Inflationary perturbations are approximately Gaussian and deviations from Gaussianity are usually calculated using in-in perturbation theory. This method, however, fails for unlikely events on the tail of the probability distribution: in this regime
non-Gaussianities are important and perturbation theory breaks down for $|zeta| gtrsim |f_{rm scriptscriptstyle NL}|^{-1}$. In this paper we show that this regime is amenable to a semiclassical treatment, $hbar to 0$. In this limit the wavefunction of the Universe can be calculated in saddle-point, corresponding to a resummation of all the tree-level Witten diagrams. The saddle can be found by solving numerically the classical (Euclidean) non-linear equations of motion, with prescribed boundary conditions. We apply these ideas to a model with an inflaton self-interaction $propto lambda dotzeta^4$. Numerical and analytical methods show that the tail of the probability distribution of $zeta$ goes as $exp(-lambda^{-1/4}zeta^{3/2})$, with a clear non-perturbative dependence on the coupling. Our results are relevant for the calculation of the abundance of primordial black holes.
We study the decay of gravitational waves into dark energy fluctuations $pi$, through the processes $gamma to pipi$ and $gamma to gamma pi$, made possible by the spontaneous breaking of Lorentz invariance. Within the EFT of Dark Energy (or Horndeski/
beyond Horndeski theories) the first process is large for the operator $frac12 tilde m_4^2(t) , delta g^{00}, left( {}^{(3)}! R + delta K_mu^ u delta K^mu_ u -delta K^2 right)$, so that the recent observations force $tilde m_4 =0$ (or equivalently $alpha_{rm H}=0$). This constraint, together with the requirement that gravitational waves travel at the speed of light, rules out all quartic and quintic GLPV theories. Additionally, we study how the same couplings affect the propagation of gravitons at loop order. The operator proportional to $tilde m_4^2$ generates a calculable, non-Lorentz invariant higher-derivative correction to the graviton propagation. The modification of the dispersion relation provides a bound on $tilde m_4^2$ comparable to the one of the decay. Conversely, operators up to cubic Horndeski do not generate sizeable higher-derivative corrections.
The CMB bispectrum generated by second-order effects at recombination can be calculated analytically when one of the three modes has a wavelength much longer than the other two and is outside the horizon at recombination. This was pointed out in cite
{Creminelli:2004pv} and here we correct their results. We derive a simple formula for the bispectrum, $f_{NL}^{loc} = - (1/6+ cos 2 theta) cdot (1- 1/2 cdot d ln (l_S^2 C_{S})/d ln l_S)$, where $C_S$ is the short scale spectrum and $theta$ the relative orientation between the long and the short modes. This formula is exact and takes into account all effects at recombination, including recombination-lensing, but neglects all late-time effects such as ISW-lensing. The induced bispectrum in the squeezed limit is small and will negligibly contaminate the Planck search for a local primordial signal: this will be biased only by $f_{NL}^{loc}approx-0.4$. The above analytic formula includes the primordial non-Gaussianity of any single-field model. It also represents a consistency check for second-order Boltzmann codes: we find substantial agreement with the CMBquick code.
