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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
Córdoba, August 2015
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
Córdoba, August 2015
Introduction
• Approaches to the DE problem:
– Mainstream Observers approach
– Theorist’s approach– Theorist’s approach
– Outlier data approach
Córdoba, August 2015
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.
Córdoba, August 2015
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).
Córdoba, August 2015
Two approaches
• A variable equation of state (EoS) parameter, w(z).
• A variable DE density, X(z).
• Cosmology• Cosmology
Córdoba, August 2015
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
Córdoba, August 2015
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
Córdoba, August 2015
[ ]( ) 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).
Córdoba, August 2015
const.gas b
total m
M
M
Ω∝ =
Ω
Variable w(z)
• Using a parametrization for w(z)
• Type Ia supernova data
10( )
1
w zw z w
z= +
+
Córdoba, August 2015
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= +
+
Córdoba, August 2015
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= +
+
Córdoba, August 2015
(1 ) ( )( ) 1
( )
z dE zq z
E z dz
+= −
VHC, C.Bernal and A.Bonilla, MNRAS 433, 3534 (2013)
Variable w(z)
• Parametrization: CPL
• Using Union 2.1 Gas mass fraction
10( )
1
w zw z w
z= +
+
Córdoba, August 2015
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−
+ + += +
Córdoba, August 2015
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?
Córdoba, August 2015
Independence of the
parametrizations
• Jassal-Bagla-Padmanabhan
• Feng-Shen-Li-Li
• Polinomial
• Barbosa-Alcaniz
Córdoba, August 2015
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
J.Magaña, VHC, V.Motta, JCAP 10, 017 2014
Córdoba, August 2015
Independence of the
parameterizations
• Barbosa-Alcaniz
• Constitution
• Union 2• Union 2
• Union 2.1
• Loss
Córdoba, August 2015
J.Magaña, VHC, V.Motta, JCAP 10, 017 2014
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
Córdoba, August 2015
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= = = = = =
Córdoba, August 2015
DE density probe
• Using each one of the data separately
• Consistency among different data sets
donde
Córdoba, August 2015
L. Perivolaropoulos, Journal of Physics Conf. Ser., 222, 012024 (2010).
Dark Energy evolution
• 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)
Dark Energy evolution
• 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−
+ + += +
J.Magaña, VHC, V.Motta, JCAP 10, 017 2014
Dark Energy evolution
• 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]
Córdoba, August 2015
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
Córdoba, August 2015
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
+= −
Theoretical thoughts
DM/DE interaction:
• Assuming
Córdoba, August 2015
33( )(1 )
( ) 1 (1 )z
X z zε ωε ω
ε ω ε
++ = + + +
Theoretical thoughts
DM/DE interaction:3
3( )(1 )( ) 1 (1 )
zX z z
ε ωε ω
ε ω ε
++ = + + +
Cases:
Córdoba, August 2015
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
Córdoba, August 2015
Aubourg et al., 1411.1074 [astro-ph.CO]
1 20.7; 0.55; 1.67; 7.8;mh f f= Ω = = − = −