The Cosmological Constant From Space-time Discreteness And Black Holes Gravitational Lensing In Nonlocal Garvity

Cosmological constant problem is one of the most important problems in modern physics.After the standard model of cosmology was established,the discovery of the accelerating universe put it in trouble.People found that there is an unknown existence dominates the evolution of the current universe,and this unknown energy has been unable to find its source.For this reason,physicists have proposed a large number of theories to explain the source of the dark energy.After decades of development,there have been a considerable number of theories to explain the cause of dark energy,which put forward new predictions and phenomena.For example,the most famous scalartensor theories,f(R)gravity,etc.Nonlocal gravity,a modified gravitational theory,has also attracted attention in recent years as a natural explanation for the accelerated expansion in the late universe.In addition,in recent years the vigorous development of the quantum gravity proposed many new point of view,there is a point of view is that the space-time is discrete near the Planck scale.According to this view,some studies think that the discrete space-time at a very small scale would lead to the violation of the law of conservation of energy,this subtle violation could make a flow of energy,which would lead to a cosmological constant close to the observed value.These phenomenological models provide ideas for solving the cosmological constant problem.In order to explore the source of the cosmological constant,we consider the discreteness of space-time near the Planck scale.Space-time background was supposed to have a set of interacting discrete element which is analogous to the solid model.We found that the thermal motion part of the space-time element could provide a minimum energy filter condition for the content which was embedded in the background,according to this energy limit,a change number of the particles which increase with the decrease of the universe temperature was obtained.Calculations show that this increase of the energy with the expansion of the universe could provide a cosmological constant which closes to the observed value and limit the temperature of reheating temperature after the electroweak phase transition in the early universe.On the other hand,the nonlocal gravity has good features in explaining the accel-eration of the late universe.In order to test the correctness of the model intuitively,we focus on the gravitational lensing effect of static and rotating black hole in the nonlocal gravity.We calculated the deflection angle of the light passing through the vicinity of the black hole.The properties of the gravitational lensing effect of the nonlocal gravity black holes are discussed.