Quintessence – Phenomenology

How can quintessence be distinguished from a cosmological constant ?

Early dark energy

…predicted in models where dark energy is naturally of the same order as matter

Time dependence of dark energy cosmological constant : Ω h ~ t² ~ (1+z) -3 M.Doran,…

Early dark energy A few percent in the early Universe Not possible for a cosmological constant

Structure formation Structures in the Universe grow from tiny Structures in the Universe grow from tiny fluctuations in density distribution fluctuations in density distribution stars, galaxies, clusters stars, galaxies, clusters One primordial fluctuation spectrum describes all correlation functions ! all correlation functions !

Early quintessence slows down the growth of structure

Growth of density fluctuations Matter dominated universe with constant Ω h : Matter dominated universe with constant Ω h : Dark energy slows down structure formation Dark energy slows down structure formation Ω h < 10% during structure formation Ω h < 10% during structure formation Substantial increase of Ω h (t) since structure has formed! Substantial increase of Ω h (t) since structure has formed! negative w h negative w h Question “why now” is back ( in mild form ) Question “why now” is back ( in mild form ) P.Ferreira,M.Joyce

Fluctuation spectrum Caldwell,Doran,Müller,Schäfer,…

normalization of matter fluctuations rms density fluctuation averaged over 8h -1 Mpc spheres compare quintessence with cosmological constant Doran, Schwindt,…

Early quintessence and growth of matter fluctuations early quintessence for small Ω h : ε/2 = 3/5

for varying early dark energy : weighted average of Ω influence of late evolution of quintessence through conformal time τ 0 and averaged equation of state a tr : transition from slow early evolution of Ω h to more rapid late evolution

at most a few percent dark energy in the early universe !

effect of early quintessence presence of early dark energy decreases ρ for given t slower growth of perturbation

Equation of state p=T-V pressure kinetic energy p=T-V pressure kinetic energy ρ=T+V energy density ρ=T+V energy density Equation of state Equation of state Depends on specific evolution of the scalar field

Negative pressure w < 0 Ω h increases (with decreasing z ) w < 0 Ω h increases (with decreasing z ) w < -1/3 expansion of the Universe is w < -1/3 expansion of the Universe is accelerating accelerating w = -1 cosmological constant w = -1 cosmological constant late universe with small radiation component :

small early and large present dark energy fraction in dark energy has substantially increased since end of structure formation fraction in dark energy has substantially increased since end of structure formation expansion of universe accelerates in present epoch expansion of universe accelerates in present epoch

exact relation between w h and change in Ω h eq

+ (

Time dependence of dark energy cosmological constant : Ω h ~ t² ~ (1+z) -3 M.Doran,…

Quintessence becomes important “today”

w h close to -1 inferred from supernovae and WMAP

Supernova cosmology Riess et al. 2004

Dark energy and SN Ω M = 0.29 Ω M = (SN alone, for Ω tot =1) (SN alone, for Ω tot =1)

SN and equation of state Riess et al. 2004

Supernova cosmology Riess et al. 2004

supernovae : negative equation of state and recent increase in fraction of dark energy are consistent !

quintessence and CMB anisotropies influence by influence by early dark energy early dark energy present equation of state present equation of state

Anisotropy of cosmic background radiation Caldwell,Doran,Müller,Schäfer,…

separation of peaks depends on dark energy at last scattering and on conformal time involves the integral ( with weighted w )

Peak location in quintessence models for fixed cosmological parameters

phenomenological parameterization of quintessence

…based on parameterization of Ω natural “time” variable use relation ( matter domination ) define

three parameter family of models fraction in matter Ω M present equation of state w 0 bending parameter b

relation of b to early dark energy Taylor expansion does nor make much sense for large z

average equation of state yields simple formula for H simple relation with b

equation of state changes between w 0 and 0

reconstruction of cosmon potential or kinetial

Dynamics of quintessence Cosmon  : scalar singlet field Cosmon  : scalar singlet field Lagrange density L = V + ½ k(φ)  Lagrange density L = V + ½ k(φ)  (units: reduced Planck mass M=1) (units: reduced Planck mass M=1) Potential : V=exp[-  Potential : V=exp[-  “Natural initial value” in Planck era  “Natural initial value” in Planck era  today:  =276 today:  =276

for “ standard “ exponential potential : construction of kinetial from equation of state

How to distinguish Q from Λ ? A) Measurement Ω h (z) H(z) i) Ω h (z) at the time of i) Ω h (z) at the time of structure formation, CMB - emission structure formation, CMB - emission or nucleosynthesis or nucleosynthesis ii) equation of state w h ( today ) > -1 ii) equation of state w h ( today ) > -1 B) Time variation of fundamental “constants”

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cosmological equations