planck satellite measurements of the cosmic microwave background (CMB) anisotropies constrain the kinematic properties of the reheating era for most of the inflationary models. This result is obtained by deriving the marginalized posterior distributions of the reheating parameter for about 200 models of slow-roll inflation. Weighted by the statistical evidence of each model to explain the data, we show that the Planck 2013 measurements induce an average reduction of the posterior-to-prior volume by 40%. Making some additional assumptions on reheating, such as specifying a mean equation of state parameter, or focusing the analysis on peculiar scenarios, can enhance or reduce this constraint. Our study also indicates that the Bayesian evidence of a model can substantially be affected by the reheating properties. The precision of the current CMB data is therefore such that estimating the observational performance of a model now requires incorporating information about its reheating history.

We investigate the quantumness of primordial cosmological fluctuations and its detectability. The quantum discord of inflationary perturbations is calculated for an arbitrary splitting of the system, and shown to be very large on super-Hubble scales. This entails the presence of large quantum correlations, due to the entangled production of particles with opposite momentums during inflation. To determine how this is reflected at the observational level, we study whether quantum correlators can be reproduced by a nondiscordant state, i.e. a state with vanishing discord that contains classical correlations only. We demonstrate that this can be done for the power spectrum, the price to pay being twofold: first, large errors in other two-point correlation functions that cannot however be detected since they are hidden in the decaying mode; second, the presence of intrinsic non-Gaussianity, the detectability of which remains to be determined but which could possibly rule out a nondiscordant description of the cosmic microwave background. If one abandons the idea that perturbations should be modeled by quantum mechanics and wants to use a classical stochastic formalism instead, we show that any two-point correlators on super-Hubble scales can be exactly reproduced regardless of the squeezing of the system. The latter becomes important only for higher order correlation functions that can be accurately reproduced only in the strong squeezing regime.

In this work we show that the gravitational Chern-Simons term, aside from being a key ingredient in inflationary baryogenesis, modifies superhorizon gravitational waves produced during inflation. We compute the super-Hubble gravitational power spectrum in the slow-roll approximation and show that its overall amplitude is modified while its spectral index remains unchanged (at leading order in the slow-roll parameters). Then, we calculate the correction to the tensor to scalar ratio, $T/S$. We find a correction of $T/S$ which is dependent on $\mathcal{N}$ (more precisely quadratic in $\mathcal{N}$), the parameter characterizing the amplitude of the Chern-Simons terms. In a stringy embedding of the leptogenesis mechanism, $\mathcal{N}$ is the ratio between the Planck scale and the fundamental string scale. Thus, in principle, we provide a direct probe of leptogenesis due to stringy dynamics in the cosmic microwave background. However, we demonstrate that the corresponding correction of $T/S$ is in fact very small and not observable in the regime where our calculations are valid. To obtain a sizable effect, we argue that a nonlinear calculation is necessary.