Well-posed UV completion for simulating scalar Galileons

Numerical relativity for Horndeski gravity

“…This fix has been found to be helpful for evolving outside of the weakly-coupled regime in the numerical evolution of this class of theories. 89,99,107 Beyond quadratic Horndeski gravity, this method has been applied to cubic Horndeski, 108 and ESGB gravity. 109 The fixing approach has also be applied to higher-derivative theories of gravity.…”

The well-posedness of the Cauchy problem for self-interacting vector fields

“…If such conditions are not satisfied (as for the cases studied in [1][2][3]) an alternative possibility is to employ a "fixing-equation" [15] approach inspired by the Müller-Israel-Stewart formulation of viscous relativistic hydrodynamics [16][17][18]. These approaches have been successfully applied in [11,15,[19][20][21][22][23] to ameliorate the stability of the fully numerical evolutions in theories with either changes of character of the Cauchy problem, higher-order derivatives, or derivative self-interactions. This method consists of modifying the field equations by introducing extra fields and "fixing equations" (i.e.…”

Self-Consistent Modeling of Gravitational Theories beyond General Relativity

“…As a result, beyond a length scale ≃σ 1=2 (for our choices, up to ≃0.2M S ) the system reduces to the original one, while shorter ones are damped and controlled, and we can explore even shorter scales through suitable extrapolation of our results, as we discuss in the Supplemental Material [27]. The new variable b C, in essence, brings back (some of) the degree(s) of freedom integrated out to arrive to the EFT theory, in this case a massive scalar (see e.g., [12]) and our strategy defines a completion of the EFT. Notice the operator ∂ 0 ≡ ∂ t − β i ∂i with the advection vector (corresponding to the shift vector in the 3 þ 1 decomposition) helps ensuring inflow towards the BH(s).…”

“…Unfortunately, the majority of proposed beyond GR theories have, at a formal level, mathematical pathologies which makes their understanding in general scenarios difficult [4]. Such pathologies may include loss of uniqueness, a dynamical change of character in the equations of motion (e.g., from hyperbolic to elliptic) or, even worse, having equations of motion (EOM) of unknown mathematical type (e.g., [6][7][8][9][10][11][12]). This, combined with the need to use computational simulations to study the (nonlinear or dynamical) regime of interest, pose unique challenges.…”