Quantum corrections to scalar field dynamics in a slow-roll space-time

We consider the dynamics of a quantum scalar field in the background of a slow-roll inflating Universe. We compute the one-loop quantum corrections to the field and Friedmann equation of motion, in both a 1PI and a 2PI expansion, to leading order in slow-roll. Generalizing the works of [1-3], we then solve these equations to compute the effect on the primordial power spectrum, for the case of a self-interacting inflaton and a self-interacting spectator field. We find that for the inflaton the corrections are negligible due to the smallness of the coupling constant despite the large IR enhancement of the loop contributions. For a curvaton scenario, on the other hand, we find tension in using the 1PI loop corrections, which may indicate that the quantum corrections could be non-perturbatively large in this case, thus requiring resummation.Comment: 33 pages, 1 figure. Version published in JHE

Quantum kinetic theory with nonlocal coherence

In this thesis we develop a novel approximation scheme (eQPA), where the effects of nonlocal coherence are included in the kinetic approach to nonequilibrium quantum dynamics. The key element in our formalism is the finding of new singular shell solutions, located at $k_{0,z} = 0$ in the phase space of 2-point Wightman function, which describe the nonlocal quantum coherence between the ``opposite'' mass-shell excitations for spatially homogeneous and static planar symmetric problems, respectively. This phase space structure leads to a closed set of transport equations for the corresponding on-shell distribution functions $f$, providing an extension to the standard quantum Boltzmann equation. We have considered a number of applications to demonstrate the use of our formalism, including the Klein problem, quantum reflection from a CP-violating mass wall and coherent production of (fermionic and scalar) particles in an oscillating background. Our formalism should be of relevance for many problems in particle physics and cosmology, including baryogenesis and neutrino flavour oscillations in an inhomogeneous background.Comment: 90 pages, 19 figures; PhD Thesi

Quantum corrections to inflaton dynamics, the semi-classical approach and the semi-classical limit

Computations of quantum corrections to the CMB spectrum and to scalar field dynamics during inflation very often take advantage of the "semi-classical" approach, where the metric fluctuations are simply omitted. On the other hand, a complete computation ought to take into account that the matter field perturbation and scalar metric perturbation together constitute a single physical degree of freedom. The question then naturally arises, in which sense the semi-classical approach is an approximation to the complete calculation, and whether there are specific limits where this is also a good approximation. We consider the quantum corrected dynamics of interacting scalar fields in an expanding inflationary background. We demonstrate this by explicitly computing the leading quantum radiative corrections to the evolution equation of the mean field ("condensate") and the Friedmann equations taking into account scalar perturbations of both the matter field and the metric, and when omitting the latter. We find that the two agree in the limit H << M_pl , but one is not a limit of the other. We also find that in simple models of inflation, H/M_pl is not small enough that the two approaches can be said to agree. By direct comparison, we demonstrate how to interpret the "semi-classical" approach often employed in more complex computations as a well-defined approximation, and quantify its validity.Comment: Some revision and rewordings, added references. 16 page

Kinetic theory for scalar fields with nonlocal quantum coherence

We derive quantum kinetic equations for scalar fields undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). Our central finding is that in systems with certain space-time symmetries, quantum coherence manifests itself in the form of new spectral solutions for the dynamical 2-point correlation function. This spectral structure leads to a consistent approximation for dynamical equations that describe coherent evolution in presence of decohering collisions. We illustrate the method by solving the bosonic Klein problem and the bound states for the nonrelativistic square well potential. We then compare our spectral phase space definition of particle number to other definitions in the nonequilibrium field theory. Finally we will explicitly compute the effects of interactions to coherent particle production in the case of an unstable field coupled to an oscillating background.Comment: 33 pages, 7 figures, replaced with the version published in JHE

Spacetime curvature and the Higgs stability during inflation

It has been claimed that the electroweak vacuum may be unstable during inflation due to large fluctuations of order $H$ in case of a high inflationary scale as suggested by BICEP2. We compute the Standard Model Higgs effective potential including UV-induced curvature corrections at one-loop level. We find that for a high inflationary scale a large curvature mass is generated due to RG running of non-minimal coupling $\xi$, which either stabilizes the potential against fluctuations for $\xi_{\rm EW} \gtrsim 6\cdot 10^{-2}$, or destabilizes it for $\xi_{\rm EW} \lesssim 2 \cdot 10^{-2}$ when the generated curvature mass is negative. Only in the narrow intermediate region the effect of the curvature mass may be significantly smaller.Comment: 5 pages, 4 figures. Version published in PR

Spacetime curvature and Higgs stability after inflation

We investigate the dynamics of the Higgs field at the end of inflation in the minimal scenario consisting of an inflaton field coupled to the Standard Model only through the non-minimal gravitational coupling $\xi$ of the Higgs field. Such a coupling is required by renormalisation of the Standard Model in curved space, and in the current scenario also by vacuum stability during high-scale inflation. We find that for $\xi\gtrsim 1$, rapidly changing spacetime curvature at the end of inflation leads to significant production of Higgs particles, potentially triggering a transition to a negative-energy Planck scale vacuum state and causing an immediate collapse of the Universe.Comment: 5 pages, 1 figure. Updated to match version to appear in PR

Coherent quantum Boltzmann equations from cQPA

We reformulate and extend our recently introduced quantum kinetic theory for interacting fermion and scalar fields. Our formalism is based on the coherent quasiparticle approximation (cQPA) where nonlocal coherence information is encoded in new spectral solutions at off-shell momenta. We derive explicit forms for the cQPA propagators in the homogeneous background and show that the collision integrals involving the new coherence propagators need to be resummed to all orders in gradient expansion. We perform this resummation and derive generalized momentum space Feynman rules including coherent propagators and modified vertex rules for a Yukawa interaction. As a result we are able to set up self-consistent quantum Boltzmann equations for both fermion and scalar fields. We present several examples of diagrammatic calculations and numerical applications including a simple toy model for coherent baryogenesis.Peer reviewe

Quantum kinetic theory for fermions in temporally varying backrounds

We derive quantum kinetic equations for fermions in a homogeneous time-dependent background in presence of decohering collisions, by use of the Schwinger-Keldysh CTP-formalism. The quantum coherence (between particles and antiparticles) is found to arise from new spectral solutions for the dynamical 2-point correlation function in the mean field limit. The physical density matrix $\rho$ and its dynamics is shown to be necessarily dependent on the extrenous information on the system, and expressions that relate $\rho$ to fundamental coherence functions and fermionic particle and antiparticle numbers are derived. For an interacting system we demonstrate how smooth decoherence effects are induced by collisions. As special applications we study the production of unstable particles during the preheating stage of the inflation and an evolution of an initially quantum $\rho$ towards a statistical limit including decoherence and thermalisation.Comment: 34 pages, 8 figure