Linear stability of Einstein and de Sitter universes in the quadratic theory of modified gravity

We consider the Einstein static and the de Sitter universe solutions and examine their instabilities in a subclass of quadratic modified theories for gravity. This modification proposed by Nash is an attempt to generalize general relativity. Interestingly, we discover that the Einstein static universe is unstable in the context of the modified gravity. In contrast to Einstein static universe, the de Sitter universe remains stable under metric perturbation up to the second order.

Exact multi-instanton solutions to self-dual Yang–Mills equation on curved spaces

We find exact multi-instanton solutions to the self-dual Yang–Mills equation on a large class of curved spaces with [Formula: see text] isometry, generalizing the results previously found on [Formula: see text]. The solutions are featured with explicit multi-centered expressions and topological properties. As examples, we demonstrate the approach on several different curved spaces, including the Einstein static universe and [Formula: see text], and show that the exact multi-instanton solutions exist on these curved backgrounds.

Stability of anisotropic perturbed Einstein universe in f(R) gravity

The aim of this paper is to investigate the existence of stable modes of the Einstein static universe in the background of [Formula: see text] theory. For this purpose, we take homogeneous anisotropic perturbations in scale factors as well as matter contents. We construct static and perturbed field equations that are further parameterized by linear equation of state parameter. We obtain the Einstein static solutions for two specific [Formula: see text] models and graphically analyze their stable regions. It is concluded that contrary to general relativity, there exists stable Einstein static universe with anisotropic perturbations.

Einstein static universe, GUP, and natural IR and UV cut-offs

We study the Einstein static universe (ESU) in the framework of Generalized Uncertainty Principle (GUP) constructed by the Snyder non-commutative space. It is shown that the deformation parameter can induce an effective energy density subject to GUP which obeys the holographic principle (HP) and plays the role of a cosmological constant. Using the holographic feature of this effective energy density, we introduce natural IR and UV cut-offs which depend on the GUP-based effective equation of state. Moreover, we propose a solution to the cosmological constant problem (CCP). This solution is based on the result that the Einstein equations just couple to the tiny holographic-based surface energy density (cosmological constant) induced by the deformation parameter, rather than the large quantum gravitational-based volume energy density (vacuum energy) having contributions of order [Formula: see text].