Cosmological Perturbations And Large Scale Structure Formation In EiBI Gravity

Recently, Banados and Ferreira proposed an alternative theory, the so-called "Eddington-inspired Born-Infeld"(EiBI) gravity, inspired by Eddington’s theory and the Born-Infeld model. EiBI gravity is equivalent to general relativity in vacuum; but when matter fields are included, it presents many interesting properties.In EiBI gravity, the universe has a finite maximal density, so the singularity at the beginning of the universe can be avoided. And it is also claimed to be singularity free during the non-relativistic collapse of non-interacting particles. EiBI gravity can even be an alternative to inflation, in which several cosmological problems can be solved. For example, in a recent paper by Macarena Lagos, et al., the authors pointed out that, we can obtain a nearly scale-invariant primordial power spectrum without inflation.In this paper, we will focus on two important questions:(1) whether EiBI gravity can solve the singularity problem at the beginning of the universe as it promised;(2) whether it can be consistent with the current observations.Firstly, we derive the linear perturbed equations for cosmological perturbations from the action and field equations of EiBI gravity, and decompose them into scalar, vector, and tensor modes. We obtain and analyse the behaviors of the asymptotic analytic solutions for the perturbed equations for both cases:k>0and k<0(k is an extra parameter introduced in EiBI gravity). We find that, for k>0, when the density of the universe approached to the maximum (tâ†'-∞), the tensor perturbation and the nonzero wavenumber modes of scalar perturbations are unstable, while the vector perturbations and the zero wavenumber modes of the scalar perturbations are stable. For k<0, when the density of the universe approached to the maximum (tâ†'0), scalar, vector, and tensor perturbations are all unstable. So it seems that the singularity at the beginning of the universe still can not be avoided from the analysis of liner perturbations. However, at very early time of the universe, the perturbations were large, so linear analysis was unsuitable any more. If we consider higher order corrections, this problem of instability may be solved.Then we use the linear perturbed equations derived before to further analyse the evolution of the perturbations and some observational effects. We focus on the scalar perturbations, which are most relevant with observations, and discuss the large scale structure formation in EiBI gravity. We find that, for large κ, EiBI gravity deviates from general relativity. These deviations lead to enhancement or suppression of the growth of density perturbations at early time, which will finally affect the formation of large scale structure at latter time. We calculate the integrated Sachs-Wolfe effect in EiBI gravity, and find that its contribution to the angular power spectrum of the anisotropy of the cosmic microwave background is nearly indistinguishable with that in ACDM model. Thus it will not violate the observations. Furthermore, we calculate the linear matter power spectrum in EiBI gravity, and deviation is found for k≥0.1hiMpc-1. And the deviation becomes larger with bigger k. So in the future, we may be able to test EiBI gravity through observations from galaxy surveys.