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      Feynman Diagrams for Stochastic Inflation and Quantum Field Theory in de Sitter Space

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          Abstract

          We consider a massive scalar field with quartic self-interaction \(\lambda/4!\,\phi^4\) in de~Sitter spacetime and present a diagrammatic expansion that describes the field as driven by stochastic noise. This is compared with the Feynman diagrams in the Keldysh basis of the Amphichronous (Closed-Time-Path) Field Theoretical formalism. For all orders in the expansion, we find that the diagrams agree when evaluated in the leading infrared approximation, i.e. to leading order in \(m^2/H^2\), where \(m\) is the mass of the scalar field and \(H\) is the Hubble rate. As a consequence, the correlation functions computed in both approaches also agree to leading infrared order. This perturbative correspondence shows that the stochastic Theory is exactly equivalent to the Field Theory in the infrared. The former can then offer a non-perturbative resummation of the Field Theoretical Feynman diagram expansion, including fields with \(0\leq m^2\ll\sqrt \lambda H^2\) for which the perturbation expansion fails at late times.

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          Brownian Motion of a Quantum Oscillator

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            Statistical Dynamics of Classical Systems

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              Planck 2013 results. XVI. Cosmological parameters

              We present the first results based on Planck measurements of the CMB temperature and lensing-potential power spectra. The Planck spectra at high multipoles are extremely well described by the standard spatially-flat six-parameter LCDM cosmology. In this model Planck data determine the cosmological parameters to high precision. We find a low value of the Hubble constant, H0=67.3+/-1.2 km/s/Mpc and a high value of the matter density parameter, Omega_m=0.315+/-0.017 (+/-1 sigma errors) in excellent agreement with constraints from baryon acoustic oscillation (BAO) surveys. Including curvature, we find that the Universe is consistent with spatial flatness to percent-level precision using Planck CMB data alone. We present results from an analysis of extensions to the standard cosmology, using astrophysical data sets in addition to Planck and high-resolution CMB data. None of these models are favoured significantly over standard LCDM. The deviation of the scalar spectral index from unity is insensitive to the addition of tensor modes and to changes in the matter content of the Universe. We find a 95% upper limit of r<0.11 on the tensor-to-scalar ratio. There is no evidence for additional neutrino-like relativistic particles. Using BAO and CMB data, we find N_eff=3.30+/-0.27 for the effective number of relativistic degrees of freedom, and an upper limit of 0.23 eV for the summed neutrino mass. Our results are in excellent agreement with big bang nucleosynthesis and the standard value of N_eff=3.046. We find no evidence for dynamical dark energy. Despite the success of the standard LCDM model, this cosmology does not provide a good fit to the CMB power spectrum at low multipoles, as noted previously by the WMAP team. While not of decisive significance, this is an anomaly in an otherwise self-consistent analysis of the Planck temperature data.
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                Author and article information

                Journal
                16 December 2014
                Article
                10.1103/PhysRevD.91.063520
                1412.4893
                3cef242b-a956-4646-8ff0-37b4a67d8e19

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                TUM-HEP-971-14
                Phys. Rev. D 91, 063520 (2015)
                25 pages, 4 figures
                hep-th astro-ph.CO gr-qc hep-ph

                Cosmology & Extragalactic astrophysics,General relativity & Quantum cosmology,High energy & Particle physics

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