Cosmography of f(R) gravity

It is nowadays accepted that the universe is undergoing a phase of accelerated expansion as tested by the Hubble diagram of Type Ia Supernovae (SNeIa) and several LSS observations. Future SNeIa surveys and other probes will make it possible to better characterize the dynamical state of the universe renewing the interest in cosmography which allows a model independent analysis of the distance - redshift relation. On the other hand, fourth order theories of gravity, also referred to as $f(R)$ gravity, have attracted a lot of interest since they could be able to explain the accelerated expansion without any dark energy. We show here how it is possible to relate the cosmographic parameters (namely the deceleration $q_0$, the jerk $j_0$, the snap $s_0$ and the lerk $l_0$ parameters) to the present day values of $f(R)$ and its derivatives $f^{(n)}(R) = d^nf/dR^n$ (with $n = 1, 2, 3$) thus offering a new tool to constrain such higher order models. Our analysis thus offers the possibility to relate the model independent results coming from cosmography to the theoretically motivated assumptions of $f(R)$ cosmology.Comment: 18 pages, 4 figure

Reconciling dark energy models with f(R) theories

Higher order theories of gravity have recently attracted a lot of interest as alternative candidates to explain the observed cosmic acceleration without the need of introducing any scalar field. A critical ingredient is the choice of the function f(R) of the Ricci scalar curvature entering the gravity Lagrangian and determining the dynamics of the universe. We describe an efficient procedure to reconstruct f(R) from the Hubble parameter $H$ depending on the redshift z. Using the metric formulation of f(R) theories, we derive a third order linear differential equation for f(R(z)) which can be numerically solved after setting the boundary conditions on the basis of physical considerations. Since H(z) can be reconstructed from the astrophysical data, the method we present makes it possible to determine, in principle, what is the f(R) theory which best reproduces the observed cosmological dynamics. Moreover, the method allows to reconcile dark energy models with f(R) theories finding out what is the expression of f(R) which leads to the same H(z) of the given quintessence model. As interesting examples, we consider "quiessence" (dark energy with constant equation of state) and the Chaplygin gas.Comment: 15 pages, 4 figures, accepted for publication on Physical Review

Constraints on the slope of the dark halo mass function by microlensing observables

We investigate the dark halo lens mass function (MF) for a wide class of spheroidal non singular isothermal models comparing observed and observable microlensing quantities for MACHO observations towards LMC and taking into account the detection efficiency. We evaluate the microlensing observable quantities, i.e. observable optical depth, number of events and mean duration, for models with homogenous power - law MF changing the upper and lower mass limits and the flattening of the dark halo. By applying the simple technique of the inverse problem method we are then able to get some interesting constraints on the slope $\alpha$ of the MF and on the dark halo mass fraction f made out by MACHOs consistently with previous results.Comment: 10 LaTex pages, 2 postscript figures, accepted on 21/5/2001 for pubblication on A&A; title changed, completely revised version : a new definition of observable optical depth is used and all the MACHO results from 5.7 years of observations are used to constrain the slope of the dark halo mass functio

Cosmography in f(T)-gravity

Being based on the only assumption that the universe is homogenous and isotropic on large scales, cosmography is an ideal tool to investigate the cosmic expansion history in a almost model-independent way. Fitting the data on the luminosity distance and Baryon Acoustic Oscillations allows to determine the confidence ranges for the cosmographic parameters hence giving some quantitative constraints that a whatever theory has to fulfill. As an application, we consider here the case of teleparallel gravity (TEGR) also referred to as f(T)-gravity. To this end, we first work out analytical expressions to express the present day values of f(T)-derivatives as a function of the cosmographic parameters which hold under quite general and physically motivated conditions. We then use the constraints coming from cosmography to find out the confidence ranges for f(T)-derivatives up to the fifth order and show how these can be used to check the viability of given TEGR models without the need to explicitly solve the second order dynamic equations.Comment: 12 pages, 1 figure, to appear in Phys. Rev.

