Dark Energy: the Cosmological Challenge of the Millennium

TL;DR

The work surveys the dark energy problem within modern cosmology, contrasting the cosmological constant with scalar-field alternatives. It shows that although quintessence and tachyon models can mimic a time‑varying equation of state, they introduce degeneracies and fine‑tuning, and current data favor $w\approx -1$, reinforcing the cosmological constant as the baseline. It then presents three non‑standard avenues—nonlinear averaging corrections, unimodular gravity, and scale‑dependent vacuum energy fluctuations—as potential resolutions that connect horizon-scale physics to Planck-scale quantum fluctuations. A central idea is that the observed dark-energy density may arise from vacuum fluctuations constrained by the cosmic horizon, giving $\rho_{DE} \sim \sqrt{\rho_P \rho_\Lambda}$ and linking quantum gravity with cosmology. Overall, the paper frames dark energy as a probe of spacetime structure and quantum fluctuations, beyond a single scalar field interpretation.

Abstract

Recent cosmological observations suggest that nearly seventy per cent of the energy density in the universe is unclustered and has negative pressure. Several conceptual issues related to the modeling of this component (`dark energy'), which is driving an accelerated expansion of the universe, are discussed with special emphasis on the cosmological constant as the possible choice for the dark energy. Some curious geometrical features of a universe with a cosmological constant are described and a few attempts to understand the nature of the cosmological constant are reviewed.

Figures (3)

• Figure 1: The "velocity" $\dot a$ of the universe is plotted against the "position" $a$ in the form of a phase portrait. The different curves are for models parameterized by the value of $\Omega_{DM}(=\Omega_m)$ keeping $\Omega_{tot}=1$. The top-most curve has $\Omega_m=1$ with no dark energy and the universe is decelerating at all epochs. The bottom-most curve has $\Omega_m=0$ and $\Omega_{DE}=1$ and the universe is accelerating at all epochs. The in-between curves show universes which were decelerating in the past and began to accelerate when the dark energy started dominating. The supernova data clearly favours such a model. (For a more detailed discussion of the figure, see tptirthsn1tptirthsn2.)
• Figure 2: Constraints on the possible variation of the dark energy density with redshift. The darker shaded region (magenta) is excluded by SN observations while the lighter shaded region (green) is excluded by WMAP observations. It is obvious that WMAP puts stronger constraints on the possible variations of dark energy density. The cosmological constant corresponds to the horizontal line at unity. The region between the dotted lines has $w>-1$ at all epochs. (For more details, see jbp.)
• Figure 3: The geometrical structure of a universe with two length scales $L_P$ and $L_\Lambda$ corresponding to the Planck length and the cosmological constant plumianbjorken. Such a universe spends most of its time in two De Sitter phases which are (approximately) time translation invariant. The first De Sitter phase corresponds to the inflation and the second corresponds to the accelerated expansion arising from the cosmological constant. Most of the perturbations generated during the inflation will leave the Hubble radius (at some A, say) and re-enter (at B). However, perturbations which exit the Hubble radius earlier than C will never re-enter the Hubble radius, thereby introducing a specific dynamic range CE during the inflationary phase. The epoch F is characterized by the redshifted CMB temperature becoming equal to the De Sitter temperature $(H_\Lambda / 2\pi)$ which introduces another dynamic range DF in the accelerated expansion after which the universe is dominated by vacuum noise of the De Sitter spacetime.