We consider $f(R,T)$ modified theories of gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$ and of the trace of the stress-energy tensor $T$. We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the stress-energy tensor. Generally, the gravitational field equations depend on the nature of the matter source. The field equations of several particular models, corresponding to some explicit forms of the function $f(R,T)$, are also presented. An important case, which is analyzed in detail, is represented by scalar field models. We write down the action and briefly consider the cosmological implications of the $f(R,{T}^{\ensuremath{\phi}})$ models, where ${T}^{\ensuremath{\phi}}$ is the trace of the stress-energy tensor of a self-interacting scalar field. The equations of motion of the test particles are also obtained from a variational principle. The motion of massive test particles is nongeodesic, and takes place in the presence of an extra-force orthogonal to the four velocity. The Newtonian limit of the equation of motion is further analyzed. Finally, we provide a constraint on the magnitude of the extra acceleration by analyzing the perihelion precession of the planet Mercury in the framework of the present model.

$f(R,T)$ gravity

We review the problem of dark energy, including a survey of theoretical models and some aspects of numerical studies

Dark Energy

We present distance measurements to 71 high redshift type Ia supernovae discovered during the first year of the 5-year Supernova Legacy Survey (SNLS). These events were detected and their multi-color light-curves measured using the MegaPrime/MegaCam instrument at the Canada-France-Hawaii Telescope (CFHT), by repeatedly imaging four one-square degree fields in four bands. Follow-up spectroscopy was performed at the VLT, Gemini and Keck telescopes to confirm the nature of the supernovae and to measure their redshift. With this data set, we have built a Hubble diagram extending to z = 1, with all distance measurements involving at least two bands. Systematic uncertainties are evaluated making use of the multiband photometry obtained at CFHT. Cosmological fits to this first year SNLS Hubble diagram give the following results: {Omega}{sub M} = 0.263 {+-} 0.042 (stat) {+-} 0.032 (sys) for a flat {Lambda}CDM model; and w = -1.023 {+-} 0.090 (stat) {+-} 0.054 (sys) for a flat cosmology with constant equation of state w when combined with the constraint from the recent Sloan Digital Sky Survey measurement of baryon acoustic oscillations.

The Supernova Legacy Survey: Measurement of Omega_m, Omega_l and w from the First Year Data Set

Deriving the expansion history of the Universe is a major goal of modern cosmology. To date, the most accurate measurements have been obtained with Type Ia Supernovae (SNe) and Baryon Acoustic Oscillations (BAO), providing evidence for the existence of a transition epoch at which the expansion rate changes from decelerated to accelerated. However, these results have been obtained within the framework of specific cosmological models that must be implicitly or explicitly assumed in the measurement. It is therefore crucial to obtain measurements of the accelerated expansion of the Universe independently of assumptions on cosmological models. Here we exploit the unprecedented statistics provided by the Baryon Oscillation Spectroscopic Survey (BOSS, [1-3]) Data Release 9 to provide new constraints on the Hubble parameter H(z) using the cosmic chronometers approach. We extract a sample of more than 130000 of the most massive and passively evolving galaxies, obtaining five new cosmology-independent H(z) measurements in the redshift range 0.3 < z < 0.5, with an accuracy of ~11–16% incorporating both statistical and systematic errors. Once combined, these measurements yield a 6% accuracy constraint of H(z = 0.4293) = 91.8 ± 5.3 km/s/Mpc. The new data are crucial to provide the first cosmology-independent determination of the transition redshift at high statistical significance, measuring zt = 0.4 ± 0.1, and to significantly disfavor the null hypothesis of no transition between decelerated and accelerated expansion at 99.9% confidence level. This analysis highlights the wide potential of the cosmic chronometers approach: it permits to derive constraints on the expansion history of the Universe with results competitive with standard probes, and most importantly, being the estimates independent of the cosmological model, it can constrain cosmologies beyond—and including—the ΛCDM model.

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A 6% measurement of the Hubble parameter at z∼0.45: direct evidence of the epoch of cosmic re-acceleration

Deriving the expansion history of the Universe is a major goal of modern cosmology. To date, the most accurate measurements have been obtained with Type Ia Supernovae and Baryon Acoustic Oscillations, providing evidence for the existence of a transition epoch at which the expansion rate changes from decelerated to accelerated. However, these results have been obtained within the framework of specific cosmological models that must be implicitly or explicitly assumed in the measurement. It is therefore crucial to obtain measurements of the accelerated expansion of the Universe independently of assumptions on cosmological models. Here we exploit the unprecedented statistics provided by the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 to provide new constraints on the Hubble parameter $H(z)$ using the em cosmic chronometers approach. We extract a sample of more than 130000 of the most massive and passively evolving galaxies, obtaining five new cosmology-independent $H(z)$ measurements in the redshift range $0.3<z<0.5$, with an accuracy of $\sim$11-16\% incorporating both statistical and systematic errors. Once combined, these measurements yield a 6\% accuracy constraint of $H(z=0.4293)=91.8\pm5.3$ km/s/Mpc. The new data are crucial to provide the first cosmology-independent determination of the transition redshift at high statistical significance, measuring $z_{t}=0.4\pm0.1$, and to significantly disfavor the null hypothesis of no transition between decelerated and accelerated expansion at 99.9\% confidence level. This analysis highlights the wide potential of the cosmic chronometers approach: it permits to derive constraints on the expansion history of the Universe with results competitive with standard probes, and most importantly, being the estimates independent of the cosmological model, it can constrain cosmologies beyond -and including- the $\Lambda$CDM model.

