# quintessence – phenomenology

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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,…. - PowerPoint PPT PresentationTRANSCRIPT

Quintessence Phenomenology

How can quintessence be distinguished from a cosmological constant ?

Early dark energy

predicted in models wheredark energy is naturally of the same order as matter

Time dependence of dark energycosmological constant : h ~ t ~ (1+z)-3M.Doran,

Early dark energyA few percent in the early Universe

Not possible for a cosmological constant

Structure formation Structures in the Universe grow from tiny fluctuations in density distribution

stars , galaxies, clusters

One primordial fluctuation spectrum describes all correlation functions !

Early quintessence slows down the growth of structure

Growth of density fluctuationsMatter dominated universe with constant h :

Dark energy slows down structure formation h < 10% during structure formationSubstantial increase of h(t) since structure has formed! negative wh

Question why now is back ( in mild form )P.Ferreira,M.Joyce

Fluctuation spectrumCaldwell,Doran,Mller,Schfer,

normalization of matter fluctuationsrms density fluctuation averaged over 8h-1 Mpc spherescompare quintessence with cosmological constantDoran, Schwindt,

Early quintessence and growth of matter fluctuationsearly quintessencefor small h :/2 = 3/5

for varying early dark energy :weighted average of influence of late evolution ofquintessence throughconformal time 0 andaveraged equation of stateatr : transition from slow early evolution of h to more rapid late evolution

at most a few percent dark energyin the early universe !

effect of early quintessencepresence of early dark energy decreases for given tslower growth of perturbation

Equation of state p=T-V pressure kinetic energy =T+V energy density

Equation of state

Depends on specific evolution of the scalar field

Negative pressurew < 0 h increases (with decreasing z )

w < -1/3 expansion of the Universe is accelerating

w = -1 cosmological constant

late universe withsmall radiation component :

small early and large presentdark energyfraction in dark energy has substantially increased since end of structure formationexpansion of universe accelerates in present epoch

exact relation between whand change in heqeq

+ (

Time dependence of dark energycosmological constant : h ~ t ~ (1+z)-3M.Doran,

Quintessence becomes important today

wh close to -1

inferred from supernovae and WMAP

Supernova cosmologyRiess et al. 2004

Dark energy and SN

M = 0.29 +0.05-0.03

(SN alone, for tot=1)

SN and equation of stateRiess et al. 2004

Supernova cosmologyRiess et al. 2004

supernovae :negative equation of state andrecent increase in fraction of dark energyare consistent !

quintessence and CMB anisotropies influence byearly dark energypresent equation of state

Anisotropy of cosmic background radiationCaldwell,Doran,Mller,Schfer,

separation of peaks depends on dark energy at last scatteringand on conformal timeinvolves the integral( with weighted w )

Peak location in quintessence models for fixed cosmological parameters

phenomenological parameterization of quintessence

based on parameterization of natural time variableuse relation( matter domination )define

three parameter family of modelsfraction in matter M present equation of state w0bending parameter b

relation of b to early dark energyTaylor expansiondoes nor make much sense for large z

average equation of stateyields simple formula for Hsimple relation with b

equation of state changes between w0 and 0

reconstruction of cosmon potential or kinetial

Dynamics of quintessenceCosmon j : scalar singlet fieldLagrange density L = V + k() j j (units: reduced Planck mass M=1)

Potential : V=exp[-j]

Natural initial value in Planck era j=0

today: j=276

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

How to distinguish Q from ?A) Measurement h(z) H(z)

i) h(z) at the time of structure formation , CMB - emission or nucleosynthesis ii) equation of state wh(today) > -1

B) Time variation of fundamental constants

end

cosmological equations