On dark energy evolution - famaf.unc.edu.ar fileIntroduction • Dark Energy (DE) is the name of the...

On dark energy evolution

Víctor H. Cárdenas

Instituto de Física y Astronomía

Universidad de Valparaíso

Córdoba, August 2015

Contents

• Introduction

• The main approach

• Data

• First results

• Theoretical thoughts• Theoretical thoughts

• Final comments

Along collaboration with:

Verónica Motta, Carla Bernal, and Juan Magaña


Introduction

• Dark Energy (DE) is the name of the cause of the cosmic acceleration in expansion detected in 1998.

• So far, the best model that fits observational data, is the LCDM; a cosmological constant.is the LCDM; a cosmological constant.

• We do not know what this contribution comes from, neither why it has that value

• The model generates a “cosmic” coincidence, which makes it unnatural


Introduction

• Approaches to the DE problem:

– Mainstream Observers approach

– Theorist’s approach– Theorist’s approach

– Outlier data approach


L. Perivolaropoulos, Journal of Cosmology, 15, 6054, (2011), 1104.0539 [astro-ph.CO]

Introduction

• We look for hints of DE evolution (with redshift):

– A variable equation of state (EoS) parameter, w(z).

– A variable DE density, X(z).– A variable DE density, X(z).

• LCDM is by definition a model where X(z) and w(z)

are constants.


E. Di Valentino et al., Beyond six parameters: extending LCDM, 1507.06646 [astro-ph.CO]

Two approaches

• A variable equation of state (EoS) parameter, w(z).

• A variable DE density, X(z).


Two approaches

• A variable equation of state (EoS) parameter, w(z).

• A variable DE density, X(z).

• Cosmology• Cosmology


2 3 4( ) (1 ) (1 ) (1 ) ( )m r m rE z z z X z= Ω + + Ω + + − Ω − Ω

0

1 ( )( ) exp[ 3 ]

1

zw x

X z dxx

+=

+∫

Data

• Type Ia supernova

• Gas mas fraction in clusters

• BAO points• BAO points

• CMB background


0

'( )

( ')

c dzr z

H E z= ∫

Data: type Ia supernova

• Union 2 (Amanullah et al. 2010)

– 557 points in 0.015<z<1.4

• Union 2.1 (Suzuki et al. 2011)

– 580 points in 0.015<z<1.414– 580 points in 0.015<z<1.414

• LOSS-Union (Filipenko et al. 2013)

– 586 SNIa in 0.01<z<1.34


[ ]( ) 25 5log ( )L

z d zµ = +

Data: gas mass fraction

• Assuming that gas traced baryons, Sasaki in 1996 showed how to use it as an observational probe

• Theoretically we expect

M Ω

• Data from Allen et al. 2008 (42 data points).


const.gas b

total m

M

M

Ω∝ =

Ω

Variable w(z)Variable w(z)


Variable w(z)

• Using a parametrization for w(z)

• Type Ia supernova data

10( )

1

w zw z w

z= +

+


M.Chevalier, D.Polarski, IJMPD 10, 213 ( 2001); E.Linder, PRD 90, 091301 (2003).

1/23

0

(1 )( ) ' (1 ') (1 ) ( ')

L m m

z cd z dz z X z

H

−+ = Ω + + − Ω ∫

[ ]( ) 25 5log ( )L

z d zµ = +

1

0 13

3(1 ) 1( ) (1 )w z

w w zX z z e−

+ + += +

Variable w(z)

• Parameterization: CPL

Using the Constitution set (Hicken et al. 2009)

10( )

1

w zw z w

z= +

+


A.Shafieloo,V.Sahni, and A.A.Starobinsky, PRD80, 101301 (2009)

(1 ) ( )( ) 1

( )

z dE zq z

E z dz

+= −

Variable w(z)

• Parametrization: CPL

Using the Union 2 set (Amanullah et al. 2010)

10( )

1

w zw z w

z= +

+


(1 ) ( )( ) 1

( )

z dE zq z

E z dz

+= −

VHC, C.Bernal and A.Bonilla, MNRAS 433, 3534 (2013)

Variable w(z)

• CPL

– Union 2.1

– Gas mass fraction

– LOSS-Union


Variable w(z)

• Parametrization: CPL

• Using Union 2.1 Gas mass fraction

10( )

1

w zw z w

z= +

+


VHC, C.Bernal and A.Bonilla, MNRAS 433, 3534 (2013)

Variable w(z)

• SNIa (LOSS)+fgas: CPL1

0 13

3(1 ) 1( ) (1 )w z

w w zX z z e−

+ + += +


at low redshift

• This can be an artifact of the CPL parameterization

on SNIa, however data supported it.

• Curiously this behavior does not manifest using

the Union 2.1 data.

( )q z

gasf

the Union 2.1 data.

• Is there any dependence on the parameterization?

• Is there any theoretical idea of what does this

behavior means?


