The Well-Tempered Cosmological Constant

Self tuning is one of the few methods for dynamically cancelling a large cosmological constant and yet giving an accelerating universe. Its drawback is that it tends to screen all sources of energy density, including matter. We develop a model that tempers the self tuning so the dynamical scalar field still cancels an arbitrary cosmological constant, including the vacuum energy through any high energy phase transitions, without affecting the matter fields. The scalar-tensor gravitational action is simple, related to cubic Horndeski gravity, with a nonlinear derivative interaction plus a tadpole term. Applying shift symmetry and using the property of degeneracy of the field equations we find families of functions that admit de Sitter solutions with expansion rates that are independent of the magnitude of the cosmological constant and preserve radiation and matter dominated phases. That is, the method can deliver a standard cosmic history including current acceleration, despite the presence of a Planck scale cosmological constant.Comment: 19 pages, 4 figure

Cluster Probes of Dark Energy Clustering

Cluster abundances are oddly insensitive to canonical early dark energy. Early dark energy with sound speed equal to the speed of light cannot be distinguished from a quintessence model with the equivalent expansion history for $z<2$ but negligible early dark energy density, despite the different early growth rate. However, cold early dark energy, with a sound speed much smaller than the speed of light, can give a detectable signature. Combining cluster abundances with cosmic microwave background power spectra can determine the early dark energy fraction to 0.3 % and distinguish a true sound speed of 0.1 from 1 at 99 % confidence. We project constraints on early dark energy from the Euclid cluster survey, as well as the Dark Energy Survey, using both current and projected Planck CMB data, and assess the impact of cluster mass systematics. We also quantify the importance of dark energy perturbations, and the role of sound speed during a crossing of $w=-1$

An Expansion of Well Tempered Gravity

When faced with two nigh intractable problems in cosmology -- how to remove the original cosmological constant problem and how to parametrize modified gravity to explain current cosmic acceleration -- we can make progress by counterposing them. The well tempered solution to the cosmological constant through degenerate scalar field dynamics also relates disparate Horndeski gravity terms, making them contrapuntal. We derive the connection between the kinetic term $K$ and braiding term $G_3$ for shift symmetric theories (including the running Planck mass $G_4$), extending previous work on monomial or binomial dependence to polynomials of arbitrary finite degree. We also exhibit an example for an infinite series expansion. This contrapuntal condition greatly reduces the number of parameters needed to test modified gravity against cosmological observations, for these "golden" theories of gravity.Comment: 7 page

The Well-Tempered Cosmological Constant: Fugue in B♭^\flat

Zero point fluctuations of quantum fields should generate a large cosmological constant energy density in any spacetime. How then can we have anything other than de Sitter space without fine tuning? Well tempering -- dynamical cancellation of the cosmological constant using degeneracy within the field equations -- can replace a large cosmological constant with a much lower energy state. Here we give an explicit mechanism to obtain a Minkowski solution, replacing the cosmological constant with zero, and testing its attractor nature and persistence through a vacuum phase transition. We derive the general conditions that Horndeski scalar-tensor gravity must possess, and evolve in a fugue of functions, to deliver nothing and make the universe be flat.Comment: 15 pages, 3 figure

The Well-Tempered Cosmological Constant: The Horndeski Variations

Well tempering is one of the few classical field theory methods for solving the original cosmological constant problem, dynamically canceling a large (possibly Planck scale) vacuum energy and leaving the matter component intact, while providing a viable cosmology with late time cosmic acceleration and an end de Sitter state. We present the general constraints that variations of Horndeski gravity models with different combinations of terms must satisfy to admit an exact de Sitter spacetime that does not respond to an arbitrarily large cosmological constant. We explicitly derive several specific scalar-tensor models that well temper and can deliver a standard cosmic history including current cosmic acceleration. Stability criteria, attractor behavior of the de Sitter state, and the response of the models to pressureless matter are considered. The well tempered conditions can be used to focus on particular models of modified gravity that have special interest -- not only removing the original cosmological constant problem but providing relations between the free Horndeski functions and reducing them to a couple of parameters, suitable for testing gravity and cosmological data analysis.Comment: 25 pages, 3 figure

The Role of Cumulative Risk Assessment in Decisions about Environmental Justice

There is strong presumptive evidence that people living in poverty and certain racial and ethnic groups bear a disproportionate burden of environmental health risk. Many have argued that conducting formal assessments of the health risk experienced by affected communities is both unnecessary and counterproductive—that instead of analyzing the situation our efforts should be devoted to fixing obvious problems and rectifying observable wrongs. We contend that formal assessment of cumulative health risks from combined effects of chemical and nonchemical stressors is a valuable tool to aid decision makers in choosing risk management options that are effective, efficient, and equitable. If used properly, cumulative risk assessment need not impair decision makers’ discretion, nor should it be used as an excuse for doing nothing in the face of evident harm. Good policy decisions require more than good intentions; they necessitate analysis of risk-related information along with careful consideration of economic issues, ethical and moral principles, legal precedents, political realities, cultural beliefs, societal values, and bureaucratic impediments. Cumulative risk assessment can provide a systematic and impartial means for informing policy decisions about environmental justice

Statistical uncertainty of eddy flux–based estimates of gross ecosystem carbon exchange at Howland Forest, Maine

We present an uncertainty analysis of gross ecosystem carbon exchange (GEE) estimates derived from 7 years of continuous eddy covariance measurements of forest-atmosphere CO2fluxes at Howland Forest, Maine, USA. These data, which have high temporal resolution, can be used to validate process modeling analyses, remote sensing assessments, and field surveys. However, separation of tower-based net ecosystem exchange (NEE) into its components (respiration losses and photosynthetic uptake) requires at least one application of a model, which is usually a regression model fitted to nighttime data and extrapolated for all daytime intervals. In addition, the existence of a significant amount of missing data in eddy flux time series requires a model for daytime NEE as well. Statistical approaches for analytically specifying prediction intervals associated with a regression require, among other things, constant variance of the data, normally distributed residuals, and linearizable regression models. Because the NEE data do not conform to these criteria, we used a Monte Carlo approach (bootstrapping) to quantify the statistical uncertainty of GEE estimates and present this uncertainty in the form of 90% prediction limits. We explore two examples of regression models for modeling respiration and daytime NEE: (1) a simple, physiologically based model from the literature and (2) a nonlinear regression model based on an artificial neural network. We find that uncertainty at the half-hourly timescale is generally on the order of the observations themselves (i.e., ∼100%) but is much less at annual timescales (∼10%). On the other hand, this small absolute uncertainty is commensurate with the interannual variability in estimated GEE. The largest uncertainty is associated with choice of model type, which raises basic questions about the relative roles of models and data