Renormalization group fixed points of foliated gravity-matter systems

Abstract

We employ the Arnowitt-Deser-Misner formalism to study the renormalization group flow of gravity minimally coupled to an arbitrary number of scalar, vector, and Dirac fields. The decomposition of the gravitational degrees of freedom into a lapse function, shift vector, and spatial metric equips spacetime with a preferred (Euclidean) "time"-direction. In this work, we provide a detailed derivation of the renormalization group flow of Newton's constant and the cosmological constant on a flat Friedmann-Robertson-Walker background. Adding matter fields, it is shown that their contribution to the flow is the same as in the covariant formulation and can be captured by two parameters $d_g$, $d_\lambda$. We classify the resulting fixed point structure as a function of these parameters finding that the existence of non-Gaussian renormalization group fixed points is rather generic. In particular the matter content of the standard model and its most common extensions gives rise to one non-Gaussian fixed point with real critical exponents suitable for Asymptotic Safety. Moreover, we find non-Gaussian fixed points for any number of scalar matter fields, making the scenario attractive for cosmological model building.Comment: 42 pages, 6 figure

On avoiding Ostrogradski instabilities within Asymptotic Safety

“…[17][18][19][20] studied projections of the full RG flow where the matter sector contained an arbitrary number of minimally coupled scalars N s , vectors N v , and Dirac fermions N D . Complementary results for the case where spacetime carries a foliation structure have been reported in [21]. While all studies agree on the statement that the matter content of the standard model of particle physics leads to a fixed point structure suitable for realizing the Asymptotic Safety mechanism, the precise values for N s , N v , and N D supporting a NGFP are different.…”

“…While all studies agree on the statement that the matter content of the standard model of particle physics leads to a fixed point structure suitable for realizing the Asymptotic Safety mechanism, the precise values for N s , N v , and N D supporting a NGFP are different. Restricting to the cases where the matter sector contains scalar fields only, [17][18][19][20] report an upper bound N s 16 − 20, while in [21] no such bound is present in agreement with the initial works [22,23]. This difference can be traced back to different choices for the coarse graining operators and definitions of Newton's constant employed in these works.…”

“…In particular, refs. [18][19][20] define Newton's constant based on the flat space graviton propagator while [17,21] resort to a background Newton's constant. As argued in [19] matter degrees of freedom contribute differently in these settings.…”

Upper bound on the Abelian gauge coupling from asymptotic safety

“…Within the single-metric approximation, the inclusion of fermions results in a shift of the fixed point towards large negative Λ [15,16,19,90]. In turn, this leads to a signficantly smaller value of f g , shifting the fixed-point value of g Y and accordingly also its IR value much closer to the observed value.…”

“…We focus on an asymptotically safe model of quantum gravity [4]. Based on the groundbreaking work of Reuter [5], compelling evidence for the existence of an asymptotically safe fixed point in pure gravity [6][7][8][9][10][11][12][13][14] as well as with matter [15][16][17][18][19] has been discovered, for reviews see, e.g., [20][21][22][23][24][25][26][27][28][29][30][31][32]. This fixed point provides a UV completion for a quantum field theory of the…”