Exploring the Evolution of Dark Energy and its Equation of ...cristinae/CV/docs/tesiSlides.pdf ·...

Exploring the Evolution of Dark Energy

and its Equation of State

Cristina Espana i Bonet

Universitat de Barcelona

12th February, 2008

Advisor: Dra. Pilar Ruiz-Lapuente

Overview

1 Motivacio

2 Introduction

3 Evolving Cosmological Constant

4 Non-Parametric Reconstructions

5 Future Perspectives

6 Summary and Conclusions

L’Univers

Si l’Univers fos estatic...

Cristina Espana i Bonet Exploring the Evolution of Dark Energy and its Equation of State

L’Univers

...pero esta en expansio (model de Big Bang)


L’Univers

...i accelerada


Com ho observem?

+ Necessitem un objecte delluminositat coneguda

+ La llum que rebem ensindica la distancia

Candela estandard

Candela estandard per exel·lencia:

Supernoves del tipus Ia (SNe Ia)


Com ho observem?

Necessitem un objecte delluminositat coneguda

La llum que rebem ensindica la distancia

+ Candela estandard




Com ho observem?

Necessitem un objecte delluminositat coneguda

La llum que rebem ensindica la distancia

Candela estandard




Com ho observem?

+ Sistema binari enacrecio

+ Explosio a MCh + Mateixalluminositat

Lluminositat inferior a Ld ⇒ mes lluny ⇒ expansio mes rapida

Lluminositat superior a Ld ⇒ mes a prop ⇒ expansio mes lenta


Com ho observem?

Sistema binari enacrecio

Explosio a MCh Mateixalluminositat

Lluminositat inferior a Ld

⇒ mes lluny ⇒ expansio mes rapida

Lluminositat superior a Ld

⇒ mes a prop ⇒ expansio mes lenta


Com ho observem?



Lluminositat inferior a Ld ⇒ mes lluny

⇒ expansio mes rapida

Lluminositat superior a Ld ⇒ mes a prop

⇒ expansio mes lenta


Com ho observem?



Lluminositat inferior a Ld ⇒ mes lluny ⇒ expansio mes rapida

Lluminositat superior a Ld ⇒ mes a prop ⇒ expansio mes lenta


Que observem?

+ Supernoves llunyanes: coherent amb BB estandard

Supernoves meitat de l’edat de l’Univers: sublluminoses

Supernoves properes: canvis imperceptibles

⇓Expansio recent accelerada

⇓Per que? i Perque?


Que observem?

Supernoves llunyanes: coherent amb BB estandard

+ Supernoves meitat de l’edat de l’Univers: sublluminoses





Que observem?



+ Supernoves properes: canvis imperceptibles




Que observem?







Objectius

Estudi i caracteritzacio del component que accelera l’expansio,l’energia fosca, mitjancant:

1 Aproximacio directa:Construccio d’un model i contrast amb observacions

2 Aproximacio inversa:Reconstruccio del model subjacent a partir de lesobservacions

Eina principal:

1 Variacio de la magnitud de les SNe Ia amb la distancia


Let’s start

1 Motivacio

2 IntroductionCosmological ConstantGeneral Dark Energy SourceObtaining Information with Observations





Introduction

Why this thesis?

Clear evidence of theacceleration

Attribution to acosmological constant(CC)

I ...but other candidates

I ...possible evolution

What is the CC?


Introduction

Why this thesis?


Attribution to acosmological constant(CC): Λ ≈ 10−47 GeV 4



What is the CC?


Introduction

Why this thesis?


Attribution to acosmological constant(CC)...



What is the CC?


Cosmological constant (CC)The Einstein’s term

+ Interpretation:antigravitationalforce

Nothing forbids λ(t)

Gµν−λ(t)gµν = −8πGNTµν .

Inclusion of the CC inEinstein’s Field Equations

A. Einstein,Kosmologische betrachtungen zur allgemeinen Relativitatstheorie.S.-B. Preuss. Akad. Wiss. (1917), pp. 142-152.


Cosmological constant (CC)The Einstein’s term

Interpretation:antigravitationalforce

+ Nothing forbids λ(t)

Gµν−λ(t)gµν = −8πGNTµν .

