Current status of an interacting dark sector withcosmological observations
Jurgen Mifsud
Korea Astronomy and Space Science InstituteCosmic Controversies Conference
Kavli Institute for Cosmological Physics
The University of Chicago
Gleacher Center
Chicago06/10/19

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Outline

1Introduction

2

Theoretical Framework3

Growth History

4

The ISW Effect5

Parameter Constraints

6Conclusion

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Introduction
There is overwhelming observational evidence that the Universe isundergoing accelerated expansion.
This late–time acceleration of the Universe must be driven by someunidentified energy source, generally referred to as dark energy (DE).
The ΛCDM model is in an excellent agreement with thesecosmological probes and its parameters have now been determined toa very good accuracy.
30z√
distance/rd20√
DM (z)/rd z√
DV (z)/rd z√
zDH (z)/rd z

10
0.1
J. Mifsud

arXiv:1607.03155

6dFGS
SDSS MGSSDSS DR7WiggleZ
BOSS Galaxy DR12BOSS Lyα-auto DR11BOSS Lyα-cross DR110.2

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Introduction

From a theoretical viewpoint, this concordance cosmology issomewhat troubling
the observed cosmological constant is surprisingly small
4
4
Λobs. ∼ 10−3 eV ∼ 10−30 MPl ,when compared with the theoretical expectation of the cosmologicalconstant44
Λtheory ∼ (TeV) ∼ 10−60 MPl.

Rather than dealing directly with the cosmological constant, anumber of alternative routes have been proposed which skirt aroundthis thorny issue.
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Introduction
Quintessence models invoke
an evolving canonical scalar
field with a potential andmake use of the scaling
properties and tracking natureof such scalar fields evolving
in the presence of otherbackground matter fields.

Phys. Rev. D 59, 123504
matradQ

It is often simply assumed that the components of the dark sector are
independent and do not interact directly with each other.
However, there is no fundamental principle which forbids some formof interplay between dark matter (DM) and DE.
Indeed, whereas new forces between DE and normal matter particles
are heavily constrained by observations (for e.g. by solar systemtests), this is not the case for DM particles.
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1

Introduction

2

Theoretical Framework3

Growth History

4

The ISW Effect5

Parameter Constraints

6Conclusion

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Theoretical Framework
We consider the scalar–tensor theory described by the following action,
expressed in the Einstein frame:
 2ZMPl1 µν4 √S = d x −g
R − g ∂µ φ ∂ν φ − V (φ) + LSM
22Zp+ d4 x −g̃ L̃DM (g̃µν , ψ)−2where κ2 = MPl= 8πG together withφ – the DE scalar field
V (φ) – potential of the scalar field
LSM – the Lagrangian which includes a relativistic component (r)and a baryon component (b)[JCAP 1504 (2015) 036, JCAP 1711 (2017) 001]
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Theoretical Framework
We consider the scalar–tensor theory described by the following action,expressed in the Einstein frame: 2ZMPl1 µν4 √R − g ∂µ φ ∂ν φ − V (φ) + LSM
S = d x −g
22Zp+ d4 x −g̃ L̃DM (g̃µν , ψ)Particle quanta of the DM fields ψ, propagate on geodesics defined by themetricg̃µν = C(φ)gµν + D(φ) ∂µ φ ∂ν φC(φ) – conformal couplingD(φ) – disformal coupling[Phys. Rev. D48 (1993) 3641]
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Theoretical Framework - Field Equations
φThe dark sector coupling leads to the non-conservation of Tµν:φ = V,φ − Q ,whereD,φ µν
C,φD µν
TDM +T∇µ φ∇ν φ − ∇µT∇ν φ ,Q=2C
2C DM
C DMµν
and TDM is the trace of TDM, which satisfies a modified conservation
equationDM∇µ Tµν= Q∇ν φ .

