2018/06/30 by Salvatore Capozziello, Salvatore Capozzıello, Rocco D'Agostino +2 · 62 citations
Mathematics · Physics and Astronomy · #Astrophysics #Black Holes and Theoretical Physics #Cosmology #Cosmology and Gravitation Theories #Dark energy #Galaxies: Formation, Evolution, Phenomena #Luminosity distance #Mathematical physics #Metric expansion of space #Physics #Redshift #astro-ph.CO #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/s10714-018-2483-0
published in General Relativity and Gravitation 51(1) (Springer Science+Business Media) · 10 pages, 6 figures. Accepted for publication in Gen. Rel. Grav
arxiv created 2018/11/09 · openalex publication_date 2018/11/23 · arxiv updated 2019/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A kinematic treatment to trace out the form of f(R) cosmology, within the Palatini formalism, is discussed by only postulating the universe homogeneity and isotropy. To figure this out we build model-independent approximations of the luminosity distance through rational expansions. These approximants extend the Taylor convergence radii computed for usual cosmographic series. We thus consider both Padé and the rational Chebyshev polynomials. They can be used to accurately describe the universe late-time expansion history, providing further information on the thermal properties of all effective cosmic fluids entering the energy momentum tensor of Palatini's gravity. To perform our numerical analysis, we relate the Palatini's Ricci scalar with the Hubble parameter H and thus we write down a single differential equation in terms of the redshift z. Therefore, to bound f(R), we make use of the most recent outcomes over the cosmographic parameters obtained from combined data surveys. In particular our clue is to select two scenarios, i.e. (2,2) Padé and (2,1) Chebyshev approximations, since they well approximate the luminosity distance at the lowest possible order. We find that best analytical matches to the numerical solutions lead to f(R)=a+bRn with free parameters given by the set (a, b, n)=(-1.627, 0.866, 1.074) for (2,2) Padé approximation, whereas f(R)=α+βRm with (α, β, m)=(-1.332, 0.749, 1.124) for (2,1) rational Chebyshev approximation. Finally, our results are compared with the ΛCDM predictions and with previous studies in the literature. Slight departures from General Relativity are also discussed.