The constancy of \zeta in single-clock Inflation at all loops

Studying loop corrections to inflationary perturbations, with particular emphasis on infrared factors, is important to understand the consistency of the inflationary theory, its predictivity and to establish the existence of the slow-roll eternal inflation phenomena and its recently found volume bound. In this paper we show that \zeta-correlators are time-independent at large distances at all-loop level in single clock inflation. We write the n-th order correlators of \dot\zeta\ as the time-integral of Green's functions times the correlators of local sources that are function of the lower order fluctuations. The Green's functions are such that only non-vanishing correlators of the sources at late times can lead to non-vanishing correlators for \dot\zeta\ at long distances. When the sources are connected by high wavenumber modes, the correlator is peaked at short distances, and these diagrams cannot lead to a time-dependence by simple diff. invariance arguments. When the sources are connected by long wavenumber modes one can use similar arguments once the constancy of \zeta\ at lower orders was established. Therefore the conservation of \zeta\ at a given order follows from the conservation of \zeta\ at the lower orders. Since at tree-level \zeta\ is constant, this implies constancy at all-loops by induction.Comment: 14 pages, 3 figure

The IR-resummed Effective Field Theory of Large Scale Structures

We present a new method to resum the effect of large scale motions in the Effective Field Theory of Large Scale Structures. Because the linear power spectrum in $\Lambda$CDM is not scale free the effects of the large scale flows are enhanced. Although previous EFT calculations of the equal-time density power spectrum at one and two loops showed a remarkable agreement with numerical results, they also showed a 2% residual which appeared related to the BAO oscillations. We show that this was indeed the case, explain the physical origin and show how a Lagrangian based calculation removes this differences. We propose a simple method to upgrade existing Eulerian calculations to effectively make them Lagrangian and compare the new results with existing fits to numerical simulations. Our new two-loop results agrees with numerical results up to $k\sim 0.6 h/$Mpc to within 1% with no oscillatory residuals. We also compute power spectra involving momentum which is significantly more affected by the large scale flows. We show how keeping track of these velocities significantly enhances the UV reach of the momentum power spectrum in addition to removing the BAO related residuals. We compute predictions for the real space correlation function around the BAO scale and investigate its sensitivity to the EFT parameters and the details of the resummation technique.Comment: 37 pages, 9 figures. v2: JCAP published version, added references and extended explanation

CMB Anisotropies from a Gradient Mode

A linear gradient mode must have no observable dynamical effect on short distance physics. We confirm this by showing that if there was such a gradient mode extending across the whole observable Universe, it would not cause any hemispherical asymmetry in the power of CMB anisotropies, as long as Maldacena's consistency condition is satisfied. To study the effect of the long wavelength mode on short wavelength modes, we generalize the existing second order Sachs-Wolfe formula in the squeezed limit to include a gradient in the long mode and to account for the change in the location of the last scattering surface induced by this mode. Next, we consider effects that are of second order in the long mode. A gradient mode $\Phi = \boldsymbol q\cdot \boldsymbol x$ generated in Single-field inflation is shown to induce an observable quadrupole moment. For instance, in a matter-dominated model it is equal to $Q=5 (\boldsymbol q\cdot \boldsymbol x)^2 /18$. This quadrupole can be canceled by superposition of a quadratic perturbation. The result is shown to be a nonlinear extension of Weinberg's adiabatic modes: a long-wavelength physical mode which looks locally like a coordinate transformation.Comment: 21+8 pages. improved presentatio

Double Soft Limits of Cosmological Correlations

Correlation functions of two long-wavelength modes with several short-wavelength modes are shown to be related to lower order correlation functions, using the background wave method, and independently, by exploiting symmetries of the wavefunction of the Universe. These soft identities follow from the non-linear extension of the adiabatic modes of Weinberg, and their generalization by Hinterbichler et. al. The extension is shown to be unique. A few checks of the identities are presented.Comment: 18+16 page