Testing homogeneity with galaxy number counts : light-cone metric and general low-redshift expansion for a central observer in a matter dominated isotropic universe without cosmological constant

As an alternative to dark energy it has been suggested that we may be at the center of an inhomogeneous isotropic universe described by a Lemaitre-Tolman-Bondi (LTB) solution of Einstein's field equations. In order to test this hypothesis we calculate the general analytical formula to fifth order for the redshift spherical shell mass. Using the same analytical method we write the metric in the light-cone by introducing a gauge invariant quantity $G(z)$ which together with the luminosity distance $D_L(z)$ completely determine the light-cone geometry of a LTB model.Comment: 13 page

The Self-Calibrating Hubble Diagram

As an increasing number of well measured type Ia supernovae (SNe Ia) become available, the statistical uncertainty on w has been reduced to the same size as the systematic uncertainty. The statistical error will decrease further in the near future, and hence the improvement of systematic uncertainties needs to be addressed, if further progress is to be made. We study how uncertainties in the primary reference spectrum - which are a main contribution to the systematic uncertainty budget - affect the measurement of the Dark Energy equation of state parameter w from SNe Ia. The increasing number of SN observations can be used to reduce the uncertainties by including perturbations of the reference spectrum as nuisance parameters in a cosmology fit, thus "self-calibrating" the Hubble diagram. We employ this method to real SNe data for the first time and find the perturbations of the reference spectrum consistent with zero at the 1%-level. For future surveys we estimate that ~3500 SNe will be required for our method to outperform the standard method of deriving the cosmological parameters.Comment: 17 pages, 8 figures, 1 table. Update to revised version accepted for publication in JCA

General Non-minimal Kinetic coupling to gravity

We study a new model of scalar field with a general non-minimal kinetic coupling to itself and to the curvature, as a source of dark energy, and analyze the cosmological dynamics of this model and the issue of accelerated expansion. A wide variety of scalar fields and potentials giving rise to power-law expansion have been found. The dynamical equation of state is studied for the two cases, without and with free kinetic term . In the first case, a behavior very close to that of the cosmological constant was found. In the second case, a solution was found, which match the current phenomenology of the dark energy. The model shows a rich variety of dynamical scenarios.Comment: 25 pages, 3 figures; figure added, references adde

The imprint of the interaction between dark sectors in galaxy clusters

Based on perturbation theory, we study the dynamics of how dark matter and dark energy in the collapsing system approach dynamical equilibrium while interacting. We find that the interaction between dark sectors cannot ensure the dark energy to fully cluster along with dark, leading to the energy non-conservation problem in the collapsing system We examine the cluster number counts dependence on the interaction between dark sectors. Furthermore, we analyze how dark energy inhomogeneities affect cluster abundances. It is shown that cluster number counts can provide specific signature of dark sectors interaction and dark energy inhomogeneities.Comment: revised version. New treatment has been provided on studying the structure formation in the spherical collapsing system where DE does not cluster together with DM. Accepted for publication in JCA

A minimal set of invariants as a systematic approach to higher order gravity models: Physical and Cosmological Constraints

We compare higher order gravity models to observational constraints from magnitude-redshift supernova data, distance to the last scattering surface of the CMB, and Baryon Acoustic Oscillations. We follow a recently proposed systematic approach to higher order gravity models based on minimal sets of curvature invariants, and select models that pass some physical acceptability conditions (free of ghost instabilities, real and positive propagation speeds, and free of separatrices). Models that satisfy these physical and observational constraints are found in this analysis and do provide fits to the data that are very close to those of the LCDM concordance model. However, we find that the limitation of the models considered here comes from the presence of superluminal mode propagations for the constrained parameter space of the models.Comment: 12 pages, 6 figure