The uncoupled SM particles are governed by the standard
conservation equationSM∇µ Tµν=0.
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Theoretical Framework - Background Evolution
Consider the spatially–flat FLRW line-element:ds2 = gµν dxµ dxν = a2 (τ ) −dτ 2 + δij dxi dxj ,with conformal time τ , and scale factor a(τ ).
The Friedmann equations are given byκ2 2a (ρφ + ρb + ρr + ρc ) ,3
κ2= − a2 (ρφ + 3pφ + ρb + 2ρr + ρc ) .
6H2 =H0The evolution equations of radiation and baryons are respectivelygiven byρ0r + 4Hρr = 0 ,J. Mifsud

ρ0b + 3Hρb = 0 ,where we denote a conformal time derivative by a prime, and theconformal Hubble parameter by H = a0 /a.
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Theoretical Framework - Background Evolution
The modified Klein-Gordon equation simplifies to
φ00 + 2Hφ0 + a2 V,φ = a2 Q ,and the DM conservation equation reduces toρ0c + 3Hρc = −Qφ0 ,with the coupling function
Ca2 C,φ + D,φ φ0 2 − 2D C,φ φ0 2 + a2 V,φ + 3Hφ0
Q=−ρc .
2 a2 C + D a2 ρc − φ0 2This simplifies considerably in the pure conformal case to1
Q(c) = − (ln C),φ ρc .
2
[JCAP 1711 (2017) 001]
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Theoretical Framework - Background Evolution
0.4
Uncoupled
Conformal
DisformalMixed

0.35
0.3

−Q/ρc0.25
0.2
0.15
0.1
0.05
000.2

0.4

0.60.8a1

1.05
Uncoupled
Conformal
DisformalMixed

1.04

a3 ρc

1.03
1.02
1.01
10.99

00.5

11.5

2z

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1Introduction

2

Theoretical Framework3

Growth History

4

The ISW Effect5

Parameter Constraints

6Conclusion

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Growth History
Using the conformal Newtonian gauge line-elementds2 = a2 (τ ) − (1 + 2Ψ) dτ 2 + (1 − 2Φ) δij dxi dxj ,we get the perturbed continuity and Euler equations of the coupled
DM: QQ
φ0δc0 = − θc − 3Φ0 + φ0 δc − δφ0 − δQ ,ρcρcρcθc0 + Hθc = k 2 Ψ +Q 0Q
φ θc − k 2 δφ .
ρc
ρc

The evolution of the perturbed scalar field is governed byδφ00 + 2Hδφ0 + k 2 + a2 V,φφ δφ = Ψ0 + 3Φ0 φ0 − 2a2 V,φ Ψ+ a2 δQ + 2a2 QΨ .
[JCAP 1711 (2017) 001]
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Growth History
The generic perturbed coupling function reads as follows−ρce 1 δc + B
e 2 Φ0 + B
e 3Ψ + B
e 4 δφ0 + Be 5 δφ
δQ = 2Ba C + D a2 ρc − φ0 2
We consider the matter growth rate function defined by
fm =d ln δm
δ0= m ,d ln aHδmwhere we define the matter density contrast byδm =ρb δb + ρc δc,ρb + ρcwith δb , δc being the baryon and coupled DM density contrasts,respectively.
[JCAP 1711 (2017) 001]
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Growth History
Uncoupled
Conformal
DisformalMixedz = 0.5
z=1z=2

3.5

H/H03

2.5

2

1.5

1
0.3

0.35

0.4

0.45

0.5

fm σ8

α = 0.05, DM = 0.43 meV−1 , and λ = 1.
[JCAP 1711 (2017) 001]
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Growth History
The DM density contrast evolution on the small–scales is governed by
3Geff
3δc00 + Heff δc0 − H2Ωc δc = H2 (Ωb δb + Ωr δr ) ,2G2with
1 Q 0
Heff=1−φ ,HH ρcGeff
2 Q2=1+ 2 2 .
Gκ ρcCoupled models are characterised by an enhancement in the growthrate function on the small–scales when compared with thelarge–scales.
In disformally coupled models, it is the increase in the effective
gravitational constant which gives rise to this enhanced growth.
[JCAP 1711 (2017) 001]
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Growth History
1.3
Uncoupled
Conformal
DisformalMixed

1.25

Geff /G

1.2
1.15
1.1
1.05
100.2

0.4

0.6

0.8

1a

α = 0.05, DM = 0.43 meV−1 , and λ = 1.
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Growth History
Conformal Coupling
0.76z∗ = 0.50z∗ = 0.52z∗ = 0.54z∗ = 0.56

0.755
0.75

fm (k, z∗ )

0.745
0.74
0.735
0.73
0.725
0.72
0.715
10 -6

10 -5

10 -4-3! 10"
k h Mpc−1

0.01

0.1

1

[JCAP 1711 (2017) 001]
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Growth History
Disformal Coupling
0.8z∗ = 0.50z∗ = 0.52z∗ = 0.54z∗ = 0.56

fm (k, z∗ )

