Studies On The Mimetic Gravity And Stabilities Of Its Perturbations

Lots of theories that attempt to explain the nature of dark matter have emerged since the presence of dark matter was suggested by numerous observations such as galaxy rotation curves,large scale structure of the universe and gravitational lensing.One viewpoint is that dark matter consists of particles beyond the standard model.For instance,the WIMPs(weakly interaction massive particles)are an ideal candidate for cold dark matter.An alternative viewpoint is to consider dark matter the result of modified gravity.In this thesis we have mainly studied mimetic gravity first coined in a 2013 paper by Chamseddine and Mukhanov,and focused on stabilities of the generalized mimetic theory with higher-order derivative term.Firstly,we will give a brief review of modern cosmology and the theoretical framework of cosmological perturbations.Secondly we will discuss the original mimetic dark matter presented by Mukhanov as a dark matter model,and show that mimetic gravity as a conformal gravity can be rewritten as a new formalism with Lagrangian multiplier which impose the mimetic constraint.The Lagrange multiplier formalism largely simplified the subsequent works of extending the theory of mimetic gravity,such as:mimetic f(R)gravity,mimetic Horndeski scalar-tensor theory and mimetic Gauss-Bonnet theory.Mimetic gravity with a potential term has significant implications on cosmology,and can provide us with the background of inflation and bounce,but can't produce primordial cosmological perturbations due to its vanishing sound speed.Mimetic gravity with higher-order terms allows for perturbation equations with nontrival speed of sound;unfortunately this theory suffers from gradient and ghost instabilities as Steinhardt and Ijjas have shown by analysing the second-order action.Note that the same thing happens in Horava-Lifshitz gravity.Thirdly,we further prove the result of Steinhardt and Ijjas,showing that the simple extension of mimetic gravity action by introducing f(??),??v,and f(?)R terms can not tame the instabilities.Neither can the mimetic version of f(R)gravity which suffers from the well-known Ostrogradski instabiliity.Fourthly,we consider a more complex extension in which the curvature scalar couples to the higher derivative terms directly,and we show the possibility of circumventing the instability problem through a concrete toy model with appropriate choice of functions and parameters.By finding healthy extension of mimetic theory from the viewpoint of effective field theory,we show again that direct couplings of the curvature to the higher derivative terms of the mimetic field have the potential to cure the instability problem.Finally we summarize the main contents in this paper,illuminate the present state of the mimetic scenario including its deficiencies,and prospects for the future research.