An updated dark energy view of inflation.

The present epoch of accelerated cosmic expansion is supposed to be driven by an unknown constituent called dark energy, which in the standard model takes the form of a cosmological constant, characterized by a constant equation of state with $w=-1$. An interesting perspective over the role and nature of dark energy can be achieved by drawing a parallel with a previous epoch of accelerated expansion, inflation, which we assume to be driven by a single scalar field, the inflaton. Since the Planck satellite has constrained the value of the scalar spectral index $n_s$ away from 1, the inflaton cannot be identified with a pure cosmological constant, as is also suggested by the fact that inflation ended. Thus, it is interesting to verify whether a hypothetical observer would have been able to measure the deviation of the equation of state parameter of the inflaton from $-1$. In this study, we analyze this question by considering three single-field slow-roll inflationary models that we call HSR$\{2\}$, HSR$\{3\}$ and HSR$\{4\}$, where the hierarchy of Hubble slow-roll parameters is truncated to second, third and fourth order respectively. The models are tested through a Markov Chain Monte Carlo analysis based on combinations of the latest Planck and BICEP2/Keck data sets, and the resulting chains are converted into sets of allowed evolution histories of $w$. This analysis yields a 68$\%$ upper bound of $1+w < 0.0014$ for HSR$\{3\}$, which provides the overall best description for the data. Therefore, if the current era of accelerated expansion happens to have the same equation of state as inflation during the observable epoch, then current and upcoming cosmological observations will not be able to detect that $w \neq -1$. This provides a cautionary tale for drawing conclusions about the nature of dark energy on the basis of the non-observation of a deviation from $w=-1$.