Energy conditions and cosmic acceleration

In general relativity, the energy conditions are invoked to restrict general energy-momentum tensors $T_{\mu \nu }$ in different frameworks, and to derive general results that hold in a variety of general contexts on physical grounds. We show that in the standard Friedmann-Lemaître-Robertson-Walker (FLRW) approach, where the equation of state of the cosmological fluid is unknown, the energy conditions provide model-independent bounds on the behavior of the distance modulus of cosmic sources as a function of the redshift for any spatial curvature. We use the most recent type Ia supernovae (SNe Ia) observations, which include the new Hubble Space Telescope SNe Ia events, to carry out a model-independent analysis of the energy conditions violation in the context of the standard cosmology. We show that both the null (NEC), weak (WEC), and dominant (DEC) conditions, which are associated with the existence of the so-called phantom fields, seem to have been violated only recently ($z\lesssim 0.2$), whereas the condition for attractive gravity, i.e., the strong energy condition (SEC) was first violated billions of years ago, at $z\gtrsim 1$.

Figure 1

Model-independent bounds on the distance modulus $\mu (z)$ as a function of the redshift for different signs of the curvature parameter ${\Omega }_k$. Panel (a): Bounds from the NEC/WEC are shown in the top set of curves, while the upper and lower bounds from the DEC correspond, respectively, to the top and bottom sets of curves. Panel (b): Upper bounds from the SEC for all signs of the spatial curvature.

Figure 2

NEC/WEC and DEC predictions for the distance modulus $\mu (z)$. The data points in the panels correspond to the new gold sample of 182 SNe Ia. Panel (a) shows the NEC/WEC and DEC bounds and the data points in the entire redshift interval $0.01\lesssim z\lesssim 1.755$ while panels (b) and (c) show the curves and data for a smaller range of the redshift ($0.01\lesssim z\lesssim 0.2$ and $0.2\lesssim z\lesssim 1.755$, respectively). As discussed in the text, these panels indicate that these energy conditions seem to have been violated by a considerable number of nearby ($z\lesssim 0.2$) SNe Ia. For the sake of comparison, the best-fit $\Lambda \mathrm{CDM}$ model for the new gold sample of 182 SNe Ia is also shown.

Figure 3

The SEC upper-bounds predictions for the distance modulus $\mu (z)$ are shown in the panels (a) to (c) for three different redshift subintervals of $0.01\lesssim z\lesssim 1.8$. As in the previous panels, the data points are from the new gold sample of 182 SNe Ia. This figure shows that apart from a few SNe events the SEC seems to have been violated in the whole redshift range. As discussed in the text, the panel (c) shows that even at high redshifts ($z\gtrsim 1$) a considerable number of SNe Ia points lie above the SEC-fulfillment curves. In all panels the best-fit $\Lambda \mathrm{CDM}$ model for the new gold sample of 182 SNe Ia is also shown.