Status of the Dortmund TGM3-Beamline

Does the observable spectrum of cosmic fluctuations depend on detailed initial conditions? This addresses the question if the general inflationary paradigm is sufficient to predict within a given model the spectrum and amplitude of cosmic fluctuations, or if additional particular assumptions about the initial conditions are needed. The answer depends on the number of e-foldings Nin between the beginning of inflation and horizon crossing of the observable fluctuations. We discuss an interacting inflaton field in an arbitrary homogeneous and isotropic geometry, employing the quantum effective action Γ. An exact time evolution equation for the correlation function involves the second functional derivative Γ (2) . The operator formalism and quantum vacua for interacting fields are not needed. Use of the effective action also allows one to address the change of frames by field transformations (field relativity). Within the approximation of a derivative expansion for the effective action we find the most general solution for the correlation function, including mixed quantum states. For not too large Nin the memory of the initial conditions is preserved. In this case the cosmic microwave background cannot disentangle between the initial spectrum and its processing at horizon crossing. The inflaton potential cannot be reconstructed without assumptions about the initial state of the universe. We argue that for very large Nin a universal scaling form of the correlation function is reached for the range of observable modes. This can be due to symmetrization and equilibration effects, not yet contained in our approximation, which drive the short distance tail of the correlation function towards the Lorentz invariant propagator in flat space.

“…(25) and (26). The universal propagator in Minkowski space can be extended to a large class of homogeneous and isotropic cosmologies.…”

Section: Propagator In Flat Spacementioning

confidence: 99%

“…Approximative forms can be computed using appropriate non-equilibration quantum field theoretical methods in the in-in-formalism [26,27]. Our task is more modest here -we will compute the consequences of a given assumed form of the effective action.…”

Section: Introductionmentioning

confidence: 99%

Cosmic fluctuations from a quantum effective action

Wetterich

2015

“…Therefore one has to look for nonperturbative approaches providing infinite partial resummations of Feynman diagrams [1,2]. The simplest of such schemes are the mean-field approximations such as the leading-order large-N expansion [3][4][5][6] and the Hartree or Hartree-Fock (HF) variational method [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Renormalized and renormalization-group invariant Hartree-Fock approximation

Destri

Sartirana

2005

We study the renormalization problem for the Hartree-Fock approximation of the ON invariant 4 model in the symmetric phase and show how to systematically improve the corresponding diagrammatic resummation to achieve the correct renormalization properties of the effective field equations, including renormalization-group invariance with the one-loop beta function. These new Hartree-Fock dynamics is still of a mean-field type but includes memory effects which are generically nonlocal also in space.

“…As described in detail in [15], they arise from a local Ansatz for quasiparticle self-energies, and it is not easy to assess how good an approximation this is. For the purposes of estimating the nonequilibrium behaviour numerically, other approximation schemes have recently become available (see, for example, [16,17,18,19]) which are in some respects superior to this one. However for the purpose of deriving a local effective equation of motion, approximations more or less equivalent to ours would seem to be inevitable.…”

Section: Summary and Discussionmentioning

confidence: 99%

Numerical investigation of friction in inflaton equations of motion

Lawrie

2005

The equation of motion for the expectation value of a scalar quantum field does not have the local form that is commonly assumed in studies of inflationary cosmology. We have recently argued that the true, temporally non-local equation of motion does not possess a time-derivative expansion and that the conversion of inflaton energy into particles is not, in principle, described by the friction term estimated from linear response theory. Here, we use numerical methods to investigate whether this obstacle to deriving a local equation of motion is purely formal, or of some quantitative importance. Using a simple scalar-field model, we find that, although the non-equilibrium evolution can exhibit significant damping, this damping is not well described by the local equation of motion obtained from linear response theory. It is possible that linear response theory does not apply to the situation we study only because thermalization turns out to be slow, but we argue that that the large discrepancies we observe indicate a failure of the local approximation at a more fundamental level.