Quintessence Potential Research Articles

Constraining the quintessence equation of state with SnIa data and CMB peaks

Quintessence has been introduced as an alternative to the cosmological constant scenario to account for the current acceleration of the universe. This new dark energy component allows values of the equation of state parameter ${w}_{Q}^{0}>~\ensuremath{-}1$ and in principle measurements of cosmological distances to type Ia supernovae can be used to distinguish between these two types of models. Assuming a flat universe, we use the supernovae data and measurements of the position of the acoustic peaks in the cosmic microwave background spectra to constrain a rather general class of quintessence potentials, including inverse power law models and recently proposed supergravity inspired potentials. In particular we use a likelihood analysis, marginalizing over the dark energy density ${\ensuremath{\Omega}}_{Q},$ the physical baryon density ${\ensuremath{\Omega}}_{b}{h}^{2}$ and the scalar spectral index n, to constrain the slopes of our quintessence potential. Considering only the first Doppler peak the best fit in our range of models gives ${w}_{Q}^{0}\ensuremath{\sim}\ensuremath{-}0.8.$ However, including the SnIa data and the three peaks, we find an upper limit on the present value of the equation of state parameter, $\ensuremath{-}1<~{w}_{Q}^{0}<~\ensuremath{-}0.93$ at $2\ensuremath{\sigma},$ a result that appears to rule out a class of recently proposed potentials.

Quintessence cosmology and the cosmic coincidence

Within present constraints on the observed smooth energy and its equation of state parameter ${w}_{Q}=P/{\ensuremath{\rho}}_{Q},$ it is important to find out whether the smooth energy is static (cosmological constant) or dynamic (quintessence). The most dynamical quintessence fields observationally allowed are now still fast rolling and no longer satisfy the tracker approximation if the equation of state parameter varies moderately with cosmic scale $a=1/1+z.$ We are optimistic about distinguishing between a cosmological constant and appreciably dynamic quintessence by measuring average values for the effective equation of state parameter ${w}_{Q}(a).$ However, reconstructing the quintessence potential from observations of any scale dependence ${w}_{Q}(a)$ appears problematic in the near future. For our flat universe, at present dominated by smooth energy in the form of either a cosmological constant (LCDM) or quintessence (QCDM), we calculate the asymptotic collapsed mass fraction to be maximal at the observed smooth energy-matter ratio ${\mathcal{R}}_{0}\ensuremath{\sim}2.$ Identifying this collapsed fraction as a conditional probability for habitable galaxies, we infer that the prior distribution is flat in ${\mathcal{R}}_{0}$ or ${\ensuremath{\Omega}}_{m0}.$ Interpreting this prior as a distribution over theories, rather than as a distribution over unobservable subuniverses, leads us to heuristic predictions about the class of future quasistatic quintessence potentials.

Hybrid quintessence with an end or quintessence from branes and large dimensions

We describe a model of hybrid quintessence in which in addition to the tracker field there is a trigger field which is responsible for ending quintessence. As a result, hybrid quintessence does not suffer from the problems associated with the eternal acceleration of the universe. We derive the hybrid quintessence potential on branes from the interbrane interaction in string theory and show that it requires TeV scale strings and two millimeter size dimensions. This scenario predicts a dark energy density of $O(mm^{-4})$ and relates the smallness of this energy to the large size of the extra dimensions.

Feasibility of reconstructing the quintessential potential using type Ia supernova data

We investigate the feasibility of the method for reconstructing the equation of state and the effective potential of the quintessence field from type Ia supernova (SNIa) data. We introduce a useful functional form to fit the luminosity distance with good accuracy (the relative error is less than 0.1%). We assess the ambiguity in reconstructing the equation of state and the effective potential, which originates from the uncertainty in ${\ensuremath{\Omega}}_{M}.$ We find that the equation of state is sensitive to the assumed ${\ensuremath{\Omega}}_{M},$ while the shape of the effective potential is not. We also demonstrate the actual reconstruction procedure using the data created by Monte Carlo simulations. Future high precision measurements of distances to thousands of SNIa could reveal the shape of the quintessential potential.

