Early dark energy constraints on growing neutrino quintessence cosmologies

We investigate cosmological models in which dynamical dark energy consists of a scalar field whose present-day value is controlled by a coupling to the neutrino sector. The behavior of the scalar field depends on three functions: a kinetic function, the scalar field potential, and the scalar field-neutrino coupling function. We present an analytic treatment of the background evolution during radiation and matter domination for exponential and inverse power law potentials, and find a relaxation of constraints compared to previous work on the amount of early dark energy in the exponential case. We then carry out a numerical analysis of the background cosmology for both types of potential and various illustrative choices of the kinetic and coupling functions. By applying bounds from Planck on the amount of early dark energy, we are able to constrain the magnitude of the kinetic function at early times.

Figure 1

The late-time evolution of the scalar field for an exponential potential $V_{\exp }(\phi )=M_{\mathrm{P}}^4\exp (-\alpha \phi /M_{\mathrm{P}})$, kinetic function $k_1^2(\phi )=M_{\mathrm{P}}\alpha /(2\kappa (\phi -\overline{\phi }))$, and coupling function ${\beta }_1(\phi )=-M_{\mathrm{P}}/({\phi }_{\mathrm{c}}-\phi )$ with $\alpha =300$, $\kappa =1.8$ $\overline{\phi }=0.0933$, and ${\phi }_{\mathrm{c}}=0.933$.

Figure 2

The evolution of the equation of state of the scalar field, $w_{\phi }$, for the same functions and parameters as in Fig. 1. The dashed and dotted lines show the equation of state during radiation and matter domination respectively.

Figure 3

The evolution of the energy density fraction of the scalar field, ${\mathrm{\Omega }}_{\phi }$ during radiation and matter domination (solid line) for the same functions and parameters as in Fig. 1. The dashed and dotted lines respectively show the predicted evolution of ${\mathrm{\Omega }}_{\phi }$ under the assumption of a radiation-dominated and matter-dominated universe where the scalar field obeys the scaling solution discussed in Sec. 3.

Figure 4

The evolution of the energy density fraction of the scalar field for a range of values of $\kappa$ and otherwise the same functions and parameters as in Fig. 1. Also shown is the Planck upper bound on ${\mathrm{\Omega }}_{\mathrm{e}}<0.0036$.

Figure 5

The evolution of the logarithm of the scalar field for inverse power law potentials of the form $V_{\mathrm{IPL}}(\phi )=\tilde{V}{M}_{\mathrm{P}}^4(M_{\mathrm{P}}/\phi {)}^{\lambda }$ with kinetic function $k_1^2(\phi )=M_{\mathrm{P}}/(2\kappa \phi )$ and coupling function ${\beta }_1(\phi )=-M_{\mathrm{P}}/({\phi }_{\mathrm{c}}-\phi )$. We fix $\kappa =1.8$ and the parameters $\tilde{V}$ and ${\phi }_{\mathrm{c}}$ take different values for different values of $\lambda$ (see text for details).

Figure 6

The evolution of the logarithm of the energy fraction of the scalar field for the same functions and parameters as in Fig. 5.