On Semi-classical Degravitation and the Cosmological Constant Problems

In this report, we discuss a candidate mechanism through which one might address the various cosmological constant problems. We first observe that the renormalization of gravitational couplings (induced by integrating out various matter fields) manifests non-local modifications to Einstein's equations as quantum corrected equations of motion. That is, at the loop level, matter sources curvature through a gravitational coupling that is a non-local function of the covariant d'Alembertian. If the functional form of the resulting Newton's `constant' is such that it annihilates very long wavelength sources, but reduces to $1/M^2_{pl}$ ($M_{pl}$ being the 4d Planck mass) for all sources with cosmologically observable wavelengths, we would have a complimentary realization of the degravitation paradigm-- a realization through which its non-linear completion and the corresponding modified Bianchi identities are readily understood. We proceed to consider various theories whose coupling to gravity may a priori induce non-trivial renormalizations of Newton's constant in the IR, and arrive at a class of non-local effective actions which yield a suitably degravitating filter function for Newton's constant upon subsequently being integrated out. We motivate this class of non-local theories through several considerations, discuss open issues, future directions, the inevitable question of scheme dependence in semi-classical gravitational calculations and comment on connections with other meditations in the literature on relaxing of the cosmological constant semi-classically.Comment: 15 pages, 2 appendices. References added

Relaxing the Electroweak Scale: the Role of Broken dS Symmetry

Recently, a novel mechanism to address the hierarchy problem has been proposed \cite{Graham:2015cka}, where the hierarchy between weak scale physics and any putative `cutoff' $M$ is translated into a parametrically large field excursion for the so-called relaxion field, driving the Higgs mass to values much less than $M$ through cosmological dynamics. In its simplest incarnation, the relaxion mechanism requires nothing beyond the standard model other than an axion (the relaxion field) and an inflaton. In this note, we critically re-examine the requirements for successfully realizing the relaxion mechanism and point out that parametrically larger field excursions can be obtained for a given number of e-folds by simply requiring that the background break exact de Sitter invariance. We discuss several corollaries of this observation, including the interplay between the upper bound on the scale $M$ and the order parameter $\epsilon$ associated with the breaking of dS symmetry, and entertain the possibility that the relaxion could play the role of a curvaton. We find that a successful realization of the mechanism is possible with as few as $\mathcal O (10^3)$ e-foldings, albeit with a reduced cutoff $M \sim 10^6$ GeV for a dark QCD axion and outline a minimal scenario that can be made consistent with CMB observations.Comment: 16 pages, 3 figures. Version to appear in JHE

On the Predictiveness of Single-Field Inflationary Models

We re-examine the predictiveness of single-field inflationary models and discuss how an unknown UV completion can complicate determining inflationary model parameters from observations, even from precision measurements. Besides the usual naturalness issues associated with having a shallow inflationary potential, we describe another issue for inflation, namely, unknown UV physics modifies the running of Standard Model (SM) parameters and thereby introduces uncertainty into the potential inflationary predictions. We illustrate this point using the minimal Higgs Inflationary scenario, which is arguably the most predictive single-field model on the market, because its predictions for $A_s$, $r$ and $n_s$ are made using only one new free parameter beyond those measured in particle physics experiments, and run up to the inflationary regime. We find that this issue can already have observable effects. At the same time, this UV-parameter dependence in the Renormalization Group allows Higgs Inflation to occur (in principle) for a slightly larger range of Higgs masses. We comment on the origin of the various UV scales that arise at large field values for the SM Higgs, clarifying cut off scale arguments by further developing the formalism of a non-linear realization of $\rm SU_L(2) \times U(1)$ in curved space. We discuss the interesting fact that, outside of Higgs Inflation, the effect of a non-minimal coupling to gravity, even in the SM, results in a non-linear EFT for the Higgs sector. Finally, we briefly comment on post BICEP2 attempts to modify the Higgs Inflation scenario.Comment: 31 pp, 4 figures v4: Minor correction to section 3.1. Main arguments and conclusions unchange

Inflating in a Trough: Single-Field Effective Theory from Multiple-Field Curved Valleys

We examine the motion of light fields near the bottom of a potential valley in a multi-dimensional field space. In the case of two fields we identify three general scales, all of which must be large in order to justify an effective low-energy approximation involving only the light field, $\ell$. (Typically only one of these -- the mass of the heavy field transverse to the trough -- is used in the literature when justifying the truncation of heavy fields.) We explicitly compute the resulting effective field theory, which has the form of a $P(\ell,X)$ model, with $X = - 1/2(\partial \ell)^2$, as a function of these scales. This gives the leading ways each scale contributes to any low-energy dynamics, including (but not restricted to) those relevant for cosmology. We check our results with the special case of a homogeneous roll near the valley floor, placing into a broader context recent cosmological calculations that show how the truncation approximation can fail. By casting our results covariantly in field space, we provide a geometrical criterion for model-builders to decide whether or not the single-field and/or the truncation approximation is justified, identify its leading deviations, and to efficiently extract cosmological predictions.Comment: 28 pages + 3 appendices, references added and typos corrected, matches published versio