f(R)gravity theories in Palatini formalism: Cosmological dynamics and observational constraints

Abstract

We make a systematic study of the cosmological dynamics for a number of f (R) gravity theories in Palatini formalism, using phase space analysis as well as numerical simulations. Considering homogeneous and isotropic models, we find a number of interesting results: (i) models based on theories of the type (a) f (R) = R − β/R n and (b) f (R) = R + αln R − β, unlike the metric formalism, are capable of producing the sequence of radiation-dominated, matter-dominated and de-Sitter periods, and (ii) models based on theories of the type (c) f (R) = R + αR m − β/R n can produce early as well as late accelerating phases but an early inflationary epoch does not seem to be compatible with the presence of a subsequent radiation-dominated era. Thus for the classes of models considered here, we have been unable to find the sequence of all four dynamical epochs required to account for the complete cosmological dynamics, even though three out of four phases are possible.We also place observational constraints on these models using the recently released supernovae data by the Supernova Legacy Survey as well as the baryon acoustic oscillation peak in the SDSS luminous red galaxy sample and the CMB shift parameter. The best-fit values are found to be n = 0.027, α = 4.63 for the models based on (a) and α = 0.11, β = 4.62 for the models based on (b), neither of which are significantly preferred over the ΛCDM model. Moreover, the logarithmic term alone is not capable of explaining the late acceleration. The models based on (c) are also consistent with the data with suitable choices of their parameters.We also find that some of the models for which the radiation-dominated epoch is absent prior to the matter-dominated era also fit the data. The reason for this apparent contradiction is that the combination of the data considered here does not place stringent enough constraints on the cosmological evolution prior to the decoupling epoch, which highlights the importance of our combined theoretical-observational approach to constrain models.

Beyond the cosmological standard model

“…It has been argued that higher-curvature theories can arise naturally from string theory under appropriate assumptons [356,357]. Like Einstein gravity, these theories admit a Palatini formulation, which is quite subtle and has been extensive studied [180,[358][359][360][361][362][363][364][365][366][367][368][369][370][371][372]. Models which can cross the phantom divide and have effective equations of state w < −1 have been studied [373][374][375][376], along with investigations into energy conditions in f (R) gravity [377][378][379].…”

Viable Palatini-f(R)cosmologies with generalized dark matter

“…This suggests it worthwhile to seriously reconsider the cosmology of the Palatini-f (R) models. Expansionwise, they can generate a viable sequence of radiation dominated, matter dominated and accelerating era matching with the constraints, as has been shown for various parameterizations of the function f (R), most often with some power-law forms (with one, two or three * Electronic address: tomikoiv@pcu.helsinki.fi powers of R), but also with square-root, logarithmic and exponential forms for the curvature correction terms [26,27,28,29,30]. However, the inhomogeneous evolution present in any realistic universe has not been succesfully reconciled with observations in these models.…”

Models off(R)cosmic acceleration that evade solar system tests

“…The addition of a non-linear function of the Ricci scalar R to the Einstein-Hilbert action has been demonstrated to cause acceleration for a wide variety of f (R) functions [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,…”