Cosmic acceleration in unimodular gravity

We study unimodular gravity in the context of cosmology, particularly some interesting consequences that might be able to describe the background cosmology and the late cosmic acceleration. We focus our attention on the hypothesis of nonconservation of the energy momentum tensor. This characteristic has an interesting outcome: we can obtain a modified Friedmann equation along with the acceleration equation and also new fluid equations related to a third order derivative of the scale factor, known in cosmography as the jerk parameter. As a consequence of this theory, it seems that radiation and the cosmological constant are intimately related, in agreement with what some authors have called the third coincidence problem. Their connection is the parameter $z_{\mathrm{ini}}$, which has a value of 11.29 and coincides with the reionization epoch. As a result, we are able to explain the late acceleration as a natural consequence of the equations, associating the new fluid with radiation and, thus, eliminating the need for another component (i.e., dark energy). Finally, we interpret the results and discuss the pros and cons of using the cosmological constant under the hypothesis of nonconservation of the energy momentum tensor in the unimodular gravity scenario.

Figure 1

Jerk parameter for UG and $\mathrm{\Lambda }\mathrm{CDM}$, assuming ${\mathrm{\Omega }}_{0r}=9.07\times {10}^{-5}$ for both theories and $w_r=0.33$, $w_X=0.25$, and $w_X=0.2$. We observe that UG coincide with $\mathrm{\Lambda }\mathrm{CDM}$-like only when $w_X=w_r=0.33$, as expected. JP for $\mathrm{\Lambda }\mathrm{CDM}$-like is computed through the formula $j(q)=q(2q+1)+(1+z)dq/dz$ [25], assuming also ${\mathrm{\Omega }}_{0m}=0.31$ and with that ${\mathrm{\Omega }}_{0\mathrm{\Lambda }}=0.69$ [3].