Abstract: We study the possibility that the approximate time shift symmetry during inflation is promoted to the full invariance under time reparametrization t -> (t) over tilde (t), or equivalently under field redefinition of the inflaton phi -> (phi) over tilde(phi). The symmetry allows only two operators at leading order in derivatives, so that all n-point functions of scalar perturbations are fixed in terms of the power spectrum normalization and the speed of sound. During inflation the decaying mode only decays as 1/a and this opens up the possibility to violate some of the consistency relations in the squeezed limit, although this violation is suppressed by the (small) breaking of the field reparametrization symmetry. In particular one can get terms in the 3-point function that are only suppressed by 1/k(L) in the squeezed limit k(L) -> 0 compared to the local shape.

Abstract: We show that the Higgs portal interactions involving extra dark Higgs field can save generically the original Higgs inflation of the standard model (SM) from the problem of a deep non-SM vacuum in the SM Higgs potential. Specifically, we show that such interactions disconnect the top quark pole mass from inflationary observables and allow multi-dimensional parameter space to save the Higgs inflation, thanks to the additional parameters (the dark Higgs boson mass m(phi), the mixing angle a between the SM Higgs H and dark Higgs Phi, and the mixed quartic coupling) affecting RG-running of the Higgs quartic coupling. The effect of Higgs portal interactions may lead to a larger tensor-to-scalar ratio, 0.08 less than or similar to r less than or similar to 0.1, by adjusting relevant parameters in wide ranges of alpha and m(phi), some region of which can be probed at future colliders. Performing a numerical analysis we find an allowed region of parameters, matching the latest Planck data.

Abstract: We study the impact of stochastic noise on the generation of primordial black hole (PBH) seeds in ultra-slow-roll (USR) inflation with numerical simulations. We consider the non-linearity of the system by consistently taking into account the noise dependence on the inflaton perturbations, while evolving the perturbations on the coarse-grained background affected by the noise. We capture in this way the non-Markovian nature of the dynamics, and demonstrate that non-Markovian effects are subleading. Using the Delta N formalism, we find the probability distribution P(R) of the comoving curvature perturbation R. We consider inflationary potentials that fit the CMB and lead to PBH dark matter with i) asteroid, ii) solar, or iii) Planck mass, as well as iv) PBHs that form the seeds of supermassive black holes. We find that stochastic effects enhance the PBH abundance by a factor of O(10)-O(10(8)), depending on the PBH mass. We also show that the usual approximation, where stochastic kicks depend only on the Hubble rate, either underestimates or overestimates the abundance by orders of magnitude, depending on the potential. We evaluate the gauge dependence of the results, discuss the quantum-to-classical transition, and highlight open issues of the application of the stochastic formalism to USR inflation.