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We present an Effective Field Theory based reconstruction of quintessence models of dark energy directly from cosmological data. We show that current cosmological data possess enough constraining power to test several quintessence model properties for redshifts $zin [0,1.5]$ with no assumptions about the behavior of the scalar field potential. We use measurements of the cosmic microwave background, supernovae distances, and the clustering and lensing of galaxies to constrain the evolution of the dark energy equation of state, Swampland Conjectures, the shape of the scalar field reconstructed potential, and the structure of its phase space. The standard cosmological model still remains favored by data and, within quintessence models, deviations from its expansion history are bounded to be below the 10% level at 95% confidence at any redshift below $z=1.5$.
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We derive the slow-roll conditions for a non-minimally coupled scalar field (extended quintessence) during the radiation/matter dominated era extending our previous results for thawing quintessence. We find that the ratio $ddotphi/3Hdotphi$ becomes constant but negative, in sharp contrast to the ratio for the minimally coupled scalar field. We also find that the functional form of the equation of state of the scalar field asymptotically approaches that of the minimally coupled thawing quintessence.
The dynamical properties of a model of dark energy in which two scalar fields are coupled by a non-canonical kinetic term are studied. We show that overall the addition of the coupling has only minor effects on the dynamics of the two-field system for both potentials studied, even preserving many of the features of the assisted quintessence scenario. The coupling of the kinetic terms enlarges the regions of stability of the critical points. When the potential is of an additive form, we find the kinetic coupling has an interesting effect on the dynamics of the fields as they approach the inflationary attractor, with the result that the combined equation of state of the scalar fields can approach -1 during the transition from a matter dominated universe to the recent period of acceleration.
We examine the plausibility of crossing the cosmological constant ($L$) barrier in a two-field quintessence model of dark energy, involving a kinetic interaction between the individual fields. Such a kinetic interaction may have its origin in the four dimensional effective two-field version of the Dirac-Born-Infeld action, that describes the motion of a D3-brane in a higher dimensional space-time. We show that this interaction term could indeed enable the dark energy equation of state parameter $wx$ to cross the $L$-barrier (i.e., $wx = -1$), keeping the Hamiltonian well behaved (bounded from below), as well as satisfying the condition of stability of cosmological density perturbations, i.e., the positivity of the squares of the sound speeds corresponding to the adiabatic and entropy modes. The model is found to fit well with the latest Supernova Union data and the WMAP results. The best fit curve for $wx$ crosses -1 at red-shift $z$ in the range $sim 0.215 - 0.245$, whereas the transition from deceleration to acceleration takes place in the range of $z sim 0.56 - 0.6$. The scalar potential reconstructed using the best fit model parameters is found to vary smoothly with time, while the dark energy density nearly follows the matter density at early epochs, becomes dominant in recent past, and slowly increases thereafter without giving rise to singularities in finite future.
We examine hilltop quintessence models, in which the scalar field is rolling near a local maximum in the potential, and w is close to -1. We first derive a general equation for the evolution of the scalar field in the limit where w is close to -1. We solve this equation for the case of hilltop quintessence to derive w as a function of the scale factor; these solutions depend on the curvature of the potential near its maximum. Our general result is in excellent agreement (delta w < 0.5%) with all of the particular cases examined. It works particularly well (delta w < 0.1%) for the pseudo-Nambu-Goldstone Boson potential. Our expression for w(a) reduces to the previously-derived slow-roll result of Sen and Scherrer in the limit where the curvature goes to zero. Except for this limiting case, w(a) is poorly fit by linear evolution in a.
We investigate the cosmological observational test of the extended quintessence model, i.e. a scalar-tensor gravity model with a scalar field potential serving as dark energy, by using the Planck 2018 cosmic microwave background (CMB) data, together with the baryon acoustic oscillations (BAO) and redshift-space distortion (RSD) data. As an example, we consider the model with a Brans-Dicke kinetic term $frac{omega(phi)}{phi} phi_{;mu} phi^{;mu} $ and a quadratic scalar potential $V (phi) = A + B (phi - phi_0) + frac{C}{2} (phi - phi_0)^2$, which reduces to general relativity (GR) in the limit $omega(phi) to infty$, and the cosmological constant in the limit $B=C=0$. In such a model the scalar field typically rolls down the potential and oscillates around the minimum of $V (phi)$. We find that the model parameter estimate for the CMB+BAO+RSD data set is given by $lg alpha = -3.6 _{-0.54}^{+0.66}~ (68%)$, corresponding to $ 3.8 times 10^5 < omega_0 < 9.5 times 10^7~ (68%)$, and $lg C = 4.9 pm 1.4~ (68%) $. However, the GR $Lambda$CDM model can fit the data almost as good as this extended quintessence model, and is favored by the Akaike information criterion (AIC). The variation of the gravitational constant since the epoch of Recombination is constrained to be $0.97 < G_{rm rec}/G_0 < 1.03~ (1 sigma)$. In light of recent report that the CMB data favors a closed universe, we consider the case with non-flat geometry in our fit, and find that the mean value of $Omega_k$ shifts a little bit from $-0.049$ to $-0.036$, and the parameters in our model are not degenerate with $Omega_k$.
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