We consider, in Palatini formalism, a modified gravity of which the scalar field derivative couples to Einstein tensor. In this scenario, Ricci scalar, Ricci tensor and Einstein tensor are functions of connection field. As a result, the connection field gives rise to relation, hµν = f gµν between effective metric, hµν and the usual metric gµν where f = 1 − κφ ,α φ,α/2. In FLRW universe, NMDC coupling constant is limited in a range of −2/φ 2 < κ ≤ ∞ preserving Lorentz signature of the effective metric. Slowly-rolling regime provides κ < 0 forbidding graviton from travelling at superluminal speed. Effective gravitational coupling and entropy of blackhole's apparent horizon are derived. In case of negative coupling, acceleration could happen even with w eff > −1/3. Power-law potentials of chaotic inflation are considered. For V ∝ φ 2 and V ∝ φ 4 , it is possible to obtain tensor-to-scalar ratio lower than that of GR so that it satisfies r < 0.12 as constrained by Planck 2015 [35]. The V ∝ φ 2 case yields acceptable range of spectrum index and r values. The quartic potential's spectrum index is disfavored by the Planck results. Viable range of κ for V ∝ φ 2 case lies in positive region, resulting in less blackhole's entropy, superluminal metric, more amount of inflation, avoidance of super-Planckian field initial value and stronger gravitational constant. *

In cosmological framework, Noether symmetry technique has revealed a useful tool in order to examine exact solutions. In this work, we first introduce the Jordan-frame Lagrangian and apply the conformal transformation in order to obtain the Lagrangian equivalent to Einstein-frame form. We then analyse the dynamics of the field in the cosmological alpha-attractors using the Noether sysmetry approach by focusing on the single field scenario in the Einstein-frame form. We show that with a Noether symmetry the coresponding dynamical system can be completely integrated and the potential exhibited by the symmetry can be exactly obtained. With the proper choice of parameters, the behavior of the scale factor displays an exponential (de Sitter) behavior at the present epoch. Moreover, we discover that the Hubble parameters strongly depends on the initial values of parameters exhibited by the Noether symmetry. Interestingly, it can retardedly evolve and becomes a constant in the present epoch in all cases.PACS numbers: 98.80.Cq,98.80.Hw I. INTRODUCTIONIn modern cosmology, the mechanism of cosmic inflation seems conceivable. Inflation marks nowadays an inevitable ingredient when studying very early evolution of the universe. The reason stems from the fact that it solves most of the puzzles that plague the standard Big Bang theory, and simultaneously is consistent with recent observational data. In other words, it not only gives sensible explanations for the horizon, flatness, and relic abundant problems, but also provides us primordial density perturbation as seeds of the formation for a large-scale structure in the universe.Despite all its success, however, the underlying mechanism of the inflationary physics is still unknown. Recent observational data much flavors large field inflationary models with plateau-like inflaton potentials. However, there are several different ways of constructing successful inflationary models. In the supergravity context, a model with plateau potentials was proposed by the authors of Refs. [1,2]. Here it describes a potential which is exponentially approaching a positive constant for super-Planckian values of the inflaton field. Later on, a theory with a similar potential was realized as the Starobinsky model [3], and then the Higgs inflation model with a similar potential was developed [4,5]. It is worth noting that these models lead to nearly identical predictions, providing the best fit to the latest Planck data [6,7]. Moreover, recent investigation shows the inflaton field can emerge as a composite state of a new strongly interacting gauge theory [8,9]. More recently, a broad class of inflationary models, dubbed cosmological attractors [10][11][12][13][14][15][16], yields very similar inflationary predictions.Interestingly, the cosmological α-attractors incorporate most of the existing inflationary models with plateau-like potentials including the Starobinsky model and some generalized versions of the Higgs inflation. Regarding the α-attractors, the flatness of the inflaton potential is i...

In this letter, cosmology of a simple NMDC gravity with ξRφ,µφ ,µ term and a free kinetic term is considered in flat geometry and in presence of dust matter. A logarithm field transformation φ ′ = µ ln φ is proposed phenomenologically. Assuming slow-roll approximation, equation of motion, scalar field solution and potential are derived as function of kinematic variables. The field solution and potential are found straightforwardly for power-law, de-Sitter and super-acceleration expansions. Slow-roll parameters and slow-roll condition are found to depend on more than one variable. At large field the re-scaling effect can enhance the acceleration. For slow-rolling field, the negative coupling ξ could enhance the effect of acceleration. * buring@nu.ac.th †

In this work, we take a short recap of a formal framework of the Eddington-inspired Born–Infeld (EiBI) theory of gravity and derive the point-like Lagrangian for underlying theory based on the use of Noether gauge symmetries (NGS). We study a Hessian matrix and quantify Euler–Lagrange equations of EiBI universe. We discuss the NGS approach for the Eddington-inspired Born–Infeld theory and show that there exists the de Sitter solution in this gravity model.

No abstract