Abstract
We show that the effective brane-world and the loop quantum cosmology background expansion histories can be reproduced from a modified gravity perspective in terms of an f(R) gravity action plus a g(R) term non-minimally coupled with the matter Lagrangian. The reconstruction algorithm that we provide depends on a free function of the matter density that must be specified in each case and allows to obtain analytical solutions always. In the simplest cases, the function f(R) is quadratic in the Ricci scalar, R, whereas g(R) is linear. Our approach is compared with recent results in the literature. We show that working in the Palatini formalism there is no need to impose any constraint that keeps the equations second-order, which is a key requirement for the successful implementation of the reconstruction algorithm.
Highlights
In the context of the early-time cosmology, the approaches based on brane-world models [1] and loop quantum gravity [2] seem to favour a specific model of cosmic evolution characterized by quadratic relations between the Hubble parameter and the energy density of the fluid, dubbed quadratic cosmology
We show that a natural alternative formulation of the problem presented above exists
We find that working in the Palatini formalism, the restriction imposed in [3] is not essential, as the field equations that one obtains are of second-order by construction
Summary
In the context of the early-time cosmology, the approaches based on brane-world models [1] and loop quantum gravity [2] seem to favour a specific model of cosmic evolution characterized by quadratic relations between the Hubble parameter and the energy density of the fluid, dubbed quadratic cosmology. We shall explicitly show that the field equations of this setting are always second-order and, in vacuum, boil down to those of GR This allows to study the gravitymatter coupling framework from a more general perspective than in the standard (metric) approach, since the functions f (R) and g(R) are not forced to satisfy a specific constraint. We shall work out this scenario and show that any given cosmological background history can be obtained from a Palatini f (R) theory with gravity-matter couplings To illustrate this point we will consider the particular case of quadratic cosmology
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