Independence of the

parametrizations

• Jassal-Bagla-Padmanabhan

• Feng-Shen-Li-Li

• Polinomial

• Barbosa-Alcaniz


J.Magaña, VHC, V.Motta, JCAP 10, 017 2014

Independence of the

parameterizations

• Jassal-Bagla-Padmanabhan

• Constitution

• Union 2• Union 2

• Union 2.1

• Loss



Independence of the

parameterizations

• Barbosa-Alcaniz

• Constitution

• Union 2• Union 2

• Union 2.1

• Loss



Variable DE density: X(z)


Variable DE density: X(z)

• There is a problem in trying to extract information

from the EoS parameter w(z) (Maor et al. 2000)

• We are interested in test to what extend the data

suggest departures from the LCDM modelsuggest departures from the LCDM model


2 3 4( ) (1 ) (1 ) (1 ) ( )m r m rE z z z X z= Ω + + Ω + + − Ω − Ω

0

1 ( )( ) exp[ 3 ]

1

zw x

X z dxx

+=

+∫

DE density probe

• We assume a quadratic parameterization for X(z)

where

0 2 0 11 20 1 2

0 1 0 2 1 0 1 2 2 0 2 1

( )( ) ( )( )( )( )( )

( )( ) ( )( ) ( )( )

z z z z z z z zz z z zX z X X X

z z z z z z z z z z z z

− − − −− −= + +

− − − − − −

where

Wang et al. 2004 ; Cárdenas 2014

0 1 2 2 0 1 1 2 20, / 2, , and 1, , m

z z z z z X X f X f= = = = = =


DE density probe

• LCDM


1 2 1f f= =

DE density probe

• Using each one of the data separately

• Consistency among different data sets

donde


L. Perivolaropoulos, Journal of Physics Conf. Ser., 222, 012024 (2010).

DE density probe

• Each data set separately:

SNIa (LOSS) fgas BAO CMB


DE density probe

• Using each one of the data separately:

SNIa Fgas


BAO CMB

Dark Energy evolution

• SNIa+fgas:



• SNIa + fgas + BAO + CMB:



• Summary

(1) SNIa+fgas

(2) All(2) All



• Using SNIa data and fgas in clusters, imply a DE

density that has been growing with time recently

• The same is found using other SNIa data sets,

except Union 2.1except Union 2.1

• Going back to the previous analysis, based on

parameterizations of the EoS parameter w(z)


• The same trend is obtained when a EoS

parameterization is used

• Union 2 using CPL

1

0 13

3(1 ) 1( ) (1 )w z

w w zX z z e−

+ + += +



• The SNIa and fgas data suggest the DE density X(z)decrease with increasing redshifts.

• This trend also shows up in all the cases where we parameterize the EoS parameter w(z)parameterize the EoS parameter w(z)

• The hint for DE evolution disappear after we add BAO and CMB.

• This trend is in agreement with the recent results using the BAO BOSS DR11 data: negative dark energy density

Cárdenas 2014; Delubac et al. 2014

Comments

• This trend is in agreement with the recent results

using the BAO BOSS DR11 data: negative dark

energy density

Cárdenas 2014; Delubac et al. 2014

Comments

• Adding the BAO DR11 point:

( 2.34) 222 7 km/s/MpcH z = = ±

Sahni, Shafieloo, & Starobinsky, Astrophys.J. 793 (2014) L40

Abdalla, Ferreira, Quintin & Wang, 1412.2777 [astro-ph.CO]


1 20.7; 0.50; 1.0; 5.64;mh f f= Ω = = − = −

Theoretical thoughts

LTB connection:

• In LTB inhomogeneous models they match

the luminosity distance to data, and from

this they obtain an effective Hubble

function H(z)

• The behavior of q(z) at low redshift could be

associated with the existence of a void


Vanderveld, Flanagan & Wasserman, PRD74, 023506 (2006)

February et al., MNRAS 405, 2231 (2010)

Bengochea and De Rossi, PLB733, 258 (2014)

(1 ) ( )( ) 1

( )

z dH zq z

H z dz

+= −


DM/DE interaction:

• Assuming


33( )(1 )

( ) 1 (1 )z

X z zε ωε ω

ε ω ε

++ = + + +


DM/DE interaction:3

3( )(1 )( ) 1 (1 )

zX z z

ε ωε ω

ε ω ε

++ = + + +

Cases:


0.9; 0.01;ω ε= − = 1.1; 0.01;ω ε= − = 0.9; 0.01;ω ε= − = −

Cases:

Comments

• LTB inhomogeneous models would produce (in an

effective way) such a behavior assuming the

existence of a void.

• Interaction Q; it is possible to describe such a

trend even using a Q>0

Addendum

• Adding the BAO DR11 point:

( 2.34) 222 7 km/s/MpcH z = = ±

Sahni, Shafieloo, & Starobinsky, Astrophys.J. 793 (2014) L40

Abdalla, Ferreira, Quintin & Wang, 1412.2777 [astro-ph.CO]

• Adding the combined constraint


Aubourg et al., 1411.1074 [astro-ph.CO]

1 20.7; 0.55; 1.67; 7.8;mh f f= Ω = = − = −

On dark energy evolution - famaf.unc.edu.ar fileIntroduction • Dark Energy (DE) is the name of the...

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