Deformed Starobinsky model in gravity’s rainbow

Abstract

In the context of gravity's rainbow, we study the deformed Starobinsky model in which the deformations take the form f (R) ∼ R 2(1−α) , with R the Ricci scalar and α a positive parameter. We show that the spectral index of curvature perturbation and the tensor-toscalar ratio can be written in terms of N, λ and α, with N being the number of e-foldings, λ a rainbow parameter. We compare the predictions of our models with Planck data. With the sizeable number of e-foldings and proper choices of parameters, we discover that the predictions of the model are in excellent agreement with the Planck analysis. Interestingly, we obtain the upper limit and the lower limit of a rainbow parameter λ and a positive constant α, respectively.PACS numbers: I. INTRODUCTIONThe prediction of a minimal measurable length in order of Planck length in various theories of quantum gravity restricts the maximum energy that any particle can attain to the Planck energy. This could be implied the modification of linear momentum and also quantum commutation relations and results the modified dispersion relation. Moreover, as an effective theory of gravity, the Einstein general theory of gravity is valid in the low energy (IR) limit, while at very high energy regime (UV) the Einstein theory could in principle be improved.One of the interesting approaches that naturally deals with modified dispersion relations is called doubly special relativity [1][2][3]. Then Magueijo and Smolin [4] generalized this idea by including curvature. The modification of the dispersion relation results by replacing the standard one, i.e.

Traversable wormholes supported by GUP corrected Casimir energy

“…Note that the prediction of a minimal measurable length in order of Planck length in various theories of quantum gravity restricts the maximum energy that any particle can attain to the Planck energy. This implied the modification of linear momentum and also quantum commutation relations and results the modified dispersion relation, e.g., gravity's rainbow [50], see some particular cosmological [51][52][53] and astrophysical implications [54][55][56][57][58]. Moreover, this scale naturally arises in theories of quantum gravity in the form of an effective minimal uncertainly in positions ∆x 0 > 0.…”

Exact and Slow-Roll Solutions for Exponential Power-Law Inflation Connected with Modified Gravity and Observational Constraints

“…The Starobinsky gravity model as a special case of f (R) gravity was considered in astrophysics and cosmology (see, for example, [72][73][74], and literature cited therein). Also the relation of the Starobinsky model to modified gravity and supergravity is discussed in [75][76][77][78][79].…”

Gravitational collapse for the K-essence emergent Vaidya spacetime

“…Both the Vainshtein and the dRGT mechanisms are used for the energy dependent massive gravity (Vaidya spacetime). Relevant theories of rainbow gravity and their subsequent explorations in Charged dilatonic black holes, Gauss-Bonnet gravity, Lovelock gravity, combination of Rastall and rainbow theories, Ad S 4 dyonic black holes, Deformed Starobinsky model, Thermodynamics of black holes, Galileon gravity, Horizon effect, Violation of weak cosmic censorship and Branes are addressed in [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. Also, we clearly mention that in this work we cannot study the Rainbow gravity in the framework of the k-essence emergent Vaidya spacetime.…”