Inclusion of the CC inEinstein’s Field Equations

A. Einstein,Kosmologische betrachtungen zur allgemeinen Relativitatstheorie.S.-B. Preuss. Akad. Wiss. (1917), pp. 142-152.


Cosmological constant (CC)Vacuum energy

+ Interpretation:vacuum energy

Inclusion of the CC as asource of Tµν :

Gµν = −8πGN(Tµν + Λgµν) .

In the vacuum: 〈Tµν〉 = Gµν〈Vφ〉

I Particles & fields 〈Vφ〉 = 0

I but Higgs 〈VH〉 ∝ m4H ≈ 108 GeV 4

=⇒ Λind ≈ 108 GeV 4


Cosmological constant (CC)Vacuum energy

Interpretation:vacuum energy

Inclusion of the CC as asource of Tµν :

Gµν = −8πGN(Tµν + Λgµν) .

In the vacuum: 〈Tµν〉 = Gµν〈Vφ〉

I Particles & fields 〈Vφ〉 = 0

I but Higgs 〈VH〉 ∝ m4H ≈ 108 GeV 4

=⇒ Λind ≈ 108 GeV 4


Cosmological constant (CC)An only source?

Observations

Λobs ≈ 10−47 GeV 4

Theory

Λind ≈ 108 GeV 4

ΛEinstein

︸︷︷︸Λobs = ΛEinstein + Λind

|ΛEinstein| − |Λind | = 10−55 GeV 4

= 0.00000000000000000000000000000000000000000000000000000001!!

Cosmological Constant Problem


Cosmological constant (CC)An only source?

Observations

Λobs ≈ 10−47 GeV 4

Theory

Λind ≈ 108 GeV 4

ΛEinstein︸︷︷︸Λobs = ΛEinstein + Λind

|ΛEinstein| − |Λind | = 10−55 GeV 4

= 0.00000000000000000000000000000000000000000000000000000001!!

Cosmological Constant Problem


A general dark energy componentThe perfect fluid approach

+ Alternative: Inclusion of a perfect fluid extra componentcharacterized by its Equation of State (EoS)

p = wρ

Interpretation of the cosmological constant as an extracomponent of Tµν

=⇒ perfect fluid with ρ = Λ and p = −Λ=⇒ w = −1

In general, ρ(t) and p(t), so w(t)

But for Λ(t) still w = −1



Alternative: Inclusion of a perfect fluid extra componentcharacterized by its Equation of State (EoS)

p = wρ

+ Interpretation of the cosmological constant as an extracomponent of Tµν







p = wρ



+ In general, ρ(t) and p(t), so w(t)





p = wρ




+ But for Λ(t) still w = −1


A general dark energy componentAlternatives

Every component is described by its equation of state:

wR = 1/3 radiationwM = 0 non-relativistic matter

wS = −1/3 cosmic stringswW = −2/3 domain wallswT = −1/3 textureswΛ = −1 (evolving) cosmological constant

wQ(t) > −1 (dwQ/dz > 0) quintessencewK (t) > −1 (dwK/dz < 0) k-essence

wPh(t) < −1 phantoms

Multitude of possibilities for dark energy...


A general dark energy componentAlternatives

EoS index:

wR = 1/3wM = 0wS = −1/3wW = −2/3wT = −1/3wΛ = −1

wQ(t) > −1 (dwQ/dz > 0) =⇒wK (t) > −1 (dwK/dz < 0)wPh(t) < −1

Quintessence EoS

Weller & Albrecht (2002)


Obtaining information with SNe IaMagnitude-redshift relation

The relation between models and observations is encoded in:

m(z, H0, Ω0M , Ω0

X ) = M + 5 log10

ˆH0 dL(z, H0, Ω

0M , Ω0

X )˜

dL(z, Ω0M , Ω0

X ) =c (1 + z)

H0

0B@Z z

0

dz ′qΩ0

M(1 + z)3 + ΩX (z)

1CAΩX (z) = Ω0

X exp

„3

Z z

0dz ′

1 + w(z ′)

