Undulant Universe: Expansion with alternating eras of acceleration and deceleration

If the equation of state for “dark energy” varies periodically, the expansion of the Universe may have undergone alternating eras of acceleration and deceleration. We examine a specific form that survives existing observational tests, does not single out the present state of the Universe as exceptional, and suggests a future much like the matter-dominated past: a smooth expansion without a final inflationary epoch.

Figure 1

Lower panel: Evolution of the matter (thin cyan), radiation (magenta, steepest line), and vacuum (thick blue) energy densities in the undulant Universe, normalized to the critical density ${\rho }_i/{\rho }_{c0}$, versus the scale factor $a(t)$. Upper panel: Equation of state, Eq. (4), of the undulant vacuum.

Figure 2

Evolution of the scale factor $a(t)$ in three cosmologies: the canonical $\Lambda \mathrm{CDM}$ model (thin black line); a critical Universe (SCDM model) with ${\Omega }_m=1$ (dashed red line); and the periodic equation of state (4) (thick blue line).

Figure 3

The deceleration parameter as defined in Eq. (3) for the undulant Universe (thick blue line), $\Lambda \mathrm{CDM}$ model (thin black line) and SCDM model (dashed red line).

Figure 4

Angular power spectrum (top panel) and $T$-$E$ cross-correlation (middle panel) versus the multipole $\ell$, and matter power spectrum versus the wave number $k$ (bottom panel), for the periodic equation of state (4) (thick blue line) and for the $\Lambda \mathrm{CDM}$ model (thin black line). The top panel shows experimental data from the WMAP experiment (red, light gray) [33] and from the combination of all CMB data (purple, dark gray) [34]. The middle panel shows WMAP data. The data in the bottom panel are from an independent analysis of the 2dF survey [35].