The Cosmological Constant Problem and Quintessence

TL;DR

This article surveys the cosmological constant problem and the nature of dark energy, contrasting a theoretically large vacuum energy with the observed small value of $ ho_ ext{Λ}$. It surveys dynamical approaches, notably scalar-field quintessence with tracker potentials and braneworld quintessence that can connect inflation to late-time acceleration, and discusses model-independent reconstruction of $w(z)$ alongside the Statefinder diagnostic for model discrimination. It emphasizes how horizon physics in a $ ext{Λ}$-dominated universe and observational data (e.g., SN Ia, CMB, galaxy surveys) inform the viability of dynamical dark energy versus a true cosmological constant. The work highlights theoretical and observational pathways to distinguish between Λ and evolving dark energy and to understand the late-time acceleration of the universe.

Abstract

I briefly review the cosmological constant problem and the issue of dark energy (or quintessence). Within the framework of quantum field theory, the vacuum expectation value of the energy momentum tensor formally diverges as $k^4$. A cutoff at the Planck or electroweak scale leads to a cosmological constant which is, respectively, $10^{123}$ or $10^{55}$ times larger than the observed value, $ł/8πG \simeq 10^{-47}$ GeV$^4$. The absence of a fundamental symmetry which could set the value of $ł$ to either zero or a very small value leads to {\em the cosmological constant problem}. Most cosmological scenario's favour a large time-dependent $ł$-term in the past (in order to generate inflation at $z \gg 10^{10}$), and a small $ł$-term today, to account for the current acceleration of the universe at $z \lleq 1$. Constraints arising from cosmological nucleosynthesis, CMB and structure formation constrain $ł$ to be sub-dominant during most of the intermediate epoch $10^{10} < z < 1$. This leads to the {\em cosmic coincidence} conundrum which suggests that the acceleration of the universe is a recent phenomenon and that we live during a special epoch when the density in $ł$ and in matter are almost equal. Time varying models of dark energy can, to a certain extent, ameliorate the fine tuning problem (faced by $ł$), but do not resolve the puzzle of cosmic coincidence. I briefly review tracker models of dark energy, as well as more recent brane inspired ideas and the issue of horizons in an accelerating universe. Model independent methods which reconstruct the cosmic equation of state from supernova observations are also assessed. Finally, a new diagnostic of dark energy -- `Statefinder', is discussed.

Figures (5)

• Figure 1: The potential describing spontaneous symmetry breaking has the form of a Mexican top hat. The dashed line shows the potential before the cosmological constant has been 'renormalized' and the solid line after.
• Figure 2: The post-inflationary density parameter $\Omega$ is plotted for the scalar field (solid line) radiation (dashed line) and cold dark matter (dotted line) in the quintessential-inflationary model decribed by (\ref{['eq:cosh']}) with $p = 0.2$. Late time oscillations of the scalar field ensure that the mean equation of state turns negative $\langle w_\phi\rangle \simeq -2/3$, giving rise to the current epoch of cosmic acceleration with $a(t) \propto t^2$ and present day values $\Omega_{0\phi} \simeq 0.7, \Omega_{0m} \simeq 0.3$. From Sahni, Sami and Souradeep sami.
• Figure 3: The equation of state of dark energy/quintessence is reconstructed from observations of Type Ia high redshift supernovae in a model independent manner. The equation of state satisfies $-1 \leq w_\phi \leq -0.8$ at $z = 0$; and $-1 \leq w_\phi \leq -0.46$ at $z = 0.83$ ($90\%$ CL), $\Omega_m = 0.3$ is assumed. From Saini, Raychaudhury, Sahni and Starobinsky saini.
• Figure 4: The near degeneracy in the luminosity distance is shown for the pair of cosmological models with $\lbrace \Omega_m = 0.3, w_X = -1.0\rbrace$ and $\lbrace \Omega_m = 0.25, w_X = -0.8\rbrace$.
• Figure 5: The Statefinder pair $\lbrace r,s\rbrace$ is shown for dark energy consisting of a cosmological constant $\Lambda$, Quiessence 'Q' with an unevolving equation of state $w = -0.8$ and the inverse power law tracker model $V= V_0/\phi^2$, referred to as Kinessence 'K'. The lower left panel shows $r(z)$ while the lower right panel shows $s(z)$. Kinessence has a time-dependent equation of state which is shown in the top right panel. The fractional density in matter and Kinessence is shown in the top left panel. The ability of the Statefinder pair $\lbrace r,s\rbrace$ to differentiate between the different forms of dark energy is amply demonstrated by this figure which is reproduced from Sahni, Saini, Starobinsky and Alam sss01.