Consistency off(R)=R2−R02gravity with cosmological observations in the Palatini formalism

Abstract

In this work we study the dynamics of universe in f (R) = R 2 − R 2 0 modified gravity with Palatini formalism. We use data from recent observations as Supernova Type Ia (SNIa) Gold sample and Supernova Legacy Survey (SNLS) data, size of baryonic acoustic peak from Sloan Digital Sky Survey (SDSS), the position of the acoustic peak from the CMB observations and large scale structure formation (LSS) from the 2dFGRS survey to put constraint on the parameters of the model. To check the consistency of this action, we compare the age of old cosmological objects with the age of universe. In the combined analysis with the all the observations, we find the parameters of model as R0 = 6.192 [1,2]. Analysis of SNIa and the Cosmic Microwave Background radiation (CMB) observations indicates that about 70% of the total energy of the Universe is made by the dark energy and the rest of it is in the form of dark matter with a few percent of Baryonic matter [3][4][5]. The "cosmological constant" is a possible explanation of the present dynamics of the universe [6]. This term in Einstein field equations can be regarded as a fluid with the equation of state of w = −1. However, there are two problems with the cosmological constant, namely the fine-tuning and the cosmic coincidence. In the framework of quantum field theory, the vacuum expectation value is 123 order of magnitude larger than the observed value of 10 −47 GeV 4 . The absence of a fundamental mechanism which sets the cosmological constant to zero or to a very small value is the cosmological constant problem. The second problem known as the cosmic coincidence, states that why are the energy densities of dark energy and dark matter nearly equal today?There are various solutions for this problem as the decaying cosmological constant models. A non-dissipative minimally coupled scalar field, so-called Quintessence can play the role of this time varying cosmological constant [7][8][9]. The ratio of energy density of this field to the matter density in this model increases by the expansion of the universe and after a while dark energy becomes the dominant term of the energy-momentum tensor. Another approach dealing with this problem is using the modified gravity by changing the Einstein-Hilbert action. Recently a great attention has been devoted to this era because of the prediction of early and late time accelerations in these models [22]. While it seems that the modified gravity and dark energy models are completely different approaches to explain cosmic acceleration, it is possible to unify them in one formalism [23].In this work we obtain the dynamics of the modified gravity f (R) = R 2 − R 2 0 in the Palatini formalism [24] and use the cosmological observations as SNIa, SDSS acoustic peck in CMB and structure formation to put constraint on the parameter of the action. In Sec. II we derive the dynamics of Hubble parameter and scale factor in Palatini formalism for general case of f (R) gravity. In Sec. III using action f (R) = R 2 − R 2 0 we obtain the dynamics of univers...

Age problem in the holographic dark energy model

“…In fact, these three OHRO at z = 1.43, 1.55 and 3.91 have been used to test many dark energy models, such as the ΛCDM model [44,53,54], the dark energy models with different EoS parameterizations [49,50], the generalized Chaplygin gas [55], the Λ(t)CDM model [56], the model-independent EoS of dark energy [57], the scalar-tensor quintessence [58], the f (R) = R 2 − R 2 0 model [59], the DGP braneworld model [60,61], the power-law parameterized quintessence model [62], and so on. It is found that the two OHRO at z = 1.43 and 1.55 can be easily accommodated in most dark energy models, whereas the OHRO at z = 3.91 can not, even in the ΛCDM model.…”

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.…”

Modified f (R) gravity from scalar–tensor theory and inhomogeneous EoS dark energy

“…As is shown, this model is reproduced by (27) for small t when the curvature R is large, and by (31) or (33) when t is large. For a proper choice of the power α, the solution for large t is given by (31), which in combination with the solution (27) for small t, it looks like standard…”