1 + z ′

«

Double integral relating the observed m with w(z)I Smoothing of any possible evolutionI Increasing of degeneracy




m(z, H0, Ω0M , Ω0

X ) = M + 5 log10

ˆH0 dL(z, H0, Ω

0M , Ω0

X )˜

dL(z, Ω0M , Ω0

X ) =c (1 + z)

H0

0B@Z z

0

dz ′qΩ0

M(1 + z)3 + ΩX (z)

1CAΩX (z) = Ω0

X exp

„3

Z z

0dz ′

1 + w(z ′)

1 + z ′

«

+ Double integral relating the observed m with w(z)

+ Smoothing of any possible evolution+ Increasing of degeneracy




m(z, H0, Ω0M , Ω0

X ) = M + 5 log10

ˆH0 dL(z, H0, Ω

0M , Ω0

X )˜

dL(z, Ω0M , Ω0

X ) =c (1 + z)

H0

0B@Z z

0

dz ′qΩ0

M(1 + z)3 + ΩX (z)

1CAΩX (z) = Ω0

X exp

„3

Z z

0dz ′

1 + w(z ′)

1 + z ′

«

Double integral relating the observed m with w(z)

+ Smoothing of any possible evolution+ Increasing of degeneracy


Obtaining information with SNe Iam − z space

Well covered datarange: 0 < z < 1.5

Most models can befit to data

Small differencesamong models in therange

That’s a hard work!


Obtaining information with SNe IaData sets

Currently, 2 (+1) data sets available:

Riess et al.(2006)

182 SNe Ia

0.023 < z < 1.77

Wood-Vasey et al.(2007)

162 SNe Ia

0.015 < z < 0.96

Davis et al.(2007)

192 SNe Ia

0.015 < z < 1.77

Results do depend on the data set used. In the following,results for Riess et al. (2006) are shown.


Obtaining information with SNe IaComplementary probes and priors

+ Constraint on the curvature:

+ Flat Universe (WMAP3)

Constraint on ΩM :

I 0.27± 0.03 (clusters)

I BAO constraints



Constraint on the curvature:

+ Flat Universe (WMAP3)

Constraint on ΩM :

I 0.27± 0.03 (clusters)

I BAO constraints




I Flat Universe (WMAP3)

+ Constraint on ΩM :

+ 0.27± 0.03 (clusters)

+ BAO constraints





Constraint on ΩM :

+ 0.27± 0.03 (clusters)

I BAO constraints





Constraint on ΩM :

I 0.27± 0.03 (clusters)

+ BAO constraints


The dark energy model

1 Motivacio

2 Introduction

3 Evolving Cosmological ConstantFundamentalsCosmological ScenariosObservational Constraints




Evolving Cosmological ConstantThe theory behind... in a few words

Quantum Field Theory(semiclassical approximation: fields in a curved space-time)

Vacuum action at low energies

SHE = −Z

d4x√−g

„1

16πGvacR + Λvac

«

Ultraviolet divergencies → regularization, renormalization

Scale invariance broken




⇓Vacuum action at low energies

SHE = −Z

d4x√−g

„1

16πGvacR + Λvac

«






⇓Vacuum action at low energies

SHE = −Z

d4x√−g

„1

16πGvacR + Λvac

«

⇓Ultraviolet divergencies → regularization, renormalization






SHE = −Z

d4x√−g

„1

16πGvacR + Λvac

«

⇓Ultraviolet divergencies → regularization, renormalization

⇓Scale invariance broken





SHE = −Z

d4x√−g

„1

16πGvacR + Λvac

«


⇓Scale invariance broken

⇓Renormalization Group Equations (RGE)


Evolving Cosmological Constantβ-function, RGE for the Cosmological Constant

+ For the CC, the dependence on the scale is encoded inthe β-function

µd

d ln µ

„Λ

8πG

«≡ βΛ =

1

(4π)2

0@Xi

Ai m4i + µ2

Xj

BjM2j + µ4

Xj

Cj + ...

1A

with:

Dependence on the renormalization scale µ

How is decoupling produced? Which are the active dofs?I Light particles?



