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Perturbative quantum field theory in de Sitter space is known to give rise to a variety of contributions that diverge with time (secular terms). Despite significant progress, a complete understanding of the physical origin of these…
We investigate the divergent perturbative series of correlation functions for a massless, self-interacting scalar field in de Sitter space. First, we use our previously proposed method of autonomous equations to obtain finite time-dependent…
We investigate scalar field theories in de Sitter space by means of nonperturbative renormalization group techniques. We compute the functional flow equation for the effective potential of O(N) theories in the local potential approximation…
A system of stochastic differential equations for the velocity and density of a classical self-gravitating matter is investigated by means of the field theoretic renormalization group. The existence of two types of large-scale scaling…
Perturbative corrections to correlation functions for interacting theories in de Sitter spacetime often grow secularly with time, due to the properties of fluctuations on super-Hubble scales. This growth can lead to a breakdown of…
It is shown that the renormalization group method does not necessarily eliminate all secular terms in perturbation series to partial differential equations and a functional subspace of renormalizable secular solutions corresponds to a…
We consider a theory of $N$ self-interacting quantum scalar fields with quartic $O(N)$-symmetric potential, with a coupling constant $\lambda$, in a generic curved spacetime. We analyze the renormalization process of the Semiclassical…
The quantum evolution equations for the field expectation value are analytically solved to cubic order in the field amplitude and to one-loop level in the lambda phi-fourth model. We adapt and use the renormalization group (RG) method for…
In classical and quantum systems, perturbation of an evolution equation is often invalidated by secular terms which diverge at late times. The diverging behavior of evolution can be remedied by various techniques of resumma- tion such as…
For singular perturbation problems in dynamical systems, various appropriate singular perturbation methods have been proposed to eliminate secular terms appearing in the naive expansion. For example, the method of multiple time scales, the…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
The real time evolution and relaxation of expectation values of quantum fields and of quantum states are computed as initial value problems by implementing the dynamical renormalization group (DRG).Linear response is invoked to set up the…
Correlation functions of light scalar fields in de Sitter spacetime, computed via standard perturbation theory, often exhibit secular growth characterized by time-dependent divergent terms in the form of powers of $\ln a(t)$, where $a(t)$…
Using the Functional Renormalization Group approach we construct effective quantum spacetime geometries by self-consistently deforming the classical Schwarzschild-de Sitter black-hole solution. This involves studying how quantum…
We develop a renormalization group (RG)-based perturbation scheme for a class of ordinary differential equations, including first-order systems with semisimple or nilpotent linear parts, as well as scalar higher-order equations. The key…
We consider the quantum loop effects in scalar electrodynamics on de Sitter space by making use of the functional renormalization group approach. We first integrate out the photon field, which can be done exactly to leading (zeroth) order…
Nonperturbative renormalization group techniques have recently proven a powerful tool to tackle the nontrivial infrared dynamics of light scalar fields in de Sitter space. In the present article, we develop the formalism beyond the local…
We study the dynamics of light quantum scalar fields in de Sitter space on superhorizon scales. We compute the self-energy of an O(N) symmetric theory at next-to-leading order in a 1/N expansion in the regime of superhorizon momenta, and we…
Perturbation theory is a crucial tool for many physical systems, when exact solutions are not available, or nonperturbative numerical solutions are intractable. Naive perturbation theory often fails on long timescales, leading to secularly…
For perturbed ordinally differential equations, a procedure of renormalization group method is proposed. To uniquely obtain renormalized solutions for given initial conditions, the procedure assumes that the extra integral constants yielded…