Vacuum energy sequestering and cosmic dynamics

We explicitly compute the dynamics of closed homogeneous and isotropic universes permeated by a single perfect fluid with a constant equation-of-state parameter $w$ in the context of a recent reformulation of general relativity, proposed by Kaloper and Padilla [Phys. Rev. Lett. 112, 091304 (2014)], which prevents the vacuum energy from acting as a gravitational source. This is done using an iterative algorithm, taking as an initial guess the background cosmological evolution obtained using standard general relativity in the absence of a cosmological constant. We show that, in general, the impact of the vacuum energy sequestering mechanism on the dynamics of the universe is significant, except for the $w=1/3$ case where the results are identical to those obtained in the context of general relativity with a null cosmological constant. We also show that there are well-behaved models in general relativity that do not have a well-behaved counterpart in the vacuum energy sequestering paradigm studied in this paper, highlighting the specific case of a quintessence scalar field with a linear potential.

Figure 1

Evolution of the scale factor with cosmic time for a model with $w=-0.1$ considering general relativity with a null cosmological constant (model I, solid line) and the reformulation of general relativity incorporating the vacuum energy sequestering mechanism (model II, dashed line). The maximum value of the scale factor $a_{\max }$ and the universe’s lifetime $t_{\mathrm{u}}$ in model I are both normalized to unity.

Figure 2

The same as in Fig. 1 but with $w=0.9$.

Figure 3

Ratio between the universe’s lifetimes in models II and I as a function of $w$.

Figure 4

Ratio between the maximum values of the scale factor in models II and I as a function of $w$.

Figure 5

Ratio between $\mathrm{\Lambda }/3$ and $-k/a_{\max }^2$ as a function of $w$ (model II).

Figure 6

Ratio between $\mathrm{\Lambda }$ and the minimum density (obtained for $a=a_{\max }$) as a function of $w$ (model II).