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 $Λ$CDM models with sign switching cosmological constant (known as $Λ_s$ cosmology), but the sign flip is introduced into the models manually. 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 $τ= T/k$ 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.

Figures (3)

• Figure 1: Schematic figure of the time evolution (temperature, i.e., $\tau$-dependence) of the scale factor $R(t)$ and the cosmological constant $\Lambda(t)$.
• Figure 2: Thermal RG flow diagrams of CREH, QEG with $N$-component scalar field (with chosen parameters $\xi = 10$ and $N=2$) and Ghost-improved EH gravity for various $\tau$ dimensionless temperature values. With $\tau \to \infty$ the $g^* \to 0$ limit is reached in each case.
• Figure 3: QPT-CPT diagram of various AS gravity models in terms of the dimensionless temperature $\tau$ and the $g$-coordinate of the Reuter fixed point. Black lines, i.e., the function $g^\star(\tau_c)$, are critical lines which separate the $\lambda<0$ and the $\lambda>0$ phases. For a given (but fixed) $g^\star$-value, for $\tau > \tau_c$ or $\tau < \tau_c$ the particular model is in the $\lambda<0$ or its $\lambda>0$ phase. The inset shows how the positions of the Reuter fixed point ($g^\star$, $\lambda^\star$) changes by $\tau$ in case of the three variants.