Cosmological implications of interacting group field theory models: Cyclic Universe and accelerated expansion

We study the cosmological implications of interactions between spacetime quanta in the group field theory (GFT) approach to quantum gravity from a phenomenological perspective. Our work represents a first step towards understanding early Universe cosmology by studying the dynamics of the emergent continuum spacetime, as obtained from a fundamentally discrete microscopic theory. In particular, we show how GFT interactions lead to a recollapse of the Universe while preserving the bounce replacing the initial singularity, which has already been shown to occur in the free case. It is remarkable that cyclic cosmologies are thus obtained in this framework without any a priori assumption on the geometry of spatial sections of the emergent spacetime. Furthermore, we show how interactions make it possible to have an early epoch of accelerated expansion, which can be made to last for an arbitrarily large number of $e$-folds, without the need to introduce an ad hoc potential for the scalar field.

Figure 1

Plot of the potential $U(\rho )$ [Eq. (15)] for the dynamical system described by Eq. (14) and a particular choice of parameters. The three horizontal curves correspond to different values of the “GFT energy” $E$, in turn corresponding to different choices of initial conditions for $\rho$, ${\rho }^{\prime }$. The corresponding orbits in phase space are shown in Fig. 2. Recollapse is generic feature of the model and occurs for any values of the parameters, provided $\mu >0$ and $Q\ne 0$.

Figure 2

Phase portrait of the dynamical system given by Eq. (14). Orbits have energy given by the corresponding color lines as Fig. 1. Orbits are periodic and describe oscillations around the stable equilibrium point (center fixed point) given by the absolute minimum of the potential $U(\rho )$. This is a general feature of the model which does not depend on the particular choice of parameters, provided Eq. (11) is satisfied.

Figure 3

Plot of the volume of the Universe as a function of relational time $\varphi$ (in arbitrary units), corresponding to the blue orbit in Fig. 2. As a generic feature of the interacting model the Universe undergoes a cyclic evolution and its volume has a positive minimum, corresponding to a bounce.

Figure 4

Inflationary era supported by GFT interactions in the multicritical model. The blue (orange) curve represents the graph of the logarithm of the acceleration (minus the acceleration) as a function of the number of $e$-folds, in the case $\lambda <0$. The plot refers to the particular choice of parameters $n=5$, $n^{\prime }=6$, $m=1$, $Q=1$, and $\lambda =-3$. The value of $\mu$ is determined from Eq. (36) by requiring the number of $e$-folds to be $N=60$. There is a logarithmic singularity at $N\simeq 60$, marking the end of the accelerated expansion.

Figure 5

The behavior of the acceleration close to the bounce.

Figure 6

The behavior of the acceleration at the end of inflation.