Tadpole cosmology: self tuning without degeneracy

Abstract

Degeneracy is a method to accommodate exact, low energy vacuum states in scalar-tensor gravitational models despite the presence of an arbitrarily large vacuum energy. However, this approach requires very particular combinations of scalar field and metric couplings in the Lagrangian. In this work we study departures from the restrictive degeneracy condition — starting from a fiducial model containing an exact Minkowski space solution, we break the degeneracy condition in numerous simple ways to test if the resulting models maintain certain key features — specifically the dynamical cancellation of a large vacuum energy by the scalar field and the existence of a low energy vacuum state. We highlight the role the tadpole plays in eliminating the fixed points of the dynamical system, generically rendering both the scalar field and metric time dependent. Our results indicate that when violating the degeneracy condition but preserving shift symmetry, the metric maintains an asymptotic Minkowski state, irrespective of the presence of the cosmological constant. In contrast, when shift symmetry is also broken the asymptotic behaviour can radically alter. Regardless, the non-degenerate models in this work share an attractive quality; harboring low energy, late-time asymptotic states that are independent of the vacuum energy. The tadpole allows for a broader class of non-degenerate, self-tuning models than was previously realized.

Tadpole cosmology: Milne solution as a cosmological constant hideout

“…This asymptotic solution satisfies H φ → τ −3 → 0, as required. This is not dissimilar to the t → ∞, asymptotic flat Minkowski solutions found in previous work [42]. The intrinsic curvature of the constant time hypersurfaces contributes a term 3M 2 pl /α 2 0 to the asymptotic Friedmann equation, but beyond that the solution looks similar to the flat Minkowski space solution originally found.…”

“…This class of models has been studied within the context of observations [32,33], teleparallel extensions [34,35] and general cosmological [30,31,[36][37][38][39][40] solutions. Relaxing the degeneracy condition has been considered in [41][42][43]. We provide a short review of this approach in section 3.…”

Modified Gravity Approaches to the Cosmological Constant Problem

“…An issue already pointed out is that the mechanism cancels ρ vac on the attractor but does little to address the large value of ρ Λ away from the attractor, at, say, earlier times, which would change the expansion history significantly (see [182] for a discussion). Similarly, self-tuning, as discussed here, assumes some specific attractor solution at which the CC is canceled by φ rather than at the level of the field equations, as in the sequestering approach (see Section 4.2).…”

Constraining gravitational wave propagation using pulsar timing array correlations

“…The δ ab in ( 12) is considered to take care of the small scale power that is dropped when pulling the pulsars to infinity. In [37], we have proposed a physical mechanism for the GW monopole by means of a scalar field [48]. Similarly, for the HD, Γ aa = 1 is set in by hand to account for the small scale power [23,41].…”