Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A numerical approach to model independently reconstruct $f(R)$ functions
  through cosmographic data   The challenging issue of determining the correct $f(R)$ among several
possibilities is here revised by means of numerical reconstructions of the
modified Friedmann equations around the redshift interval $z\in[0,1]$.
Frequently, a severe degeneracy between $f(R)$ approaches occurs, since
different paradigms correctly explain present time dynamics. To set the initial
conditions on the $f(R)$ functions, we involve the use of the so called
cosmography of the Universe, i.e. the technique of fixing constraints on the
observable Universe by comparing expanded observables with current data. This
powerful approach is essentially model independent and correspondingly we got a
model independent reconstruction of $f(z)$ classes within the interval
$z\in[0,1]$. To allow the Hubble rate to evolve around $z\leq1$, we considered
three relevant frameworks of effective cosmological dynamics, i.e. the
$\Lambda$CDM model, the CPL parametrization and a polynomial approach to dark
energy. Finally cumbersome algebra permits to pass from $f(z)$ to $f(R)$ and
the general outcome of our work is the determination of a viable $f(R)$
function, that effectively describes the observed Universe dynamics.

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The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat