Ambiguous Tests of General Relativity on Cosmological Scales

There are a number of approaches to testing General Relativity (GR) on linear scales using parameterized frameworks for modifying cosmological perturbation theory. It is sometimes assumed that the details of any given parameterization are unimportant if one uses it as a diagnostic for deviations from GR. In this brief report we argue that this is not necessarily so. First we show that adopting alternative combinations of modifications to the field equations significantly changes the constraints that one obtains. In addition, we show that using a parameterization with insufficient freedom significantly tightens the apparent theoretical constraints. Fundamentally we argue that it is almost never appropriate to consider modifications to the perturbed Einstein equations as being constraints on the effective gravitational constant, for example, in the same sense that solar system constraints are. The only consistent modifications are either those that grant near-total freedom, as in decomposition methods, or ones which map directly to a particular part of theory space

Technically natural dark energy from Lorentz breaking

We construct a model of dark energy with a technically natural small contribution to cosmic acceleration, i.e. this contribution does not receive corrections from other scales in the theory. The proposed acceleration mechanism appears generically in the low-energy limit of gravity theories with violation of Lorentz invariance that contain a derivatively coupled scalar field Theta. The latter may be the Goldstone field of a broken global symmetry. The model, that we call Theta-CDM, is a valid effective field theory up to a high cutoff just a few orders of magnitude below the Planck scale. Furthermore, it can be ultraviolet-completed in the context of Horava gravity. We discuss the observational predictions of the model. Even in the absence of a cosmological constant term, the expansion history of the Universe is essentially indistinguishable from that of Lambda-CDM. The difference between the two theories appears at the level of cosmological perturbations. We find that in Theta-CDM the matter power spectrum is enhanced at subhorizon scales compared to Lambda-CDM. This property can be used to discriminate the model from Lambda-CDM with current cosmological data.Comment: A few equations in the Appendix correcte

A Class of Effective Field Theory Models of Cosmic Acceleration

We explore a class of effective field theory models of cosmic acceleration involving a metric and a single scalar field. These models can be obtained by starting with a set of ultralight pseudo-Nambu-Goldstone bosons whose couplings to matter satisfy the weak equivalence principle, assuming that one boson is lighter than all the others, and integrating out the heavier fields. The result is a quintessence model with matter coupling, together with a series of correction terms in the action in a covariant derivative expansion, with specific scalings for the coefficients. After eliminating higher derivative terms and exploiting the field redefinition freedom, we show that the resulting theory contains nine independent free functions of the scalar field when truncated at four derivatives. This is in contrast to the four free functions found in similar theories of single-field inflation, where matter is not present. We discuss several different representations of the theory that can be obtained using the field redefinition freedom. For perturbations to the quintessence field today on subhorizon lengthscales larger than the Compton wavelength of the heavy fields, the theory is weakly coupled and natural in the sense of t'Hooft. The theory admits a regime where the perturbations become modestly nonlinear, but very strong nonlinearities lie outside its domain of validity.Comment: 43 pages, 2 figures; Version 3 publication versio

The Distinguishability of Interacting Dark Energy from Modified Gravity

We study the observational viability of coupled quintessence models with their expansion and growth histories matched to modified gravity cosmologies. We find that for a Dvali-Gabadadze-Porrati model which has been fitted to observations, the matched interacting dark energy models are observationally disfavoured. We also study the distinguishability of interacting dark energy models matched to scalar-tensor theory cosmologies and show that it is not always possible to find a physical interacting dark energy model which shares their expansion and growth histories.Comment: 8 pages, 5 figure

Fundamental constants and tests of general relativity - Theoretical and cosmological considerations

The tests of the constancy of the fundamental constants are tests of the local position invariance and thus of the equivalence principle. We summarize the various constraints that have been obtained and then describe the connection between varying constants and extensions of general relativity. To finish, we discuss the link with cosmology, and more particularly with the acceleration of the Universe. We take the opportunity to summarize various possibilities to test general relativity (but also the Copernican principle) on cosmological scales.Comment: Proceedings of the workshop ``The nature of gravity, confronting theory and experiment in space'', ISSI, Bern, october 200

The acceleration of the universe and the physics behind it

Using a general classification of dark enegy models in four classes, we discuss the complementarity of cosmological observations to tackle down the physics beyond the acceleration of our universe. We discuss the tests distinguishing the four classes and then focus on the dynamics of the perturbations in the Newtonian regime. We also exhibit explicitely models that have identical predictions for a subset of observations.Comment: 18 pages, 18 figure

Non-minimally coupled dark matter: effective pressure and structure formation

We propose a phenomenological model in which a non-minimal coupling between gravity and dark matter is present in order to address some of the apparent small scales issues of \lcdm model. When described in a frame in which gravity dynamics is given by the standard Einstein-Hilbert action, the non-minimal coupling translates into an effective pressure for the dark matter component. We consider some phenomenological examples and describe both background and linear perturbations. We show that the presence of an effective pressure may lead these scenarios to differ from \lcdm at the scales where the non-minimal coupling (and therefore the pressure) is active. In particular two effects are present: a pressure term for the dark matter component that is able to reduce the growth of structures at galactic scales, possibly reconciling simulations and observations; an effective interaction term between dark matter and baryons that could explain observed correlations between the two components of the cosmic fluid within Tully-Fisher analysis.Comment: 18 pages, 6 figures, references added. Published in JCA

Statefinder Diagnostic for Dilaton Dark Energy

Statefinder diagnostic is a useful method which can differ one dark energy model from the others. The Statefinder pair $\{r, s\}$ is algebraically related to the equation of state of dark energy and its first time derivative. We apply in this paper this method to the dilaton dark energy model based on Weyl-Scaled induced gravitational theory. We investigate the effect of the coupling between matter and dilaton when the potential of dilaton field is taken as the Mexican hat form. We find that the evolving trajectory of our model in the $r-s$ diagram is quite different from those of other dark energy models.Comment: 6 pages, 4 figures, type errors corrected, reference no. changed, accepted by Astrophysics and Space Scienc

Tracking Extended Quintessence

We study the cosmological role of a Tracking Field $\phi$ in Extended Quintessence scenarios (TEQ), where the dynamical vacuum energy driving the acceleration of the universe today is coupled with the Ricci scalar, $R$, with a term of the form $F(\phi)R/2$, where $F(\phi) = 1/8\pi G+\xi(\phi^{2}-\phi_{0}^{2})$. Tracker solutions for these NMC models, with inverse power-law potentials, possess an initial enhancement of the scalar field dynamics, named $R$-boost, caused by the Ricci scalar in the Klein-Gordon equation. During this phase the field performs a "gravitational" slow rolling which we model analytically, with energy density scaling as $(1+z)^{2}$. We evolve linear perturbations in TEQ models assuming Gaussian scale-invariant initial spectrum. We obtain significant changes in the Integrated Sachs Wolfe effect and in the acoustic peaks locations on the Cosmic Microwave Background, as well as in the turnover on the matter power spectrum. All these corrections may assume positive as well as negative values, depending on the sign of the NMC parameter $\xi$. We give analytical formulas describing all these effects. We show that they can be as large as $10 - 30$ with respect to equivalent cosmological constant and ordinary tracking Quintessence models, respecting all the existing experimental constraints on scalar-tensor theories of gravity. These results demonstrate that the next decade data will provide deep constraints on the nature of the dark energy in the Universe, as well as the structure of the theory of gravity.Comment: 24 pages including 8 figures, final version to be published in Phys.Rev.

On Physical Equivalence between Nonlinear Gravity Theories

We argue that in a nonlinear gravity theory, which according to well-known results is dynamically equivalent to a self-gravitating scalar field in General Relativity, the true physical variables are exactly those which describe the equivalent general-relativistic model (these variables are known as Einstein frame). Whenever such variables cannot be defined, there are strong indications that the original theory is unphysical. We explicitly show how to map, in the presence of matter, the Jordan frame to the Einstein one and backwards. We study energetics for asymptotically flat solutions. This is based on the second-order dynamics obtained, without changing the metric, by the use of a Helmholtz Lagrangian. We prove for a large class of these Lagrangians that the ADM energy is positive for solutions close to flat space. The proof of this Positive Energy Theorem relies on the existence of the Einstein frame, since in the (Helmholtz--)Jordan frame the Dominant Energy Condition does not hold and the field variables are unrelated to the total energy of the system.Comment: 37 pp., TO-JLL-P 3/93 Dec 199