From negative to positive cosmological constant through decreasing temperature of the Universe: connection with string theory and spacetime foliation results

Abstract

String theories naturally predict a negative, while observations on the exponential expansion of the present Universe require a positive value for the cosmological constant. Solution to resolve this discrepancy is known in the framework of string theory however, it might describe unstable worlds. Other options include modified $\Lambda$CDM models with sign switching cosmological constant (known as $\Lambda_s$ cosmology), but the sign flip is introduced into the models {\bf {\it ad hoc}}. Additional studies consider Asymptotically Safe (AS) quantum gravity by using Renormalization Group (RG), however their disadvantage is the omission of temperature which is otherwise crucial in the early Universe. Here we present a proposal for resolving this conflict by using a modified thermal RG method where the temperature parameter $T$ is given by the inverse radius of the compactified time-like dimension, similarly to spacetime foliation. In our scenario not the dimensionful $T$, but the dimensionless temperature $\tau = T/k$ is kept constant when the RG scale $k$ is sent to zero and string theory is assumed to take place at very high while AS quantum gravity at intermediate and low temperatures. We show that the modified thermal RG study of AS quantum gravity models at very high temperatures results in a negative cosmological constant while turns it into a positive parameter for low temperatures.