Early Dark Energy Cosmologies

TL;DR

The paper introduces a three-parameter Omega_d(a) parameterization to describe dark energy that remains non-negligible at early times, enabling analytic expressions for key cosmological quantities and facilitating direct constraints on early dark energy from CMB, LSS, and SNe data. The approach yields tight bounds on the early dark-energy fraction, notably $\Omega_{early}^< 0.04$ when Boomerang data are included, and reveals a mild preference for $w_0< -1$ with some SN data while remaining consistent with LCDM. The authors demonstrate the framework’s compatibility with scalar-field models, its connection to existing $w(a)$ parameterizations, and its robustness under an extended gamma-parameter generalization. Overall, this work provides a tractable, physically transparent method to test early dark energy scenarios and quantify their observational signatures across horizons, distances, and the acoustic scale, with implications for future cosmological surveys.

Abstract

We propose a novel parameterization of the dark energy density. It is particularly well suited to describe a non-negligible contribution of dark energy at early times and contains only three parameters, which are all physically meaningful: the fractional dark energy density today, the equation of state today and the fractional dark energy density at early times. As we parameterize Omega_d(a) directly instead of the equation of state, we can give analytic expressions for the Hubble parameter, the conformal horizon today and at last scattering, the sound horizon at last scattering, the acoustic scale as well as the luminosity distance. For an equation of state today w_0 < -1, our model crosses the cosmological constant boundary. We perform numerical studies to constrain the parameters of our model by using Cosmic Microwave Background, Large Scale Structure and Supernovae Ia data. At 95% confidence, we find that the fractional dark energy density at early times Omega_early < 0.06. This bound tightens considerably to Omega_early < 0.04 when the latest Boomerang data is included. We find that both the gold sample of Riess et. al. and the SNLS data by Astier et. al. when combined with CMB and LSS data mildly prefer w_0 < -1, but are well compatible with a cosmological constant.

Figures (4)

• Figure 1: Evolution of the fractional dark energy density $\Omega_{\rm d}(z)$ and the equation of state $w(z)$ as a function of redshift. The solid (black) curve depicts the behavior for a $\Lambda$CDM cosmological constant model, in which $w_0 =-1$ by definition and the amount of dark energy at early times tends to zero. In contrast, the dashed (blue) and dotted (red) curves are early dark energy models described by our parameterization \ref{['eqn::param']}. For the models depicted, we chose $w_0=-1$ and $\Omega_{\rm d}^e= 0.01$ (blue, dashed), $\Omega_{\rm d}^e=0.07$ (red, dotted) respectively. In addition, we plot the equation of state $w$ for $\Omega_{\rm d}^e=0.01$ (blue, dashed-dotted) and $\Omega_{\rm d}^e=0.07$ (red, dashed-double-dotted)
• Figure 2: Constraints on the parameters $w_0$ and $\Omega_{\rm d}^e$ for different combinations of data sets. The blue region corresponds to the SNe Ia compilation of Riess et. al., the green region to WMAP + VSA + CBI + SDSS. The constraints obtained when combining all of these sets are shown in yellow. The result of adding the Boomerang data to this combined set is depicted in red. Black (white) lines enclose 95% (68%) confidence regions.
• Figure 3: The logarithm of the potential, $\ln(V)$ as a function of $\varphi$ in units of $M_{\rm P}$ (solid line). The exponential potentials during radiation and matter domination are indicated by the dashed (blue) and dotted (red) line. The exponent in these cases is given by Equation \ref{['eqn::expo']}. For this plot, we used $\Omega_{\rm d}^e = 0.03$ and matter-radiation equality is at $\varphi_{equ.} = -2.66$. In the recent universe, the potential flattens, leading to $w \to -0.99$ which we picked for this plot.
• Figure 4: Upper left panel: Likelihood distribution for the equation of state $w_0$ today for a phantom model with $c_{s}^2 = 1$. The solid line is for WMAP + VSA + CBI + BOOMERANG + SDSS + SNe Ia, the dashed (blue) line is without Sne Ia data. At $1\sigma$ confidence, the full data gives $w_0 = -1.08 + 0.14 - 0.17$. Upper right panel: Likelihood distribution for the scalar spectral index $n_s$ for a scalar field model. The solid line is for WMAP + VSA + CBI + BOOMERANG + SDSS + SNe Ia, the dotted (red) line is without Boomerang. At $1\sigma$ confidence, $n_s = 0.98 + 0.04 - 0.03$. Lower left panel: Likelihood distribution for $\Omega_{\rm d}^e$ for a scalar field model. The solid line is for WMAP + VSA + CBI + BOOMERANG + SDSS+SNe Ia, the dotted (red) line is without Boomerang. At $2\sigma$ confidence, $\Omega_{\rm d}^e < 0.04$ and $\Omega_{\rm d}^e < 0.06$ respectively.  Lower right panel: Comparison of the likelihood distribution for the equation of state $w_0$ today for the gold set from Riess et. al. only (green, dot-dashed line) and the SNLS data only (blue, dotted line), and their combination with the CMB+LSS data: the dashed line (red) corresponds to CMB+LSS+Riess et. al., the solid (black) line to CMB+LSS+SNLS.