String or M theory axion as a quintessence

A slow-rolling scalar field (Q\ensuremath{\equiv}quintessence) with potential energy ${V}_{Q}\ensuremath{\sim}(3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\mathrm{eV}{)}^{4}$ has been proposed as the origin of an accelerating universe at present. We investigate the effective potential of Q in the framework of a supergravity model including the quantum corrections induced by generic (nonrenormalizable) couplings of Q to the gauge and charged matter multiplets. It is argued that the K\"ahler potential, superpotential, and gauge kinetic functions of the underlying supergravity model are required to be invariant under the variation of Q with an extremely fine accuracy in order to provide a working quintessence potential. Applying these results for string or M theory, we point out that the heterotic M theory or type-I string axion can be a plausible candidate for quintessence if (i) it does not couple to the instanton number of gauge interactions not weaker than those of the standard model and (ii) the modulus partner $\mathrm{Re}(Z)$ of the periodic quintessence axion $\mathrm{Im}(Z)\ensuremath{\equiv}\mathrm{Im}(Z)+1$ has a large vacuum expectation value: $\mathrm{Re}(Z)\ensuremath{\sim}(1/2\ensuremath{\pi})\mathrm{ln}{(m}_{3/2}^{2}{M}_{\mathrm{Planck}}^{2}{/V}_{Q}).$ It is stressed that such a large $\mathrm{Re}(Z)$ gives the gauge unification scale at around the phenomenologically favored value $3\ifmmode\times\else\texttimes\fi{}{10}^{16}$ GeV. To provide an accelerating universe, the quintessence axion should be near the top of its effective potential at present, which requires severe fine tuning of the initial condition of Q and $\mathrm{Q\ifmmode \dot{}\else \.{}\fi{}}$ in the early universe. We discuss a late time inflation scenario based on the modular and $\mathrm{CP}$ invariance of the moduli effective potential, yielding the required initial condition in a natural manner if the K\"ahler metric of the quintessence axion superfield receives a sizable nonperturbative contribution.

Model-dependent axion as quintessence with almost massless hidden sector quarks

A pseudo-Goldstone boson for {\it quintessence} is known to require the decay constant $F_q\sim M_P$ and the height of the potential $(0.003 {\rm eV})^4$, and hence the pseudo-Goldstone boson mass of order $10^{-33}$ eV. The model-dependent axion in some superstring models is suggested as a good candidate for the quintessence. We realize this idea with a hidden-sector gauge group $SU(3)_H\times U(1)_H$. The hidden-sector instanton contribution to the quintessence potential is suppressed by the almost massless hidden-sector quarks. The model-independent axion is the QCD axion required for the strong CP solution.

Quintessence without the fine tuning problem of the potential

An imitation of the present cosmological constant by the slowly-rolling scalar field f (quintessence) requires an extreme fine tuning of the potential U( f), that is the problems appear related to the cosmological constant problem and flatness conditions. The field theory is presented which gives rise to the quintessence potential without any fine tuning in the very wide class of models. At the same time the models reproduce equations of Einstein's GR and allow for possibility of inflation in the very early universe.

Robustness of quintessence

Recent observations seem to suggest that our Universe is accelerating, implying that it is dominated by a fluid whose equation of state is negative. Quintessence is a possible explanation. In particular, the concept of tracking solutions permits us to address the fine-tuning and coincidence problems. We study this proposal in the simplest case of an inverse power potential and investigate its robustness to corrections. We show that quintessence is not affected by the one-loop quantum corrections. In the supersymmetric case where the quintessential potential is motivated by nonperturbative effects in gauge theories, we consider the curvature effects and the K\ahler corrections. We find that the curvature effects are negligible while the K\ahler corrections modify the early evolution of the quintessence field. Finally we study the supergravity corrections and show that they must be taken into account as $Q\ensuremath{\approx}{m}_{\mathrm{Pl}}$ at small redshifts. We discuss simple supergravity models exhibiting the quintessential behavior. In particular, we propose a model where the scalar potential is given by $V(Q)=({\ensuremath{\Lambda}}^{4+\ensuremath{\alpha}}{/Q}^{\ensuremath{\alpha}}{)e}^{(\ensuremath{\kappa}{/2)Q}^{2}}.$ We argue that the fine-tuning problem can be overcome if $\ensuremath{\alpha}g~11.$ This model leads to ${\ensuremath{\omega}}_{Q}\ensuremath{\approx}\ensuremath{-}0.82$ for ${\ensuremath{\Omega}}_{\mathrm{m}}\ensuremath{\approx}0.3$ which is in good agreement with the presently available data.