Constrainingf(R) theories with cosmography

Abstract

A method to set constraints on the parameters of extended theories of gravitation is presented. It is based on the comparison of two series expansions of any observable that depends on H(z). The first expansion is of the cosmographical type, while the second uses the dependence of H with z furnished by a given type of extended theory. When applied to f (R) theories together with the redshift drift, the method yields limits on the parameters of two examples (the theory of Hu and Sawicki [1], and the exponential gravity introduced by Linder [2]) that are compatible with or more stringent than the existing ones, as well as a limit for a previously unconstrained parameter.

Cosmography of the f(R,T) gravity theory

“…This is important in view of the fact that the higher order cosmographic parameters are poorly restricted by current cosmological data [116,119,120]. We have also shown here how these equations can be used together with the observational values of (q 0 , j 0 , s 0 ) to place restrictions on the form of the f (R, T ) function in a similar way to what was done for the f (R) theory [88,83,86]. In addition, the Equations ( 40)-( 42) have been rewritten within various dark energy scenarios.…”

“…Cosmography has already been developed to Extended Gravity Theories, particularly to the f (R) gravity [83]- [88] (the last of these references was actually applied to an f (R)-brane cosmology) and f (T ) gravity [89,90]. For a review of these approaches, check [91].…”

Black Hole Shadow Drift and Photon Ring Frequency Drift

“…explicitly depends on the variation of the angular diameter distance (8) with redshift and on the redshift driftż. The first quantity is…”

“…Optimistic estimates show that these facilities could reach a precision of 10 −10 , for example with monitoring programs of 1000 hours of exposure with a 40-meter telescope [7]. For this reason, cosmology with redshift drifts is an active field of research [8][9][10][11][12][13][14][15][16][17][18][19][20], which we advance further with this work, in which we investigate how the cosmological drift would affect the image from black hole shadows and interferometric signatures from black holes' photon rings.…”

“…Optimistic estimates show that these facilities could reach a precision of 10 −10 , for example with monitoring programs of 1000 hours of exposure with a 40-meter telescope [7]. For this reason, cosmology with redshift drifts is an active field of research [8][9][10][11][12][13][14][15][16][17][18][19][20], which we advance further with this work, in which we investigate how the cosmological drift would affect the image from black hole shadows and interferometric signatures from black holes' photon rings.Black holes were first predicted over a century ago, yet the first direct image of a black hole was reconstructed only very recently by the Event Horizon Telescope (EHT) collaboration [21][22][23][24][25][26][27]. The direct detection of the shadow of M87 , the supermassive black hole at the centre of the galaxy Messier 87, suggests we will soon be able to obtain black hole parameters such as their mass, spin and charge in a systematic way.…”