A Sudden Gravitational Transition

Abstract

We investigate the properties of a cosmological scenario which undergoes a gravitational phase transition at late times. In this scenario, the Universe evolves according to general relativity in the standard, hot Big Bang picture until a redshift z \lesssim 1. Non-perturbative phenomena associated with a minimally-coupled scalar field catalyzes a transition, whereby an order parameter consisting of curvature quantities such as R^2, R_{ab}R^{ab}, R_{abcd}R^{abcd} acquires a constant expectation value. The ensuing cosmic acceleration appears driven by a dark-energy component with an equation-of-state w < -1. We evaluate the constraints from type 1a supernovae, the cosmic microwave background, and other cosmological observations. We find that a range of models making a sharp transition to cosmic acceleration are consistent with observations.

Figures (8)

• Figure 1: The evolution of the gravitational transition model in the $w-\dot w/H$ phase plane is shown. For a given $N$, the model trajectory follows the curve indicated with $\Omega_m$ decreasing as the phase variables evolve from the starting point at $(w,\,\dot w/H)=(-\infty,\infty)$ and head towards $(-1,0)$. The values corresponding to $\Omega_m=0.3,\,0.4$ are indicated by the small squares and circles, respectively. In the case $\Omega_m=0.4$ today, $(w,\dot w/H)=(-1.55,2.4),\,(-1.45,1.6), \,(-1.35,1.0)$, with the transition occuring at $a_*/a_0 = 0.7,\,0.6,\ 0.5$ for $N=2,\,3,\,4$ respectively.
• Figure 2: The evolution of the equation-of-state $w$ as a function of the scale factor $a$ is shown. All models have $\Omega_m=0.4$ today. For decreasing $N$, the effective gravitational repulsion of the dark energy as measured by $w$ increases. The $N=4$ model is consistent with all observations, the $N=3$ is on the border, and $N=2$ is excluded.
• Figure 3: The evolution of the density parameter $\Omega_m$ as a function of the scale factor $a$ is shown. All models have $\Omega_m=0.4$ today. The matter density drops suddenly at the onset of the transition. The sharpness of the drop grows with decreasing $N$. The $N=4$ model is consistent with all observations, the $N=3$ is on the border, and $N=2$ is excluded.
• Figure 4: The observational constraints on the $\Omega_m - H_0$ parameter space for the $N=2,\,3,\,4$ gravitational transition models are shown. The red-filled contour is the WMAP CMB $2\sigma$ region, obtained from the $\Lambda$CDM $2\sigma$ region, given by the black dashed contour, by using the geometric degeneracy. The line connecting the black dots shows the mapping of the best-fit $\Lambda$CDM model to the gravitational transition model. The SN $2\sigma$ regions are shown by the wide, pale blue (Knop et al 2004) and narrow, pale grey (Riess et al 2004) bands. The shape parameter $\Gamma$$3\sigma$ region is shown by the yellow swath. The Hubble constant $2\sigma$ region is the horizontal green band. For reference, gravitational transition models with age $13.5$ Gyrs lie along the thin blue line. There is significant overlap amongst all model constraints for the cases $N=4$ for the $R^2$ transition. Sharper transitions, corresponding to $N<4$, are in conflict with some or all of the observations.
• Figure 5: Same as Fig. \ref{['fig1']} but with positive spatial curvature. In all cases $\Omega_k=-0.05$ and $\Omega_m=1.05$ at the time of the transition. The agreement with CMB and SN constraints improves significantly, particularly for the N=4 case as the CMB best-fit point falls inside the $2\sigma$ contour for all other constraints.