Inflation from asymptotically safe theories

Abstract

We investigate models in which inflation is driven by an ultraviolet safe and interacting scalar sector stemming from a new class of nonsupersymmetric gauge field theories. These new theories, differently from generic scalar models, are well defined to arbitrary short distances because of the existence of a controllable ultraviolet interacting fixed point. The scalar couplings at the ultraviolet fixed point and their overall running are predicted by the geometric structure of the underlying theory. We analyse the minimal and non-minimal coupling to gravity of these theories and the consequences for inflation. In the minimal coupling case the theory requires large non-perturbative quantum corrections to the quantum potential for the theory to agree with data, while in the nonminimal coupling case the perturbative regime in the couplings of the theory is preferred. Requiring the theory to reproduce the observed amplitude of density perturbations constrain the geometric data of the theory such as the number of colors and flavors for generic values of the non-minimal coupling.Preprint: CP 3 -Origins-2015-008 DNRF90The inflationary paradigm plays a central role in modern cosmology [1,2]. Many realisations have appeared in the literature [3] with the vast majority using elementary scalar fields to drive inflation. Theories with fundamental scalars are, however, typically trivial. Meaning that for the theory to be well defined at arbitrary short scales the renormalized coupling must vanish, and consequently the resulting theory is non-interacting. It could happen that gravitational corrections can render field theories featuring scalars well defined at short distances, but so far no formal proof exists in four dimensions, and without requiring additional (space-time) symmetries. It is therefore interesting to explore models where the issue is resolved before the underlying fundamental particle theory of the inflaton is coupled to gravity. A possible solution is to assume the inflaton to be a composite state made by a more fundamental matter [4,5] governed by an asymptotically free theory [6,7]. The gravity dual dynamics of these models has been investigated in [8].Recently, however, a novel class of non-trivial fourdimensional theories featuring elementary scalars appeared [9]. The crucial ingredient is the presence of an exact interacting ultraviolet (UV) fixed point in all the couplings of the theory, i.e. the theories are complete asymptotically safe [9]. The asymptotic safety scenario refers to the existence of high-energy fixed points [10]. It plays a relevant role as a possible UV completion of quantum gravity [10][11][12][13][14] 1 . The resulting physics is quite distinct from the tra-1 In addition several UV conformal extensions of the standard ditional complete asymptotic freedom scenario where a non-interacting UV fixed point emerges in all the couplings [44,45]; see also [46,47] for recent studies.The template that we shall consider here consists of an SU (N C ) gauge theory with N F Dirac fermions transfor...

UV conformal window for asymptotic safety

“…General scenarios have been classified and conditions for cosmological fixed points with inflationary expansions in the early universe are known [59] (see [60,61] for settings where inflation arises purely quantum gravitationally). It has also been speculated that inflation may arise from asymptotically safe toy models [22,27], neglecting quantum gravity altogether [62,63]. Compatibility with the 2015 Planck data [64] at the 2σ-level requires a large conformal window up to ≈ 0.7 .…”

An Asymptotically Safe Guide to Quantum Gravity and Matter

“…Asymptotic safety beyond the Standard Model could have intriguing phenomenological consequences in astrophysics and cosmology [126]. For instance, asymptotically safe dark matter could accommodate a significant running of the portal coupling to visible matter between the dark-matter-mass scale -relevant for thermal production of dark matter in the early universe -and the scale of direct detection experiments [127].…”

Supersymmetric asymptotic safety is not guaranteed

“…To connect with (3.8) and (3.9) note that they give (using (3.3), and R(W ) = R(H) + 2R(Q)) 4) and to the relevant order (dropping O(α 2 g,y ) and O(1/N c )) we have…”

“…maximizing a 1 (R SCFT,i ) over the R i , subject to the constraint in (5.1). This gives [27], 4) where the Lagrange multiplier is determined via (5.1). In the asymptotically free case, this yields λ = (g 2 * /2π 2 ) + O(g 4 * ) (the higher order terms are scheme dependent) [27,30,31].…”