If we take the idea of the Planck length as a fundamental (minimum) scale and if additionally we impose the Cosmological Constant ($Lambda$) as and infrared (IR) cut-off parameter. Then it is possible to demonstrate that Dark Matter effects can emerge as a consequence of an IR-UV mix effect. This opens the possibility of unifying the Dark Energy and Dark matter effects in a single approach.
Geometric Operators in Loop Quantum Gravity with a Cosmological Constant
Loop quantum gravity is a candidate to describe the quantum gravity regime with zero cosmological constant. One of its key results is that geometric operators such as area angle volume are quantized. Not much is known when the cosmological constant is not zero. It is usually believed that to introduce this parameter in the game we need to use quantum groups. However due to the complicated algebraic structure inherent to quantum groups the geometric operators are not yet properly defined (except the area operator). I will discuss how the use of tensor operators can circumvent the difficulties and allow to construct a natural set of observables. In particular I will construct the natural geometric observables such as angle or volume and discuss some of their implications.
Interplay Between Cosmological Constant and DSR Scale
I offer brief remarks on several ways in which the cosmological constant could provide a clue toward quantum gravity. I then focus on how DSR-relativistic theories can be made compatible with spacetime expansion (possibly cosmological-constant-governed spacetime expansion), and how this interplay could manifest itself in data.
Quantum Gravity RG Flow: A Cosmological Limit Cycle
I will discuss evidence for the existence of a limit cycle in the renormalization group for quantum gravity which is visible in a minisuperspace approximation. The emergence of the limit cycle can be studied through a tuning parameter representing the number of dimensions in which fluctuations of the conformal factor are suppressed. At the critical value of the tuning parameter all RG trajectories reaching the UV fixed point have an extended semiclassical regime with a small positive cosmological constant providing a possible model for a viable cosmology without fine-tuning.