The imprint of the interaction between dark sectors in galaxy clusters

Based on perturbation theory, we study the dynamics of how dark matter and dark energy in the collapsing system approach dynamical equilibrium while interacting. We find that the interaction between dark sectors cannot ensure the dark energy to fully cluster along with dark, leading to the energy non-conservation problem in the collapsing system We examine the cluster number counts dependence on the interaction between dark sectors. Furthermore, we analyze how dark energy inhomogeneities affect cluster abundances. It is shown that cluster number counts can provide specific signature of dark sectors interaction and dark energy inhomogeneities.Comment: revised version. New treatment has been provided on studying the structure formation in the spherical collapsing system where DE does not cluster together with DM. Accepted for publication in JCA

Regularizing cosmological singularities by varying physical constants

Varying physical constant cosmologies were claimed to solve standard cosmological problems such as the horizon, the flatness and the $\Lambda$-problem. In this paper, we suggest yet another possible application of these theories: solving the singularity problem. By specifying some examples we show that various cosmological singularities may be regularized provided the physical constants evolve in time in an appropriate way.Comment: 9 pages, 6 figures, Revtex4-1, an improved version to appear in JCA

Transient cosmic acceleration from interacting fluids

Recent investigations seem to favor a cosmological dynamics according to which the accelerated expansion of the Universe may have already peaked and is now slowing down again \cite{sastaro}. As a consequence, the cosmic acceleration may be a transient phenomenon. We investigate a toy model that reproduces such a background behavior as the result of a time-dependent coupling in the dark sector which implies a cancelation of the "bare" cosmological constant. With the help of a statistical analysis of Supernova Type Ia (SNIa) data we demonstrate that for a certain parameter combination a transient accelerating phase emerges as a pure interaction effect.Comment: Latex file, 23 pages, 21 figures in eps format. Discussion enlarged, new subsection on scalar field dynamics included, accepted for publication in JCAP

Effects of dark sectors' mutual interaction on the growth of structures

We present a general formalism to study the growth of dark matter perturbations when dark energy perturbations and interactions between dark sectors are present. We show that dynamical stability of the growth of structure depends on the type of coupling between dark sectors. By taking the appropriate coupling to ensure the stable growth of structure, we observe that the effect of the dark sectors' interaction overwhelms that of dark energy perturbation on the growth function of dark matter perturbation. Due to the influence of the interaction, the growth index can differ from the value without interaction by an amount within the observational sensibility, which provides a possibility to disclose the interaction between dark sectors through future observations on the growth of large structure.Comment: 15 pages, 4 figures, revised version, to appear in JCA

Corrections to the apparent value of the cosmological constant due to local inhomogeneities

Supernovae observations strongly support the presence of a cosmological constant, but its value, which we will call apparent, is normally determined assuming that the Universe can be accurately described by a homogeneous model. Even in the presence of a cosmological constant we cannot exclude nevertheless the presence of a small local inhomogeneity which could affect the apparent value of the cosmological constant. Neglecting the presence of the inhomogeneity can in fact introduce a systematic misinterpretation of cosmological data, leading to the distinction between an apparent and true value of the cosmological constant. We establish the theoretical framework to calculate the corrections to the apparent value of the cosmological constant by modeling the local inhomogeneity with a $\Lambda LTB$ solution. Our assumption to be at the center of a spherically symmetric inhomogeneous matter distribution correspond to effectively calculate the monopole contribution of the large scale inhomogeneities surrounding us, which we expect to be the dominant one, because of other observations supporting a high level of isotropy of the Universe around us. By performing a local Taylor expansion we analyze the number of independent degrees of freedom which determine the local shape of the inhomogeneity, and consider the issue of central smoothness, showing how the same correction can correspond to different inhomogeneity profiles. Contrary to previous attempts to fit data using large void models our approach is quite general. The correction to the apparent value of the cosmological constant is in fact present for local inhomogeneities of any size, and should always be taken appropriately into account both theoretically and observationally.Comment: 16 pages,new sections added analyzing central smoothness and accuracy of the Taylor expansion approach, Accepted for publication by JCAP. An essay based on this paper received honorable mention in the 2011 Essay Context of the Gravity Research Foundatio