For the CC, the dependence on the scale is encoded inthe β-function

µd

d ln µ

„Λ

8πG

«≡ βΛ =

1

(4π)2

0@Xi

Ai m4i + µ2

Xj

BjM2j + µ4

Xj

Cj + ...

1A

with:

+ Dependence on the renormalization scale µ

How is decoupling produced? Which are the active dofs?I Light particles?




µd

d ln µ

„Λ

8πG

«≡ βΛ =

1

(4π)2

0@Xi

Ai m4i + µ2

Xj

BjM2j + µ4

Xj

Cj + ...

1A

with:


+ How is decoupling produced? Which are the active dofs?

+ Light particles?




µd

d ln µ

„Λ

8πG

«≡ βΛ =

1

(4π)2

0@Xi

Ai m4i + µ2

Xj

BjM2j + µ4

Xj

Cj + ...

1A

with:


How is decoupling produced? Which are the active dofs?

+ Light particles?




µd

d ln µ

„Λ

8πG

«≡ βΛ =

1

(4π)2

0@Xi

Ai m4i + µ2

Xj

BjM2j + µ4

Xj

Cj + ...

1A

with:


How is decoupling produced? Which are the active dofs?

+ Light particles? Heavy particles with soft decoupling?


Evolving Cosmological ConstantCosmological scenarios

There are several choices in the literature. We contribute withone (Scenario 3) and test three of them:

Active dof Particles µ

Scenario 1 mi < µ neutrinos ρ1/4c (t)

Scenario 2 Mi > µ SM ρ1/4c (t)

Scenario 3 Mi > µ Plank H(t)


Cosmological scenariosScenario 3: Mi > µ, µ ∼ H(t)

Λ(H) = Λ0 +σ

2(4π)2M2(H2 − H2

0 ) RGE

Resolution of the system equation:

RGE + Friedmann Equation + Continuity Equation

Λ(z ; ν) = Λ0 + ρ0M

ν

1− ν

[(1 + z)3(1−ν) − 1

]− κ

1− 3ν

z (z + 2)

2+

ν

1− ν

[(1 + z)3(1−ν) − 1

]

κ ≡ −2 νΩ0K → proportional to curvature

ν ≡ σ12 π

M2

M2P→ cosmological index





Λ(z ; ν) = Λ0 + ρ0M

ν

1− ν

[(1 + z)3(1−ν) − 1

]− κ

1− 3ν

z (z + 2)

2+

ν

1− ν

[(1 + z)3(1−ν) − 1

]


ν ≡ σ12 π

M2






Λ(z ; ν) = Λ0 + ρ0M

ν

1− ν

[(1 + z)3(1−ν) − 1

]− κ

1− 3ν

z (z + 2)

2+

ν

1− ν

[(1 + z)3(1−ν) − 1

]

+ κ ≡ −2 νΩ0K → proportional to curvature

ν ≡ σ12 π

M2






Λ(z ; ν) = Λ0 + ρ0M

ν

1− ν

[(1 + z)3(1−ν) − 1

]− κ

1− 3ν

z (z + 2)

2+

ν

1− ν

[(1 + z)3(1−ν) − 1

]


+ ν ≡ σ12 π

M2




But sometimes an image is better than words...

Where we assumed a flat universe with Ω0M = 0.3 and Ω0

Λ = 0.7.



All the functions describing the Universe in the standard CC

cosmology can be calculated here. For example:

The decelaration parameter, q

ν > 0 ⇒ acc. farther in time

ν < 0 ⇒ acc. closer in time

Again the plot corresponds to flat universe with Ω0M = 0.3 and Ω0

Λ = 0.7.





+ The decelaration parameter, q

ν > 0 ⇒ acc. farther in time

ν < 0 ⇒ acc. closer in time


Λ = 0.7.





The decelaration parameter, q

+ ν > 0 ⇒ acc. farther in time

+ ν < 0 ⇒ acc. closer in time


Λ = 0.7.


