New integrable models and analytical solutions in f(R) cosmology with an ideal gas

Abstract

In the context of f (R)-gravity with a spatially flat FLRW metric containing an ideal fluid, we use the method of invariant transformations to specify families of models which are integrable. We find three families of f (R) theories for which new analytical solutions are given and closed-form solutions are provided.PACS numbers: 98.80.-k, 95.35.+d, 95.36.+x

Extended phase-space analysis of the Hořava–Lifshitz cosmology

“…In order to analyze the stability of de Sitter solution we can use center manifold theorem. It is more convenient to use the variables (θ,T ) whose evolution is given by the regular unconstrained 2D dynamical system (100), (101).…”

“…In the present work we provide a complete dynamical system analysis of HL cosmology keeping the potentials arbitrary, which is a major improvement since it allows for the extraction of information that is related to the foundations of the cosmological model and not to the specific potential form. In particular, we apply the method of f -devisers [99][100][101][102][103], in which one first performs the analysis without the need of an a priori specification of the potential, and in the end one just substitutes the specific potential form in the results, instead of having to repeat the whole dynamical elaboration from the start. As we will see, the results will be richer and more general, revealing the full capabilities of HL cosmology.…”

Ghost Dark Energy in the DGP Braneworld

“…Note that, in order to find the evolution of density parameter Ω , we take the time derivative of relation Ω = /(3 2 2 ), after combining the result with (7) and (17), which yields In Figure 1, we plot the evolution of Ω versus redshift parameter . It is obvious that Ω tends to 0 in the early universe where 1 + → ∞, while at the late time where 1 + → 0, we have Ω → 1.…”

“…Interacting Case. Differentiating the modified Friedmann equation (2) and using (7) and (8) we reacḣ…”

“…There are two approaches for explanation of the cosmic acceleration. The first one is the modified gravity models such as ( ) gravity [3] and scalartensor theories [4], and the second approach is the idea of the existence of a strange type of energy whose gravity is repulsive such as the cosmological constant Λ [5] and the dynamical DE models [6,7]. Against the cosmological constant Λ which has constant equation of state (EoS) parameter, = −1, further observations detect a small variation in the EoS parameter of DE in favor of a dynamical DE with > −1 in the past and even < −1 in the late time [8].…”