Jonathan A. Pearson

Effective action approach to cosmological perturbations in dark energy and modified gravity

In light of upcoming observations modelling perturbations in dark energy and modified gravity models has become an important topic of research. We develop an effective action to construct the components of the perturbed dark energy momentum tensor which appears in the perturbed generalized gravitational field equations, ?G?? = 8?G?T??+?U?? for linearized perturbations. Our method does not require knowledge of the Lagrangian density of the dark sector to be provided, only its field content. The method is based on the fact that it is only necessary to specify the perturbed Lagrangian to quadratic order and couples this with the assumption of global statistical isotropy of spatial sections to show that the model can be specified completely in terms of a finite number of background dependent functions. We present our formalism in a coordinate independent fashion and provide explicit formulae for the perturbed conservation equation and the components of ?U?? for two explicit generic examples: (i) the dark sector does not contain extra fields, = (g??) and (ii) the dark sector contains a scalar field and its first derivative = (g??,,??). We discuss how the formalism can be applied to modified gravity models containing derivatives of the metric, curvature tensors, higher derivatives of the scalar fields and vector fields.

Parametrizing dark sector perturbations via equations of state.

The evolution of perturbations is a crucial part of the phenomenology of the dark sector cosmology. We advocate parametrizing these perturbations using equations of state for the entropy perturbation and the anisotropic stress. For small perturbations, these equations of state will be linear in the density, velocity and metric perturbations, and in principle these can be related back to the field content of the underlying model allowing for confrontation with observations. We illustrate our point by constructing gauge-invariant entropy perturbations for theories where the dark sector Lagrangian is a general function of a scalar field, its first and second derivatives, and the metric and its first derivative, L = L(phi, partial derivative(mu)phi, partial derivative(mu)partial derivative(v)phi, g(mu v), partial derivative(alpha)g(mu v)). As an example, we show how to apply this approach to the case of models of kinetic gravity braiding.

Massive gravity, the elasticity of space-time, and perturbations in the dark sector

We consider a class of phenomenological modified gravity models where the terms added to the standard Einstein-Hilbert Lagrangian are just a function of the metric only. For linearized perturbations around an isotropic space-time, this class of models is entirely specified by a rank-4 tensor that encodes possibly time-dependent masses for the gravitons. This tensor has the same symmetries as an elasticity tensor, suggesting an interpretation of massive gravity as an effective rigidity of space-time. If we choose a form for this tensor that is compatible with the symmetries of Friedmann-Robertson-Walker and enforce full reparametrization invariance, then the only theory possible is a cosmological constant. However, in the case where the theory is only time translation invariant, the ghost-free massive gravity theory is equivalent to the elastic dark energy scenario with the extra Lorentz violating vector giving rise to 2 transverse and 1 longitudinal degrees of freedom, whereas when one demands spatial translation invariance one is left with a theory where the entropy perturbation is not gauge invariant.

Material models of dark energy

A new class of “dark energy” models is reviewed and developed, in which the relativistic theory of solids is used to construct material models of dark energy. These are models which include the effects of a continuous medium with well defined physical properties at the level of linearized perturbations. The formalism is constructed for a medium with arbitrary symmetry, and then specialised to isotropic media (which will be the case of interest for the majority of cosmological applications). The theory of relativistic isotropic viscoelastic media is developed whilst keeping in mind that we ultimately want to observationally constrain the allowed properties of the material model. This is done by obtaining the viscoelastic equations of state for perturbations (the entropy and anisotropic stress), as well as identifying the consistent corner of the theory which has constant equation of state parameter inline image. A connection to the non-relativistic theory of solids is obtained by identifying the two quadratic invariants that are needed to construct the energy-momentum tensor, namely the Rayleigh dissipation function and Lagrangian for perturbations. Finally, the notion is developed that the viscoelastic behavior of the medium can be thought of as a non-minimally coupled massive gravity theory. This also provides a tool-kit for constructing consistent generalizations of coupled dark energy theories.

Constraining dark sector perturbations I: cosmic shear and CMB lensing

We present current and future constraints on equations of state for dark sector perturbations. The equations of state considered are those corresponding to a generalized scalar field model and time-diffeomorphism invariant

Simple implementation of general dark energy models

L(g)

Discussion and Final Remarks

theories that are equivalent to models of a relativistic elastic medium and also Lorentz violating massive gravity. We develop a theoretical understanding of the observable impact of these models. In order to constrain these models we use CMB temperature data from Planck, BAO measurements, CMB lensing data from Planck and the South Pole Telescope, and weak galaxy lensing data from CFHTLenS. We find non-trivial exclusions on the range of parameters, although the data remains compatible with

X-type and Y-type junction stability in domain wall networks

w=-1

Simulating the symmetron: domain walls and symmetry-restoring impurities

. We gauge how future experiments will help to constrain the parameters. This is done via a likelihood analysis for CMB experiments such as CoRE and PRISM, and tomographic galaxy weak lensing surveys, focussing in on the potential discriminatory power of Euclid on mildly non-linear scales.

The Equation of State Approach to Cosmological Perturbations in f(R) Gravity

We present a formalism for the numerical implementation of general theories of dark energy, combining the computational simplicity of the equation of state for perturbations approach with the generality of the effective field theory approach. An effective fluid description is employed, based on a general action describing single-scalar field models. The formalism is developed from first principles, and constructed keeping the goal of a simple implementation into CAMB in mind. Benefits of this approach include its straightforward implementation, the generality of the underlying theory, the fact that the evolved variables are physical quantities, and that model-independent phenomenological descriptions may be straightforwardly investigated. We hope this formulation will provide a powerful tool for the comparison of theoretical models of dark energy with observational data.