Scenario 3Observational Constraints

1 free parameter, ν

Ω0M ν χ2

0.22+0.09−0.07 −0.5+0.3

−0.3 156.5

0.26+0.03−0.02 −0.3+0.2

−0.1 156.8


Cosmological scenariosScenario 2: Mi > µ, µ ∼ ρ

1/4c (t)

A quick look into the other scenarios.Scenario 2

µ ∼ ρ1/4c (t)

Mi > µ, as in Scenario 3, SM particles active

Λ(µ) = Λ0 +1

(4π)2

"µ2 1

4

m2

H + 3m2Z + 6m2

W − 4X

i

Nim2i

!+ µ4

1

2

Xi

Ni −5

4

!#

µ2 term → huge evolution

I m2H = 4

∑i Nim

2i − 3m2

Z − 6m2W ≈ (550 GeV )2



1/4c (t)


+ µ ∼ ρ1/4c (t)

+ Mi > µ, as in Scenario 3, SM particles active

Λ(µ) = Λ0 +1

(4π)2

"µ2 1

4

m2

H + 3m2Z + 6m2

W − 4X

i

Nim2i

!+ µ4

1

2

Xi

Ni −5

4

!#


I m2H = 4

∑i Nim

2i − 3m2

Z − 6m2W ≈ (550 GeV )2



1/4c (t)


µ ∼ ρ1/4c (t)


Λ(µ) = Λ0 +1

(4π)2

"µ2 1

4

m2

H + 3m2Z + 6m2

W − 4X

i

Nim2i

!+ µ4

1

2

Xi

Ni −5

4

!#


I m2H = 4

∑i Nim

2i − 3m2

Z − 6m2W ≈ (550 GeV )2



1/4c (t)


µ ∼ ρ1/4c (t)


Λ(µ) = Λ0 +1

(4π)2

"µ2 1

4

m2

H + 3m2Z + 6m2

W − 4X

i

Nim2i

!+ µ4

1

2

Xi

Ni −5

4

!#


+ m2H = 4

∑i Nim

2i − 3m2

Z − 6m2W ≈ (550 GeV )2



1 non-free parameter in SM

η ≡ 12

∑i Ni − 5

4= 10.75

Ω0M η χ2

0.35+0.04−0.04 +11+5

−55 158.6

0.35+0.04−0.04 −5+5

−5 158.6


Cosmological scenariosScenario 1: mi < µ, µ ∼ ρ

1/4c (t)

Scenario 1

+ µ ∼ ρ1/4c (t), as in Scenario 2

+ mi < µ, only lightest neutrinos active

Λ(ρ) = Λ0 +1

(4π)2

(1

2m4

S − 4∑

ν

m4ν

)ln

ρ

ρ0RGE

Inclusion of the sterile neutrino to cover both signs ofevolution



1/4c (t)

Scenario 1

µ ∼ ρ1/4c (t), as in Scenario 2

mi < µ, only lightest neutrinos active

Λ(ρ) = Λ0 +1

(4π)2

(1

2m4

S − 4∑

ν

m4ν

)ln

ρ

ρ0RGE

Inclusion of the sterile neutrino to cover both signs ofevolution



1/4c (t)

Scenario 1

µ ∼ ρ1/4c (t), as in Scenario 2

mi < µ, only lightest neutrinos active

Λ(ρ) = Λ0 +1

(4π)2

(1

2m4

S − 4∑

ν

m4ν

)ln

ρ

ρ0RGE

+ Inclusion of the sterile neutrino to cover both signs ofevolution



1 free (?) parameter

τ ≡ 12m4

S − 4∑

ν m4ν

Ω0M τ(10−9eV 4) χ2

0.20+0.10−0.08 −16+11

−12 156.5

0.27+0.02−0.04 −8+4

−5 157.1

mmaxν = 0.007± 0.006 eV

mmaxν = 0.006± 0.005 eV


The inverse approach

1 Motivacio

2 Introduction


4 Non-Parametric ReconstructionsInverse ProblemInverse MethodResults



Inverse problemsThe concept

Theory Observations

Dark energy model

n χ2 fits

Inverse method

SNe Ia magnitudes



TheoryForward problem

Observations

Dark energy model

n χ2 fits

Inverse method

SNe Ia magnitudes



Theory

Inverse problem

Observations

Dark energy model

n χ2 fits

Inverse method

SNe Ia magnitudes



Theory Observations

Dark energy model

n χ2 fits

Inverse method

SNe Ia magnitudes


Inverse problemsInverse problem’s problems

Risks with inverse problems:

