Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse problem: Reconstruction of modified gravity action in Palatini
  formalism by Supernova Type Ia data   We introduce in $f(R)$ gravity--Palatini formalism the method of inverse
problem to extract the action from the expansion history of the universe.
First, we use an ansatz for the scale factor and apply the inverse method to
derive an appropriate action for the gravity. In the second step we use the
Supernova Type Ia data set from the Union sample and obtain a smoothed function
for the Hubble parameter up to the redshift~1.7. We apply the smoothed Hubble
parameter in the inverse approach and reconstruct the corresponding action in
$f(R)$ gravity. In the next step we investigate the viability of reconstruction
method, doing a Monte-Carlo simulation we generate synthetic SNIa data with the
quality of union sample and show that roughly more than 1500 SNIa data is
essential to reconstruct correct action. Finally with the enough SNIa data, we
propose two diagnosis in order to distinguish between the $\Lambda$CDM model
and an alternative theory for the acceleration of the universe.

8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an