Null tests of the standard model using the linear model formalism

We test both the FLRW geometry and $\Lambda$CDM cosmology in a model independent way by reconstructing the Hubble function $H(z)$, the comoving distance $D(z)$ and the growth of structure $f\sigma_8(z)$ using the most recent data available. We use the linear model formalism in order to optimally reconstruct the latter cosmological functions, together with their derivatives and integrals. We then evaluate four of the null tests available in literature: $Om_{1}$ by Sahni et al., $Om_{2}$ by Zunckel \& Clarkson, $Ok$ by Clarkson et al., and $ns$ by Nesseris \& Sapone. For all the four tests we find agreement, within the errors, with the standard cosmological model.Comment: 8 pages, 7 figures and 1 tabl

Dark Energy versus Modified Gravity

There is now strong observational evidence that the expansion of the Universe is accelerating. The standard explanation invokes an unknown dark energy component. But such scenarios are faced with serious theoretical problems, which has led to increased interest in models where instead general relativity is modified in a way that leads to the observed accelerated expansion. The question then arises whether the two scenarios can be distinguished. Here we show that this may not be so easy, demonstrating explicitly that a generalized dark energy model can match the growth rate of the Dvali-Gabadadze-Porrati model and reproduce the 3+1 dimensional metric perturbations. Cosmological observations are then unable to distinguish the two cases

Accuracy of the growth index in the presence of dark energy perturbations

We present the analytical solutions for the evolution of matter density perturbations, for a model with a constant dark energy equation of state $w$ but when the effects of the dark energy perturbations are properly taken into account. We consider two cases, the first when the sound speed of the perturbations is zero $c_s^2=0$ and the general case $0<c_s^2 \leq 1$. In the first case our solution is exact, while in the second case we found an approximate solution which works to better than $0.3\%$ accuracy for $k>10 H_0$ or equivalently $k/h>0.0033 \textrm{Mpc}^{-1}$. We also estimate the corrections to the growth index $\gamma(z)$, commonly used to parametrize the growth-rate. We find that these corrections due to the DE perturbations affect the growth index $\gamma$ at the $3\%$ level. We also compare our new expressions for the growth index with other expressions already present in the literature and we find that the latter are less accurate than the ones we propose here. Therefore, our analytical calculations are necessary as the theoretical predictions for the fundamental parameters to be constrained by the upcoming surveys need to be as accurate as possible, especially since we are entering in the precise cosmology era where parameters will be measured to the percent level.Comment: 8 pages, 4 figure

Fingerprinting Dark Energy III: distinctive marks of viscosity

The characterisation of dark energy is one of the primary goals in cosmology especially now that many new experiments are being planned with the aim of reaching a high sensitivity on cosmological parameters. It is known that if we move away from the simple cosmological constant model then we need to consider perturbations in the dark energy fluid. This means that dark energy has two extra degrees of freedom: the sound speed \cs and the anisotropic stress $\sigma$. If dark energy is inhomogenous at the scales of interest then the gravitational potentials are modified and the evolution of the dark matter perturbations is also directly affected. In this paper we add an anisotropic component to the dark energy perturbations. Following the idea introduced in \cite{Sapone:2009mb}, we solve analytically the equations of perturbations in the dark sector, finding simple and accurate approximated solutions. We also find that the evolution of the density perturbations is governed by an effective sound speed which depends on both the sound speed and the anisotropic stress parameter. We then use these solutions to look at the impact of the dark energy perturbations on the matter power spectrum and on the Integrated Sachs-Wolfe effect in the Cosmic Microwave Background.Comment: 14 pages, 8 figures, to be submitted to PR

Internal Robustness of Growth Rate data

We perform an Internal Robustness analysis (iR) to a compilation of the most recent $f\sigma_8(z)$ data, using the framework of 1209.1897. The method analyzes combinations of subsets in the data set in a Bayesian model comparison way, potentially finding outliers, subsets of data affected by systematics or new physics. In order to validate our analysis and assess its sensitivity we performed several cross-checks, for example by removing some of the data or by adding artificially contaminated points, while we also generated mock data sets in order to estimate confidence regions of the iR. Applying this methodology, we found no anomalous behavior in the $f\sigma_8(z)$ data set, thus validating its internal robustness.Comment: 11 pages, 1 table, 5 figures. Changes match published versio

Fingerprinting Dark Energy II: weak lensing and galaxy clustering tests

The characterization of dark energy is a central task of cosmology. To go beyond a cosmological constant, we need to introduce at least an equation of state and a sound speed and consider observational tests that involve perturbations. If dark energy is not completely homogeneous on observable scales then the Poisson equation is modified and dark matter clustering is directly affected. One can then search for observational effects of dark energy clustering using dark matter as a probe. In this paper we exploit an analytical approximate solution of the perturbation equations in a general dark energy cosmology to analyze the performance of next-decade large scale surveys in constraining equation of state and sound speed. We find that tomographic weak lensing and galaxy redshift surveys can constrain the sound speed of the dark energy only if the latter is small, of the order of $c_{s}\lesssim0.01$ (in units of $c$). For larger sound speeds the error grows to 100% and more. We conclude that large scale structure observations contain very little information about the perturbations in canonical scalar field models with a sound speed of unity. Nevertheless, they are able to detect the presence of "cold" dark energy, i.e. a dark energy with non-relativistic speed of sound