The time evolution of cosmological redshift as a test of dark energy

The variation of the expansion rate of the Universe with time produces an evolution in the cosmological redshift of distant sources (for example quasar Lyman-$\alpha$ absorption lines), that might be directly observed by future ultra stable, high-resolution spectrographs (such as CODEX) coupled to extremely large telescopes (such as European Southern Observatory's Extremely Large Telescope, ELT). This would open a new window to explore the physical mechanism responsible for the current acceleration of the Universe. We investigate the evolution of cosmological redshift from a variety of dark energy models, and compare it with simulated data. We perform a Fisher matrix analysis and discuss the prospects for constraining the parameters of these models and for discriminating among competing candidates. We find that, because of parameter degeneracies, and of the inherent technical difficulties involved in this kind of observations, the uncertainties on parameter reconstruction can be rather large unless strong external priors are assumed. However, the method could be a valuable complementary cosmological tool, and give important insights on the dynamics of dark energy, not obtainable using other probes.Comment: 9 pages, 2 figures. Matching published versio

Constraints on coupled dark energy using CMB data from WMAP and SPT

We consider the case of a coupling in the dark cosmological sector, where a dark energy scalar field modifies the gravitational attraction between dark matter particles. We find that the strength of the coupling {\beta} is constrained using current Cosmic Microwave Background (CMB) data, including WMAP7 and SPT, to be less than 0.063 (0.11) at 68% (95%) confidence level. Further, we consider the additional effect of the CMB-lensing amplitude, curvature, effective number of relativistic species and massive neutrinos and show that the bound from current data on {\beta} is already strong enough to be rather stable with respect to any of these variables. The strongest effect is obtained when we allow for massive neutrinos, in which case the bound becomes slightly weaker, {\beta} < 0.084(0.14). A larger value of the effective number of relativistic degrees of freedom favors larger couplings between dark matter and dark energy as well as values of the spectral index closer to 1. Adding the present constraints on the Hubble constant, as well as from baryon acoustic oscillations and supernovae Ia, we find {\beta} < 0.050(0.074). In this case we also find an interesting likelihood peak for {\beta} = 0.041 (still compatible with 0 at 1{\sigma}). This peak comes mostly from a slight difference between the Hubble parameter HST result and the WMAP7+SPT best fit. Finally, we show that forecasts of Planck+SPT mock data can pin down the coupling to a precision of better than 1% and detect whether the marginal peak we find at small non zero coupling is a real effect.Comment: 22 pages, 17 figure

Testing coupled dark energy with next-generation large-scale observations

Coupling dark energy to dark matter provides one of the simplest way to effectively modify gravity at large scales without strong constraints from local (i.e. solar system) observations. Models of coupled dark energy have been studied several times in the past and are already significantly constrained by cosmic microwave background experiments. In this paper we estimate the constraints that future large-scale observations will be able to put on the coupling and in general on all the parameters of the model. We combine cosmic microwave background, tomographic weak lensing, redshift distortions and power spectrum probes. We show that next-generation observations can improve the current constraint on the coupling to dark matter by two orders of magnitude; this constraint is complementary to the current solar-system bounds on a coupling to baryons.Comment: 18 pages, 12 figs, 8 table

Mapping the galactic gravitational potential with peculiar acceleration

It has been suggested recently that the change in cosmological redshift (the Sandage test of expansion) could be observed in the next generation of large telescopes and ultra-stable spectrographs. In a recent paper we estimated the change of peculiar velocity, i.e. the peculiar acceleration, in nearby galaxies and clusters and shown it to be of the same order of magnitude as the typical cosmological signal. Mapping the acceleration field allows for a reconstruction of the galactic gravitational potential without assuming virialization. In this paper we focus on the peculiar acceleration in our own Galaxy, modeled as a Kuzmin disc and a dark matter spherical halo. We estimate the peculiar acceleration for all known Galactic globular clusters and find some cases with an expected velocity shift in excess of 20 cm/sec for observations fifteen years apart, well above the typical cosmological acceleration. We then compare the predicted signal for a MOND (modified Newtonian dynamics) model in which the spherical dark matter halo is absent. We find that the signal pattern is qualitatively different, showing that the peculiar acceleration field could be employed to test competing theories of gravity. However the difference seems too small to be detectable in the near future.Comment: 11 pages, 10 figures, 3 tables, minor changes, accepted for publication by MNRA