A 6% measurement of the Hubble parameter at $z\sim0.45$: direct evidence of the epoch of cosmic re-acceleration

A new accelerating cosmology driven only by baryons plus cold dark matter (CDM) is proposed in the framework of general relativity. In this model the present accelerating stage of the Universe is powered by the negative pressure describing the gravitationally-induced particle production of cold dark matter particles. This kind of scenario has only one free parameter and the differential equation governing the evolution of the scale factor is exactly the same of the $\Lambda$CDM model. For a spatially flat Universe, as predicted by inflation ($\Omega_{dm}+\Omega_{baryon}=1$), it is found that the effectively observed matter density parameter is $\Omega_{meff} = 1- \alpha$, where $\alpha$ is the constant parameter specifying the CDM particle creation rate. The supernovae test based on the Union data (2008) requires $\alpha\sim 0.71$ so that $\Omega_{meff} \sim 0.29$ as independently derived from weak gravitational lensing, the large scale structure and other complementary observations.

CDM Accelerating Cosmology as an Alternative to LCDM model

A new accelerating cosmology driven only by baryons plus cold dark matter (CDM) is proposed in the framework of general relativity. In this scenario the present accelerating stage of the Universe is powered by the negative pressure describing the gravitationally-induced particle production of cold dark matter particles. This kind of scenario has only one free parameter and the differential equation governing the evolution of the scale factor is exactly the same of the ΛCDM model. For a spatially flat Universe, as predicted by inflation (Ωdm+Ωbaryon = 1), it is found that the effectively observed matter density parameter is Ωmeff = 1−α, where α is the constant parameter specifying the CDM particle creation rate. The supernovae test based on the Union data (2008) requires α ~ 0.71 so that Ωmeff ~ 0.29 as independently derived from weak gravitational lensing, the large scale structure and other complementary observations.

CDM accelerating cosmology as an alternative to ΛCDM model

We analyze the interaction between dark energy and dark matter from a thermodynamical perspective. By assuming they have different temperatures, we study the possibility of occurring a decay from dark matter into dark energy, characterized by a negative parameter Q. We find that, if at least one of the fluids has nonvanishing chemical potential, for instance μ x 0, the decay is possible, where μ x and μ am are the chemical potentials of dark energy and dark matter, respectively. Using recent cosmological data, we find that, for a fairly simple interaction, the dark matter decay is favored with a probability of ∼93% over the dark energy decay. This result comes from a likelihood analysis where only background evolution has been considered.

Can dark matter decay in dark energy

We study the effect of shear and rotation on results previously obtained dealing with the application of the spherical collapse model (SCM) to generalized Chaplygin gas (gCg)-dominated universes. The system is composed of baryons and gCg and the collapse is studied for different values of the parameterof the gCg. We show that the joint effect of shear and rotation is that of slowing down the collapse with respect to the simple SCM. This result is of utmost importance for the so-called unified dark matter models, since the described slowdown in the growth of density perturbations can solve one of the main problems of the quoted models, namely the instability described in previous papers (e.g., H.B. Sandvik et al., Phys. Rev. D 69, 123524 (2004)) at the linear perturbation level.

Shear and rotation in Chaplygin cosmology

A component of dark energy has been recently proposed to explain the current acceleration of the Universe. Unless some unknown symmetry in Nature prevents or suppresses it, such a field may interact with the pressureless component of dark matter, giving rise to the so-called models of coupled quintessence. In this paper we propose a new cosmological scenario where radiation and baryons are conserved, while the dark energy component is decaying into cold dark matter. The dilution of cold dark matter particles, attenuated with respect to the usual a{sup -3} scaling due to the interacting process, is characterized by a positive parameter {epsilon}, whereas the dark energy satisfies the equation of state p{sub x}={omega}{rho}{sub x} ({omega}<0). We carry out a joint statistical analysis involving recent observations from type Ia supernovae, baryon acoustic oscillation peak, and cosmic microwave background shift parameter to check the observational viability of the coupled quintessence scenario here proposed.

J. F. Jesus

Papers

CDM Accelerating Cosmology as an Alternative to LCDM model

CDM accelerating cosmology as an alternative to ΛCDM model

Can dark matter decay in dark energy

Shear and rotation in Chaplygin cosmology

New coupled quintessence cosmology