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Register a new userCosmography and the redshift drift in Palatini $f({cal R})$ theories
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Added by
Florencia Anabella Teppa Pannia
Publication date
2018
fields
Physics
and research's language is
English
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We present an application to cosmological models in $f({cal R})$ theories within the Palatini formalism of a method that combines cosmography and the explicit form of the field equations in the calculation of the redshift drift. The method yields a sequence of constraint equations which lead to limits on the parameter space of a given $f({cal R})$-model. Two particular families of $f({cal R})$-cosmologies capable of describing the current dynamics of the universe are explored here: (i) power law theories of the type $f({cal R})={cal R}-beta /{cal R}^n$, and (ii) theories of the form $f({cal R})={cal R}+alpha ln{{cal R}} -beta$. The constraints on $(n,beta)$ and $(alpha,beta)$, respectively, limit the values to intervals that are narrower than the ones previously obtained. As a byproduct, we show that when applied to General Relativity, the method yields values of the kinematic parameters with much smaller errors that those obtained directly from observations.
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We focus on a series of $f(R)$ gravity theories in Palatini formalism to investigate the probabilities of producing the late-time acceleration for the flat Friedmann-Robertson-Walker (FRW) universe. We apply statefinder diagnostic to these cosmological models for chosen series of parameters to see if they distinguish from one another. The diagnostic involves the statefinder pair ${r,s}$, where $r$ is derived from the scale factor $a$ and its higher derivatives with respect to the cosmic time $t$, and $s$ is expressed by $r$ and the deceleration parameter $q$. In conclusion, we find that although two types of $f(R)$ theories: (i) $f(R) = R + alpha R^m - beta R^{-n}$ and (ii) $f(R) = R + alpha ln R - beta$ can lead to late-time acceleration, their evolutionary trajectories in the $r-s$ and $r-q$ planes reveal different evolutionary properties, which certainly justify the merits of statefinder diagnostic. Additionally, we utilize the observational Hubble parameter data (OHD) to constrain these models of $f(R)$ gravity. As a result, except for $m=n=1/2$ of (i) case, $alpha=0$ of (i) case and (ii) case allow $Lambda$CDM model to exist in 1$sigma$ confidence region. After adopting statefinder diagnostic to the best-fit models, we find that all the best-fit models are capable of going through deceleration/acceleration transition stage with late-time acceleration epoch, and all these models turn to de-Sitter point (${r,s}={1,0}$) in the future. Also, the evolutionary differences between these models are distinct, especially in $r-s$ plane, which makes the statefinder diagnostic more reliable in discriminating cosmological models.
Currently, in order to explain the accelerated expansion phase of the universe, several alternative approaches have been proposed, among which the most common are dark energy models and alternative theories of gravity. Although these approaches rest on very different physical aspects, it has been shown that both are in agreement with the data in the current status of cosmological observations, thus leading to an enormous degeneration between these models. So until evidences of higher experimental accuracy are available, more conservative model independent approaches are a useful tool for breaking this degenerated cosmological models picture. Cosmography as a kinematic study of the universe is the most popular candidate on this regard. Here we show how to construct the cosmographic equations for the f (R, T ) theory of gravity within a conservative scenario of this theory, where R is the Ricci curvature scalar and T is the trace of the energy-moment tensor. Such equations relate f(R,T) and its derivatives at the current time t0 to the cosmographic parameters q0, j0 and s0. In addition, we show how these equations can be written within different dark energy scenarios, thus helping to discriminate between them. We also show how different f(R,T) gravity models can be constrained using these cosmographic equations.
A method to set constraints on the parameters of extended theories of gravitation is presented. It is based on the comparison of two series expansions of any observable that depends on H(z). The first expansion is of the cosmographical type, while the second uses the dependence of H with z furnished by a given type of extended theory. When applied to f(R) theories together with the redshift drift, the method yields limits on the parameters of two examples (the theory of Hu and Sawicki (2007), and the exponential gravity introduced by Linder (2009)) that are compatible with or more stringent than the existing ones, as well as a limit for a previously unconstrained parameter.
We investigate cosmological dynamics based on $f(R)$ gravity in the Palatini formulation. In this study we use the dynamical system methods. We show that the evolution of the Friedmann equation reduces to the form of the piece-wise smooth dynamical system. This system is is reduced to a 2D dynamical system of the Newtonian type. We demonstrate how the trajectories can be sewn to guarantee $C^0$ extendibility of the metric similarly as `Milne-like FLRW spacetimes are $C^0$-extendible. We point out that importance of dynamical system of Newtonian type with non-smooth right-hand sides in the context of Palatini cosmology. In this framework we can investigate singularities which appear in the past and future of the cosmic evolution. We consider cosmological systems in both Einstein and Jordan frames. We show that at each frame the topological structures of phase space are different.
Recently D. Vollick [Phys. Rev. D68, 063510 (2003)] has shown that the inclusion of the 1/R curvature terms in the gravitational action and the use of the Palatini formalism offer an alternative explanation for cosmological acceleration. In this work we show not only that this model of Vollick does not have a good Newtonian limit, but also that any f(R) theory with a pole of order n in R=0 and its second derivative respect to R evaluated at Ro is not zero, where Ro is the scalar curvature of background, does not have a good Newtonian limit.
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