Anisotropic dark energy and ellipsoidal universe

A cosmological model with anisotropic dark energy is analyzed. The amount of deviation from isotropy of the equation of state of dark energy, the skewness \delta, generates an anisotropization of the large-scale geometry of the Universe, quantifiable by means of the actual shear \Sigma_0. Requiring that the level of cosmic anisotropization at the time of decoupling is such to solve the "quadrupole problem" of cosmic microwave background radiation, we find that |\delta| \sim 10^{-4} and |\Sigma_0| \sim 10^{-5}, compatible with existing limits derived from the magnitude-redshift data on type Ia supernovae.Comment: 10 pages, 3 figures. Revised version to match published version. References adde

ISW effect in Unified Dark Matter Scalar Field Cosmologies: an analytical approach

We perform an analytical study of the Integrated Sachs-Wolfe (ISW) effect within the framework of Unified Dark Matter models based on a scalar field which aim at a unified description of dark energy and dark matter. Computing the temperature power spectrum of the Cosmic Microwave Background anisotropies we are able to isolate those contributions that can potentially lead to strong deviations from the usual ISW effect occurring in a $\Lambda$CDM universe. This helps to highlight the crucial role played by the sound speed in the Unified Dark Matter models. Our treatment is completely general in that all the results depend only on the speed of sound of the dark component and thus it can be applied to a variety of unified models, including those which are not described by a scalar field but relies on a single dark fluid.Comment: 15 pages, LateX file; one comment after Eq.(36) and formula (44) added in order to underline procedure and main results. Accepted for publication in JCAP; some typos correcte

Constraints on perfect fluid and scalar field dark energy models from future redshift surveys

We discuss the constraints that future photometric and spectroscopic redshift surveys can put on dark energy through the baryon oscillations of the power spectrum. We model the dark energy either with a perfect fluid or a scalar field and take into account the information contained in the linear growth function. We show that the growth function helps to break the degeneracy in the dark energy parameters and reduce the errors on $w_0,w_1$ roughly by 30% making more appealing multicolor surveys based on photometric redshifts. We find that a 200 square degrees spectroscopic survey reaching $z = 3$ can constrain $w_0,w_1$ to within $\Delta w_0=0.21,\Delta w_1=0.26$ and to $\Delta w_0=0.39,\Delta w_1=0.54$ using photometric redshifts with absolute uncertainty of 0.02. In the scalar field case we show that the slope $n$ of the inverse power-law potential for dark energy can be constrained to $\Delta n=0.26$ (spectroscopic redshifts) or $\Delta n=0.40$ (photometric redshifts), i.e. better than with future ground-based supernovae surveys or CMB data.Comment: 27 pages, submitted to MNRA

Cosmological scalar fields that mimic the ΛCDM\Lambda CDM cosmological model

We look for cosmologies with a scalar field (dark energy without cosmological constant), which mimic the standard $\Lambda CDM$ cosmological model yielding exactly the same large-scale geometry described by the evolution of the Hubble parameter (i.e. photometric distance and angular diameter distance as functions on $z$). Asymptotic behavior of the field solutions is studied in the case of spatially flat Universe with pressureless matter and separable scalar field Lagrangians (power-law kinetic term + power-law potential). Exact analytic solutions are found in some special cases. A number of models have the field solutions with infinite behavior in the past or even singular behavior at finite redshifts. We point out that introduction of the cosmological scalar field involves some degeneracy leading to lower precision in determination of $\Omega_m$. To remove this degeneracy additional information is needed beyond the data on large-scale geometry.Comment: VIII International Conference "Relativistic Astrophysics, Gravitation and Cosmology": May 21-23, 2008, Kyiv, Ukrain

Light-cone averaging in cosmology: formalism and applications

We present a general gauge invariant formalism for defining cosmological averages that are relevant for observations based on light-like signals. Such averages involve either null hypersurfaces corresponding to a family of past light-cones or compact surfaces given by their intersection with timelike hypersurfaces. Generalized Buchert-Ehlers commutation rules for derivatives of these light-cone averages are given. After introducing some adapted "geodesic light-cone" coordinates, we give explicit expressions for averaging the redshift to luminosity-distance relation and the so-called "redshift drift" in a generic inhomogeneous Universe.Comment: 20 pages, 2 figures. Comments and references added, typos corrected. Version accepted for publication in JCA

A step towards testing general relativity using weak gravitational lensing and redshift surveys

Using the linear theory of perturbations in General Relativity, we express a set of consistency relations that can be observationally tested with current and future large scale structure surveys. We then outline a stringent model-independent program to test gravity on cosmological scales. We illustrate the feasibility of such a program by jointly using several observables like peculiar velocities, galaxy clustering and weak gravitational lensing. After addressing possible observational or astrophysical caveats like galaxy bias and redshift uncertainties, we forecast in particular how well one can predict the lensing signal from a cosmic shear survey using an over-lapping galaxy survey. We finally discuss the specific physics probed this way and illustrate how $f(R)$ gravity models would fail such a test.Comment: 12 pages, 10 figure