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Beyond the cosmological standard model

The Swampland program aims to distinguish effective theories which can be completed into quantum gravity in the ultraviolet from those which cannot. This article forms an introduction to the field, assuming only a knowledge of quantum field theory and general relativity. It also forms a comprehensive review, covering the range of ideas that are part of the field, from the Weak Gravity Conjecture, through compactifications of String Theory, to the de Sitter conjecture.

The Swampland: Introduction and Review

After a decade and a half of research motivated by the accelerating universe, theory and experiment have a reached a certain level of maturity. The development of theoretical models beyond \Lambda, or smooth dark energy, often called modified gravity, has led to broader insights into a path forward, and a host of observational and experimental tests have been developed. In this review we present the current state of the field and describe a framework for anticipating developments in the next decade. We identify the guiding principles for rigorous and consistent modifications of the standard model, and discuss the prospects for empirical tests. We begin by reviewing attempts to consistently modify Einstein gravity in the infrared, focusing on the notion that additional degrees of freedom introduced by the modification must screen themselves from local tests of gravity. We categorize screening mechanisms into three broad classes: mechanisms which become active in regions of high Newtonian potential, those in which first derivatives become important, and those for which second derivatives are important. Examples of the first class, such as f(R) gravity, employ the familiar chameleon or symmetron mechanisms, whereas examples of the last class are galileon and massive gravity theories, employing the Vainshtein mechanism. In each case, we describe the theories as effective theories. We describe experimental tests, summarizing laboratory and solar system tests and describing in some detail astrophysical and cosmological tests. We discuss future tests which will be sensitive to different signatures of new physics in the gravitational sector. Parts that are more relevant to theorists vs. observers/experimentalists are clearly indicated, in the hope that this will serve as a useful reference for both audiences, as well as helping those interested in bridging the gap between them.

Beyond the Cosmological Standard Model

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Gravitation And Cosmology

We derive new positivity bounds for scattering amplitudes in theories with a massless graviton in the spectrum in four spacetime dimensions, of relevance for the weak gravity conjecture and modified gravity theories. The bounds imply that extremal black holes are self-repulsive, M/|Q|<1 in suitable units, and that they are unstable to decay to smaller extremal black holes, providing an S-matrix proof of the weak gravity conjecture. We also present other applications of our bounds to the effective field theory of weakly broken Galileons, axions, and P(X) theories.

Positivity of Amplitudes, Weak Gravity Conjecture, and Modified Gravity.

We study the decay of gravitational waves into dark energy fluctuations π, through the processes γ → ππ and γ → γ π, made possible by the spontaneous breaking of Lorentz invariance. Within the EFT of Dark Energy (or Horndeski/beyond Horndeski theories) the first process is large for the operator ½ m42(t) δ g00 ( (3)R + δ Kμν δ Kμν −δ K2 ), so that the recent observations force m4 = 0 (or equivalently 0αH=). This constraint, together with the requirement that gravitational waves travel at the speed of light, rules out all quartic and quintic GLPV theories. Additionally, we study how the same couplings affect the propagation of gravitons at loop order. The operator proportional to m42 generates a calculable, non-Lorentz invariant higher-derivative correction to the graviton propagation. The modification of the dispersion relation provides a bound on m42 comparable to the one of the decay. Conversely, operators up to cubic Horndeski do not generate sizeable \hbox{higher-derivative corrections.}

https://iopscience.iop.org/article/10.1088/1475-7516/2018/12/025/pdf

Gravitational wave decay into dark energy

The large scale structures of the universe will likely be the next leading source of cosmological information. It is therefore crucial to understand their behavior. The Effective Field Theory of Large Scale Structures provides a consistent way to perturbatively predict the clustering of dark matter at large distances. The fact that baryons move distances comparable to dark matter allows us to infer that baryons at large distances can be described in a similar formalism: the backreaction of short-distance non-linearities and of star-formation physics at long distances can be encapsulated in an effective stress tensor, characterized by a few parameters. The functional form of baryonic effects can therefore be predicted. In the power spectrum the leading contribution goes as ∝ k2 P(k), with P(k) being the linear power spectrum and with the numerical prefactor depending on the details of the star-formation physics. We also perform the resummation of the contribution of the long-wavelength displacements, allowing us to consistently predict the effect of the relative motion of baryons and dark matter. We compare our predictions with simulations that contain several implementations of baryonic physics, finding percent agreement up to relatively high wavenumbers such as k 0.3 hMpc−1 or k 0.6 hMpc−1, depending on the order of the calculation. Our results open a novel way to understand baryonic effects analytically, as well as to interface with simulations.

Analytic Prediction of Baryonic Effects from the EFT of Large Scale Structures

We would like to thank Matias Zaldarriaga for discussions. C. C. acknowledges support as a MultiDark Fellow. L. S. is partially supported by DOE Early Career Award No. DE-FG02-12ER41854. F. P., C. Z., and C. C. acknowledge support from the Spanish MICINNs Consolider-Ingenio 2010 Programme under Grant No. MultiDark CSD2009-00064, MINECO Centro de Excelencia Severo Ochoa Programme under Grants No. SEV-2012-0249, and No. AYA2014-60641-C2-1-P. F. P. wishes to thank KIPAC for the hospitality during the development of this work. The BigMultidark simulations have been performed on the SuperMUC supercomputer at the Leibniz-Rechenzentrum (LRZ) in Munich, using the computing resources awarded to the PRACE Project No. 2012060963.

/pdf/eft-of-large-scale-structures-in-redshift-space-2wzv6ebh68.pdf

EFT of large scale structures in redshift space

We study the screening mechanism in the most general scalar-tensor theories that leave gravitational waves unaffected and are thus compatible with recent LIGO/Virgo observations. Using the effective field theory of the dark energy approach, we consider the general action for perturbations beyond linear order, focusing on the quasistatic limit. When restricting to the subclass of theories that satisfy the gravitational wave constraints, the fully nonlinear effective Lagrangian contains only three independent parameters. One of these, β1, is uniquely present in degenerate higher-order theories. We compute the two gravitational potentials for a spherically symmetric matter source, and we find that for β1≥0 they decrease as the inverse of the distance, as in standard gravity, while the case β1 0, the two potentials differ and their gravitational constants are not the same on the inside and outside of the body. Generically, the bound on anomalous light bending in the Solar System implies β1≲10-5. Standard gravity can be recovered outside the body by tuning the parameters of the model, in which case β1≲10-2 from the Hulse-Taylor pulsar. Theories conformally related to general relativity admit 0≤β1≲10-6, at least for a specific choice of conformal couplings.

Matthew Lewandowski

Papers

Positivity of Amplitudes, Weak Gravity Conjecture, and Modified Gravity.

Gravitational wave decay into dark energy

Analytic Prediction of Baryonic Effects from the EFT of Large Scale Structures

EFT of large scale structures in redshift space

Vainshtein regime in scalar-tensor gravity: Constraints on degenerate higher-order scalar-tensor theories