Dark matter scaling relations in intermediate z haloes

We investigate scaling relations between the dark matter (DM) halo model parameters for a sample of intermediate-redshift early-type galaxies (ETGs) resorting to a combined analysis of Einstein radii and aperture velocity dispersions. Modelling the dark halo with a Navarro-Frenk-White profile and assuming a Salpeter initial mass function (IMF) to estimate stellar masses, we find that the column density and the Newtonian acceleration within the halo characteristic radius rs and effective radius Reff are not universal quantities, but correlate with the luminosity LV, the stellar mass M★ and the halo mass M200, contrary to recent claims in the literature. We finally discuss a tight correlation among the DM mass MDM(Reff) within the effective radius Reff, the stellar mass M★(Reff) and Reff itself. The slopes of the scaling relations discussed here strongly depend, however, on the DM halo model and the IMF adopted so that these ingredients have to be better constrained in order to draw definitive conclusions on the DM scaling relations for ETG

Modelling the Milky Way through adiabatic compression of cold dark matter halo

We use the adiabatic compression theory to build a physically well - motivated Milky Way mass model in agreement with the observational data. The visible mass of the Galaxy is distributed in a spheroidal bulge and a multi - components disc parametrized by three galactic parameters, the Sun distance to the galactic centre, R_0, the total bulge mass, M_{bulge}, and the local disc surface density, \Sigma_{\odot}. To model the dark matter component, we adiabatically compress a Navarro, Frenk and White (NFW) halo (with concentration $c$ and total mass M_{vir}) for fixed values of the spin parameter, \lambda, the fraction of the mass in baryons, $m_b$, and the thin disc contribution to total angular momentum, j_d. An iterative selection procedure is used to explore in very detail the wide space of parameters only selecting those combinations of {R_0, M_{bulge}, \Sigma_{\odot}, \lambda, m_b, j_b, c, M_{vir}} that give rise to a Milky Way model in agreement with the observational constraints. This analysis leads us to conclude that only models with R_0 = 8.5 kpc, $0.8 x 10^{10} M_{\odot} < M_{bulge} < 1.6 x 10^{10} M_{\odot}$ and $49 M_{\odot} pc^{-2} \le \Sigma_{\odot} \le 56 M_{\odot} pc^{-2}$ can be reconciled with the set of observational constraints. As regard the parameters entering the adiabatic compression, we find $0.03 \le \lambda \le 0.10$ and $0.04 \le m_b \le 0.10$, while the final estimates of the parameters describing the initial halo profile turn out to be $5 \stackrel{<}{\sim} c \stackrel{<}{\sim} 12$ and $7 x 10^{11} M_{\odot} \stackrel{<}{\sim} M_\mathrm{vir} \stackrel{<}{\sim} 17 x 10^{11} M_{\odot}$ (all at 95.7% CL).Comment: 13 pages, 10 figures, accepted for publication on Astronomy & Astrophysic

Discovery of a tight correlation for gamma ray burst afterglows with `canonical' light curves

Gamma Ray Bursts (GRB) observed up to redshifts $z>8$ are fascinating objects to study due to their still unexplained relativistic outburst mechanisms and a possible use to test cosmological models. Our analysis of 77 GRB afterglows with known redshifts revealed a physical subsample of long GRBs with canonical {\it plateau breaking to power-law} light curves with a significant {\it luminosity $L^*_X$ - break time $T^*_a$} correlation in the GRB rest frame. This subsample forms approximately the {\it upper envelope} of the studied distribution. We have also found a similar relation for a small sample of GRB afterglows that belong to the intermediate class (IC) between the short and the long ones. It proves that within the full sample of afterglows there exist physical subclasses revealed here by tight correlations of their afterglow properties. The afterglows with regular (`canonical') light curves obey not only a mentioned tight physical scaling, but -- for a given $T^*_a$ -- the more regular progenitor explosions lead to preferentially brighter afterglows.Comment: 15 pages, 5 figures accepted to ApJ