The solution does not necessary exist

The solution is not unique

The solution is not stable

One can minimize the difficulties by including a priori information

⇒ We use a probabilistic approach




+ The solution does not necessary exist 7

The solution is not unique







The solution does not necessary exist 7

+ The solution is not unique 4








The solution is not unique 4

+ The solution is not stable 4







The solution is not unique 4

The solution is not stable 4




Inverse problemsThe method

Demands:

1 Inclusion of a priori information

2 Recover a function w(z) –or Λ(z)– instead ofparameterizations

Approach:

1 Through the Bayes theorem:

fpost(M|y) α L(y|M) fprior (M)

2 Working in functional spaces, were the functionals such asw(z) are defined in an infinite-dimensional space


The inverse methodMisfit function

Posterior distribution probability:

fpost(M|y) α exp [−S ]

S ≡ 12

(y− yth(M)

)∗C−1

y

(y− yth(M)

)

+ 12 (M−M0)

∗C−10 (M−M0)

Data y, covariance Cy , unknowns M

χ2 but... ∗ adjoint operator, scalar product in n-D space...

Information for the unknowns M: priors M0, C0

⇒ Data and unknowns treated at the same level

Goal: S minimization





S ≡ 12

(y− yth(M)

)∗C−1

y

(y− yth(M)

)

+ 12 (M−M0)

∗C−10 (M−M0)

+ Data y, covariance Cy , unknowns M

+ χ2 but... ∗ adjoint operator, scalar product in n-D space...








S ≡ 12

(y− yth(M)

)∗C−1

y

(y− yth(M)

)+ 1

2 (M−M0)∗C−1

0 (M−M0)



+ Information for the unknowns M: priors M0, C0







S ≡ 12

(y− yth(M)

)∗C−1

y

(y− yth(M)

)+ 1

2 (M−M0)∗C−1

0 (M−M0)







The inverse methodMinimization

Minimization steps:

1 The minimization is done in the functional space using aNewton minimization method

2 A final functional equation for w(z) is obtained

3 At this point operators are discretized and concrete valuescalculated

Results:

1 Quite a long equation for w(z):



w[k+1](z) = w0(z) +NX

i=1

Wi [k]

Z zi

0Cw (z, z ′)gw [k](z

′)dz ′ ,

where Wi [k] =PN

j=1

“S−1

[k]

”i,j

Vj[k] ,

Vi = yi +∂y th

i

∂Ω0M

(Ω0M − Ω0

M0) +

∂y thi

∂w(z)· (w − w0)− y th

i (zi , Ω0M , w(z)) ,

Si,j = δi,jσiσj +∂y th

i

∂Ω0M

CΩ0M

∂y thj

∂Ω0M

+∂y th

i

∂w(z)·

Cw ·∂y th

j

∂w(z)

!.

And uncertainty:

σw(z)(z) =q

Cw(z)(z) =

vuutσ2w(z)

−Xi,j

Cw ·∂y th

i

∂w(z)(S−1)i,j

∂y thj

∂w(z)· Cw



Results:

1 An equation for w(z) and the remaining unknowns

2 An estimation for the σ uncertainty

3 The resolving kernel K (z , zi ), a function at every zi indicatinghow well resolved it is

Comment:

Notice that both depend on the priorsI Monte Carlo exploration of the space of solutions



Results:

1 An equation for w(z) and the remaining unknowns

2 An estimation for the σ uncertainty

3 The resolving kernel K (z , zi ), a function at every zi indicatinghow well resolved it is

Comment:

+ Notice that both depend on the priors

+ Monte Carlo exploration of the space of solutions


The inverse methodResults

For the dark energy equation of state w(z):

Riess et al. (2006) data

Prior: Ω0M = 0.27± 0.03

Prior: w(z)0 = −1± 0.5

Differs from Λ at morethan 1σ



For the dark energy equation of state w(z):



Obtaining confidence regions via a Monte Carlo exploration:

As before but:

1000 reconstructions

Explored range−3 < w(z) < 1

Still differs from Λ atmore than 1σ

Wider, more reliable,confidence regions



One can do the same for the Cosmological Constant Λ(z)


Explored range0.53 < ΩΛ(z) < 0.93

A constant CC valid atthe 1σ limit

Valid for a general ΩX (z)


What the future holds in store

1 Motivacio

2 Introduction



5 Future PerspectivesOncoming SurveysNon-Parametric ReconstructionsEvolving Cosmological Constant


Future PerspectivesOncoming surveys



Space observatory

2,000 SNe/year

0.1 < z < 1.7

Spectroscopic redshifts

Vs.

Ground telescope

250,000 SNe/year (wide survey)

10,000 SNe (deep survey)

0 < z < 0.9 (wide survey)

0 < z < 1.4 (deep survey)

Photometric redshifts



Uncertaintiesin the data sets

LSST deep: σintr = 0.15, δz = 0.01 and σsys = 0.02

SNAP: σintr = 0.15, δz = 0.00 and σsys = 0.02 z/1.7

(+ SNFactory as low redshift anchor)


Future PerspectivesNon-parametric reconstructions

Flashback:Reconstruction for the dark energy equation of state w(z):

Riess et al. (2006) data


Explored range−3 < w(z) < 1


Future PerspectivesNon-parametric reconstructions

For the dark energy equation of state w(z) with:

LSST SNAP


Future PerspectivesEvolving cosmological constant

Scenario 1 (mi < µ, µ ∼ ρ1/4c ) τ ≡ 1

2m4S − 4

∑ν m4

ν



Scenario 2 (Mi > µ, µ ∼ ρ1/4c ) η ≡ 1

2

∑i Ni − 5

4 = 10.75



Scenario 3 (Mi > µ, µ ∼ H) ν ≡ σ12 π

M2

M2P


In summary

1 Motivacio

2 Introduction





Summary and conclusions

The problem

+ The Universe seems to be in accelerated expansion

Characterization of a dark energy source as the cause ofacceleration

Nowadays, it is a degenerated problem

Evolving Cosmological Constant

We motivate an evolving CC as a consequence of therenormalization effects in a Quantum Field Theory (QFT)

The running depends on the renormalization scale and theactive dofs



The problem

The Universe seems to be in accelerated expansion

+ Characterization of a dark energy source as the cause ofacceleration







The problem



+ Nowadays, it is a degenerated problem






The problem





+ We motivate an evolving CC as a consequence of therenormalization effects in a Quantum Field Theory (QFT)




The problem






+ The running depends on the renormalization scale and theactive dofs



Evolving Cosmological Constant (continued)

+ In our approach (Scenario 3), particles with M ∼ MPl areresponsible for the running

This evolution affects the standard cosmological equations

Running must be small in order to be compatible withstructure formation and CMB

Such an small evolution is difficult to detect by observations,although it is mandatory within a QFT




In our approach (Scenario 3), particles with M ∼ MPl areresponsible for the running

+ This evolution affects the standard cosmological equations








+ Running must be small in order to be compatible withstructure formation and CMB








+ Such an small evolution is difficult to detect by observations,although it is mandatory within a QFT



Non-parametric Reconstructions

+ We apply an inverse approach to estimate w(z) and Λ(z) in anon-parametric way

We introduce a priori information to regularize the inversion

Results depend on priors, but we include Monte Carloexplorations to overcome this limitation

Current data can already rule out a constant dark energysource at low redshift at 1σ level

Future surveys such as SNAP or LSST will confirm that pointup to redshift one




We apply an inverse approach to estimate w(z) and Λ(z) in anon-parametric way

+ We introduce a priori information to regularize the inversion









+ Results depend on priors, but we include Monte Carloexplorations to overcome this limitation









+ Current data can already rule out a constant dark energysource at low redshift at 1σ level









+ Future surveys such as SNAP or LSST will confirm that pointup to redshift one


Exploring the Evolution of Dark Energy

and its Equation of State

Cristina Espana i Bonet

Universitat de Barcelona

12th February, 2008

Advisor: Dra. Pilar Ruiz-Lapuente

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