Minimal cosmography

Abstract

The minimal requirement for cosmography-a non-dynamical description of the universe-is a prescription for calculating null geodesics, and time-like geodesics as a function of their proper time. In this paper, we consider the most general linear connection compatible with homogeneity and isotropy, but not necessarily with a metric. A lightcone structure is assigned by choosing a set of geodesics representing light rays. This defines a "scale factor" and a local notion of distance, as that travelled by light in a given proper time interval. We find that the velocities and relativistic energies of free-falling bodies decrease in time as a consequence of cosmic expansion, but at a rate that can be different than that dictated by the usual metric framework. By extrapolating this behavior to photons' redshift, we find that the latter is in principle independent of the "scale factor". Interestingly, redshift-distance relations and other standard geometric observables are modified in this extended framework, in a way that could be experimentally tested. An extremely tight constraint on the model, however, is represented by the blackbody-ness of the Cosmic Microwave Background. Finally, as a check, we also consider the effects of a non-metric connection in a different set-up, namely, that of a static, spherically symmetric spacetime.

Probing the cosmic distance duality relation using time delay lenses

“…al. studied the modification in the duality relation by introducing the dilaton and an axion field in a theoretical construction [6] and Piazza & Schucker (2016) try to understand the behaviour of CDDR in a non-metric theory of gravity [7].…”

Bayesian Comparison of the Cosmic Duality Scenarios

“…Here, we will compare the η(z) functions defined in the Section IV by assuming that parameterization (7) is the standard model (Model 1) and, E i are the others parameterizations Eqs. ( 8) , ( 9), (10) and, (11), Models 2, 3, 4 and, 5 respectively, in which we want to compare. If each model is assigned an equal prior probability, the Bayes factor gives the posterior odds of the two models.…”

“…Simultaneously with the increase in the number and the quality of astronomical data, different methods have been proposed to test the validity of the CDDR. We can divide them in two classes: cosmological model-dependent tests based on ΛCDM framework [5][6][7][8][9][10], and cosmological model-independent ones. The last ones have been performed by using combinations of several astronomical data: angular diameter distance of galaxy clusters, galaxy cluster gas mass fraction 1 , type Ia supernovae (SNe Ia), strong gravitational lensing, cosmic microwave background, gamma ray bursts, radio compact sources, baryon acoustic oscillations, gravitational waves, etc .…”

Strong lensing systems and galaxy cluster observations as probe to the cosmic distance duality relation

“…These methods can be divided in two classes: cosmological modeldependent tests based on the cold dark matter ( CDM) framework (see the Refs. [5,[9][10][11][12]) and cosmological modelindependent. Several astronomical data sets have been used to probe the CDDR, for instance: angular diameter distance of galaxy clusters, galaxy cluster gas mass fraction, type Ia supernovae (SNe Ia), strong gravitational lensing (SGL), cosmic microwave background, gamma ray bursts, radio compact sources, cosmic microwave background radiation, baryon acoustic oscillations, gravitational waves, etc.…”