# Reconstruction and deceleration-acceleration transitions in modified gravity

## TL;DR

This paper explores how to reconstruct cosmological models with deceleration-acceleration transitions in modified Gauss-Bonnet and F(R) gravities, highlighting the limitations of analytical solutions and the role of auxiliary fields.

## Contribution

It provides a comparative analysis of different action representations and demonstrates the reconstruction of transition cosmologies, emphasizing the necessity of auxiliary fields for certain singular solutions.

## Key findings

- Reconstruction of deceleration-acceleration transition cosmologies is feasible with auxiliary scalar fields.
- Analytical solutions for transition cosmologies are generally impossible without auxiliary fields.
- Certain singular solutions like Big Bang and Big Rip require auxiliary field representation.

## Abstract

We discuss the cosmological reconstruction in modified Gauss-Bonnet and F(R) gravities. Two alternative representations of the action (with and without auxiliary scalar) are considered. The approximate description of deceleration-acceleration transition cosmologies is reconstructed. It is shown that cosmological solution containing Big Bang and Big Rip singularities may be reconstructed only using the representation with the auxiliary field. The analytical description of the deceleration-acceleration transition cosmology in modified Gauss-Bonnet gravity is demonstrated to be impossible at sufficiently general conditions.