We reconsider an inflationary model that inflaton field is non-minimally coupled to gravity. We study parameter space of the model up to the second ( and in some cases third ) order of the slow-roll parameters. We calculate inflation parameters in both Jordan and Einstein frames and the results are compared in these two frames and also with observations. Using the recent observational data from combined WMAP5+SDSS+SNIa datasets, we study constraint imposed on our model parameters especially the nonminimal coupling ξ. PACS: 98.80.-k, 98.80.Cq

We study some aspects of cosmological inflation in the framework of unimodular f (R) gravity. To be more clarified, we consider a generic f (R) of the type f (R) = R + αR n . By considering Einstein frame counterpart of the unimodular f (R) gravity, we set the scalaron to be responsible for cosmological inflation in this setup. We confront our model parameters space with observational data and impose some constraints on the value of n in this manner. We show that for the number of e-folds N = 60, the model is consistent with observation if 1.89 < n < 1.918.1 Unimodular Gravity to drop down the giant amplitude of the order of vacuum fluctuation [7,[9][10][11][12][13][14]. Historically, four years after invention of general relativity, Einstein was proposed a different set of equations dubbed subsequently as unimodular gravity. He realized also that this is equivalent to general relativity while the cosmological constant is considered as an integration constant [15][16]. In unimodular gravity one deals with those variations of the Einstein-Hilbert action that preserve the determinant of the metric to be a fixed quantity. In other words, in this scenario one assumes the determinant of the metric to be a constant as a gauge choice. An effective cosmological constant can be extracted as a constant of integration from the trace-free part of the Einstein-Hilbert field equations in unimodular gravity. This is an advantage by itself since effectively the cosmological constant is not added by hand in the theory and arises naturally as an integration constant.An alternative to address late time cosmic speed up is modification of the background gravitational theory. Among these theories, f (R) gravities, where R is the Ricci scalar, have attracted much attention at least in past two decades [17][18][19][20][21]. This extension has the capability to address initial inflation in a unified manner as well [22]. Modified gravity of this type replaces Ricci scalar in the Einstein-Hilbert action with a generic f (R) function. In recent years a vast number of research programs have been devoted to construct f (R) gravities consistent with both local (for instance Solar System) gravitational tests and cosmological observations [23][24][25][26][27][28][29]. These studies are extended to the issues such as spectra of galaxy clustering [30][31][32][33][34][35], cosmic microwave background radiation [24,31,36,37] and weak lensing [38,39]. The first model of modified gravity of the f (R) type was introduced by Starobinsky in 1980 with f (R) = R + αR 2 [22]. Starobinsky inflation model leads to accelerated expansion of the universe due to existence of αR 2 term in the modified action. This model is compatible very well with the recent cosmological data [40][41][42][43]. A gravitational Lagrangian which is an arbitrary function of the Ricci scalar in the metric formalism corresponds to the generalized Brans-Dicke theory when the Brans-Dicke parameter vanishes, that is, ω BD = 0 [44][45][46][47]. In fact, the field equations derived from f (...

We study cosmological dynamics of a generalized Higgs inflation. By expanding the action up to the second and third order in the small perturbations, we study the primordial perturbation and its non-Gaussian distribution. We study the non-Gaussian feature in both the equilateral and orthogonal configurations. By adopting a quartic potential, we perform a numerical analysis on the model's parameter space and compare the results with Planck2015 observational data. To obtain some observational constraint, we focus on the self-coupling and the non-minimal coupling parameters. We show that, in the presence of the nonminimal coupling and the Galileon-like interaction, the self-coupling parameter can be reduced to the order of 10 −6 which is much larger than the value that CMB normalization suggests for this self-coupling.

We construct a general braneworld inflation scenario where the inflaton field evolves on the DGP brane and curvature effects are taken into account via incorporation of the Gauss-Bonnet term in the bulk action. While induced gravity on the DGP brane modifies the IR limit of general relativity, the Gauss-Bonnet term in the bulk action modifies the UV sector of the theory. In this setup, the dynamics of perturbations on the brane are studied with details and some confrontation with recent observations are discussed. While the Einstein-Gauss-Bonnet inflation scenario favors only a red spectrum of the scalar perturbation, pure DGP and GBIG inflation models have the capacity to realize the blue spectrum too. In addition, the GBIG inflation scenario in the large field limit requires a smaller number of e-folds than other proposed scenarios in the same situation. For the tensor-to-scalar ratio, the GBIG inflation scenario gives a better fit with observationally supported value of R ≈ 0.24.

In the spirit of Galileon inflation and by considering some sorts of non-canonical kinetic terms in the action, we realize a stage of super-inflation leading to a blue-tilted tensor perturbation. We show also that addition of Galileon-like term to the action leads to avoidance of ghost instabilities in this setup.