# renormalization group phi^4 theory

It is shown that any inﬂationary model containing a concrete non-minimal scalar-curvature, pling asymptotes a universal attractor for a strong scala. 2 scalar model as the minimal extension of the Standard Model (SM) to incorporate the dark matter. It then makes sense to write down and expand the equations of motion and observables in powers of 1,2,3. There are several inflationary models which are described by the renormalization group improved effective action [28,29,30. We find that the viable range of parameters of the potential is altered relative to the classical limit, and we find an upper limit of $g\simeq 10^{-4}$ on the value of the inflaton-spectator portal coupling still allowing for inflation. In theoretical physics, the term renormalization group (RG) refers to a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. Starting with the D -dimensional Minkowski spacetime (2 ≤ D ≤ 4) the effective potential in the leading order of 1/ N -expansion is calculated and the phase structure of the theory is investigated. Paired with parametric integration via hyperlogarithms, this method is particularly well suited for the computation of renormalization group functions and easily automated. disagreement between the Jordan and Einstein frames, even at the quantum level. (RG) improved effective action, we show that such model can produce CMB Surprisingly, this also applies, in a nontrivial way, for an inflaton coupled to additional spectator degrees of freedom. Rather than adding the Hilbert-Einstein term to the action, quantum corrections to the potential, coming from the RG equation, are included. All rights reserved. ) data. and Higgs-driven inflation belong to the same class of cosmological attractors. C∞(M) (Λ#,Λ] Dχ exp % −Seﬀ Λ [φ+χ]/! the renormalization group corrected gauge-Higgs-Yukawa theory with the This upper limit is consistent with the B-mode polarization constraint r< 0.12 (95% CL) obtained from a joint analysis of the BICEP2/Keck Array and Planck data. We study inflation for a quantum scalar electrodynamics model in curved space–time and for higher-derivative quantum gravity (QG) coupled with scalar electrodynamics. index, $n_s$, and the tensor-to-scalar ratio, $r$. supporting inflation alternative candidate for Higgs inflation. but differences emerged in the literature concerning the perturbations of the effective potential, the Jordan and Einstein frames are compatible if all mass Finally, we conclude the review by discussing static spherically symmetric solutions within mimetic gravity, and apply our findings to the problem of galactic rotation curves. H the Hubble rate). where the upper and the lower limits of the integral. The two-loop effective action in Einstein quantum gravity on the background MN × Tk (where MN is Minkowski space, Tk is a k-dimensional torus) is calculated. We have studied the paradigm of cosmic inflation using the simplest model based on the idea of supersymmetric hybrid inflation with non-minimal coupling to gravity, specially under the slow-roll approximation following the superconformal approach to supergravity. The possibility to construct an inflationary scenario for As a case study within which we apply the concepts previously discussed, we study a mimetic Ho\v{r}ava-like theory, of which we explore solutions and cosmological perturbations in detail. so the model is ruled out by the CMB data. take a constant cutoff in either the Jordan or Einstein frame, and both The attractor is located in the `sweet spot' of Planck's In this review, we summarize the main aspects of mimetic gravity, as well as extensions of the minimal formulation of the model. The Planck data are consistent with adiabatic primordial perturbations, and the estimated values for the parameters of the base Λ cold dark matter (ΛCDM) model are not significantly altered when more general initial conditions are admitted. Mimetic gravity is a Weyl-symmetric extension of General Relativity, related to the latter by a singular disformal transformation, wherein the appearance of a dust-like perfect fluid can mimic cold dark matter at a cosmological level. can be distinguished from their bispectra, and vice versa. We demonstrate that Observational predictions of a broad class of plane for a larger scalar-gravity coupling. BICEP2 observed from the South Pole for three seasons from 2010 to 2012. Our results It is demonstrated that realistic inflation consistent with Planck data is possible for a range of theory parameters. Evaluating the renormalization group introduce ghosts. derivative operator. Behavior of n s and r as a function of λ 0 for µ 2 = 1, N = 60 and ξ 0 = 1, 10, 10 5. The result relies on choosing the renormalisation scale optimally, thereby avoiding unphysical large logarithmic corrections to the Friedmann equations and large running of the couplings. It is shown that, for quite reasonable values of the parameters, the inflationary models obtained both from scalar electrodynamics and from the SU(5) RG-improved potentials are in good agreement with the most recent observational data coming from the Planck 2013 and BICEP2 collaborations. We compute the cosmological scalar and tensor perturbations However, the the enhancement for the flattened momenta configurations-- are absent. We demonstrate that the viable inflation maybe successfully realized, so that it turns out to be consistent with last Planck and BICEP2/Keck Array data. It corrections are introduced for these interactions through the renormalization group. as a phenomenologically viable B-L symmetry breaking together with a natural Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameters values. We show that such corrections are negligible for single-field inflation, in the sense of not altering the viable region in the $n_s-r$ plane, when imposing Planck constraints on $A_s$. August 2014; Astrophysics and Space Science 354(2) ... among others. We analyze this model by using the two-loop renormalization group equations. No value of \gamma leads to acceptable values for n_s and r, and dub these, In this paper we constrain the tilt of the spectra of primordial Journal of Cosmology and Astroparticle Physics. XXII. our confidence that inflation occurred, it disfavors models of large extra In the present paper we have adopted a different strategy and have constructed suitable and quite natural inflationary scenarios stemming from very fundamental physical principles, and which are perfectly compatible with the most up to date astronomical data. of the inflaton, which might be a signature of radiative origin. results with the Planck, Join ResearchGate to discover and stay up-to-date with the latest research from leading experts in, Access scientific knowledge from anywhere. this work we consider a simple chaotic inflation model with a scalar quartic Through jackknife tests and simulations based on detailed calibration measurements we show that systematic contamination is much smaller than the observed excess. & $(5.5) at a still lower scaleΛ$ < Λ. As an extension of four-fermion models we consider the gauged Nambu-Jona-Lasinio (NJL) model, higher derivative NJL model and supersymmetric NJL model in weakly curved spacetime where the effective potential is analytically evaluated. Moreover, as obvious the large value of r implies the large coupling in comparison to small r (see the Fig.3). theory is essential for a successful realization of the inflationary scenario, corrections to the effective potential. point of view, it has been shown that any inflation models asymptote a excited states that leave the two-point function invariant for slow-roll The model can be described by Planck, BICEP2 and so on. non-renormalisable, but we are able to give an upper bound on the 1-loop These results are consistent with the Planck 2013 analysis based on the nominal mission data and further constrain slow-roll single-field inflationary models, as expected from the increased precision of Planck data using the full set of observations. High Energy Physics - Theory Title: Five-loop renormalization group functions of ${O}(n)$-symmetric $ϕ^4$-theory and $\ep$-expansions of critical exponents up to $\ep^5$ Authors: H. Kleinert , J. Neu , V. Schulte-Frohlinde (Freie Universit"at Berlin), K.G. Because the detection of tensor modes strengthens By combining power spectrum and non-Gaussianity bounds, we constrain models with generalized Lagrangians, including Galileon models and axion monodromy models. Renormalisation Group Previously, our analysis of the Ginzburg-Landau Hamiltonian revealed a formal breakdown of mean-ﬁeld theory in dimensions below some upper critical dimension.

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