Inflationary correlation functions are potentially affected by infrared divergences. For example, the two-point correlator of curvature perturbation at momentum k receives corrections ~ln(kL), where L is the size of the region in which the measurement is performed. We define infrared-safe correlation functions which have no sensitivity to the size L of the box used for the observation. The conventional correlators with their familiar log-enhanced corrections (both from scalar and tensor long-wavelength modes) are easily recovered from our IR-safe correlation functions. Among other examples, we illustrate this by calculating the corrections to the non-Gaussianity parameter f_NL coming from long-wavelength tensor modes. In our approach, the IR corrections automatically emerge in a resummed, all-orders form. For the scalar corrections, the resulting all-orders expression can be evaluated explicitly.
It is widely known that the primordial curvature perturbation $ζ$ has several universal properties in the infrared (IR) such as the soft theorem, which is also known as the consistency relation, and the conservation in time. They are valid in rather general single clock models of inflation. It has been argued that these universal properties are deeply related to the large gauge transformations in inflationary spacetime. However, the invariance under the large gauge transformations is not sufficient to show these IR properties. In this paper, we show that the locality condition is crucial to sh…
Inflation in the early Universe is a grand phase transition which have produced the seeds of all the structures we now observe. We focus on the non-equilibrium aspect of this phase transition especially the inevitable infrared (IR) divergence associated to the the quantum and classical fields during the inflation. There is a long history of research for removing this IR divergence for healthy perturbation calculations. On the other hand, the same IR divergence is quite relevant and have developed the primordial density fluctuations in the early Universe. We develop a unified formalism in which…
We investigate a calculation method for solving the Mukhanov-Sasaki equation in slow-roll $k$-inflation based on the uniform approximation (UA) in conjunction with an expansion scheme for slow-roll parameters with respect to the number of $e$-folds about the so-called \textit{turning point}. Earlier works on this method has so far gained some promising results derived from the approximating expressions for the power spectra among others, up to second order with respect to the Hubble and sound flow parameters, when compared to other semi-analytical approaches (e.g., Green's function and WKB met…
Locality in effective field theory for inflationary soft modes
Kyoto University（京都大学）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK)（高能加速器研究机构粒子核研究研究所）；The Graduate University for Advanced Studies (SOKENDAI)（综合研究大学院大学）
String Theory and Supergravity allow, in principle, to follow the transition of the inflaton from pre-inflationary fast roll to slow roll. This introduces an infrared depression in the primordial power spectrum that might have left an imprint in the CMB anisotropy, if it occurred at accessible wavelengths. We model the effect extending $Λ$CDM with a scale $Δ$ related to the infrared depression and explore the constraints allowed by {\sc Planck} data, employing also more conservative, wider Galactic masks in the low resolution CMB likelihood. In an extended mask with $f_{sky}=39\%$, we thus fin…
Measurements of the luminosity distance have played a key role in discovering the late-time cosmic acceleration. However, when accounting for inhomogeneities in the Universe, its interpretation has been plagued with infrared divergences in its theoretical predictions, which are in some cases used to explain the cosmic acceleration without dark energy. The divergences in most calculations are artificially removed by imposing an infrared cut-off scale. For the first time, we show that a gauge-invariant calculation of the luminosity distance is devoid of such divergences and consistent with the e…
Fixing the Renormalization of Inflationary Loops via Ward Identities
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院基础科学与数学学院）
We study the Wigner function for the inflationary tensor perturbation defined in the real phase space. We compute explicitly the Wigner function including the contributions from the cubic self-interaction Hamiltonian of tensor perturbations. Then we argue that it is no longer an appropriate description for the probability distribution in the sense that quantum nature allows negativity around vanishing phase variables. This comes from the non-Gaussian wavefunction in the mixed state as a result of the non-linear interaction between super- and sub-horizon modes. We also show that this is related…
During inflationary preheating, the energy stored in the inflaton field is rapidly converted into excitations of other entropy fields. This stage is characterized by exponential particle production due to parametric resonance and is notoriously difficult to analyze using analytic methods. We develop a detailed numerical simulation to investigate inflationary preheating when the potential of the inflaton is a power-law function with arbitrary power index. To achieve a successful graceful exit from a primordial inflationary phase to a smooth, oscillatory phase during preheating, we assume the in…