0.78

0.76

0.74

0.72

0.7
10 -6

10 -5

10 -4-3! 10"
k h Mpc−1

0.01

0.1

1

[JCAP 1711 (2017) 001]
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Growth History
Mixed Couplingz∗ = 0.500.8z∗ = 0.52z∗ = 0.54z∗ = 0.56

fm (k, z∗ )

0.78

0.76

0.74

0.72

0.7
10 -6

10 -5

10 -4-3! 10"
k h Mpc−1

0.01

0.1

1

[JCAP 1711 (2017) 001]
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Growth History
Mixed Coupling[JCAP 1711 (2017) 001]
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1Introduction

2

Theoretical Framework3

Growth History

4

The ISW Effect5Parameter Constraints

6Conclusion

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22 / 31The ISW EffectMeasurements of the ISW effect provide a powerful method to probe
DE as this effect is sensitive to the time evolution of the gravitational
potential sourced by the LSS.
It is too small to be directly detected in the CMB spectrum (∼ 10times less than TT).
It is more pronounced through the correlation between the CMB
anisotropies and the LSS.
The cross–correlation angular power spectrum is given byZdkTg
C` = 4πTCMB ∆T` (k)∆g` (k)PR (k)kwhere the weight functions for the tracer overdensity and the ISW
effect are respectively denoted by ∆g` (k) and ∆T` (k), and PR (k) is
the primordial curvature power spectrum.
[In preparation]
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23 / 31The ISW EffectConformal Coupling

Disformal Coupling[In preparation]
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1Introduction2Theoretical Framework

3Growth History

4The ISW Effect5

Parameter Constraints

6Conclusion

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Parameter Constraints
TTEE+lensing+ACA+BSHE
TTEE+lensing+ACA+BSHR

TTEE+lensing+FCA+BSHE
TTEE+lensing+FCA+BSHR

TTEE+lensing+CA+BSHE

TTEE+lensing+CA+BSHR

TTEE+lensing+ACA+BSHR

Conformal Coupling
TTEE+lensing+ACA+BSHE
TTEE+lensing+ACA+BSHR
TTEE+lensing+FCA+BSHE
TTEE+lensing+FCA+BSHR
TTEE+lensing+CA+BSHE
TTEE+lensing+CA+BSHRP/Pmax

0.8
0.6
0.40.2

TTEE+BSHR

0.06

0.00
0.0

TT+BSHR

0.4
2017-04-11_305999_

2017-04-14_289000_

0.8
λ1.21.6

2017-03-12_235000_

TTEE+lensing+CA+BSHE
conformal
TTEE+lensing+CA+BSHE

0.4(DM V0 = 1)

TTEE+lensing+CA+BSHE
mixed

α0.2

0.02

0.1

0.3

0.6
λ0.9

1.2

4 , V (φ) = V 4 e−λκφC(φ) = e2ακφ , D(φ) = DM
0J. Mifsud

TTEE+lensing+ACA+BSHR
TTEE+lensing+CA+BSHRTTEE+BSHR
TT+BSHR

0.3

0.04

0.00
0.00.50
0.25

TTEE+lensing+ACA+BSHR
TTEE+lensing+CA+BSHR
TTEE+BSHR
TT+BSHR

0.08

αTTEE+lensing+CA+BSHR

TT+BSHR

0.75

0.00.000 0.025 0.050 0.075 0.100
αTTEE+lensing+ACA+BSHR

TTEE+BSHR

1.00

DM / meV −1

1.0

TTEE+lensing+CA+BSHR

Disformal & Mixed Couplings

0.0
0.0

0.4

0.8
λ1.2

[Phys. Rev. D97 (2018) 023506]

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Parameter Constraints
TTEE+lensing+CA+BSHE
TTEE+lensing+CA+BSHR

TTEE+lensing+ACA+BSHE

TTEE+BSHR

TTEE+lensing+ACA+BSHE

TTEE+BSHR

TTEE+BSHE

Planck TT+lensing
Planck lensing

TTEE+lensing

1.20 +ACA+BSHE
TTEE+lensing

σ8+ACA+BSHR
TTEE+lensing+CA+BSHE
1.05 TTEE+lensing+CA+BSHRTTEE+BSHE
TTEE+BSHR

0.90

0.80
Planck lensing
Planck TT+lensing

0.28

0.30
0.92

0.32

0.75

0.34

Ωm
α

0.88

0.08

σ80.03

TT+BSHR
TTEE+lensing+CA+BSHR
TTEE+lensing+ACA+BSHR
8101214

0.02

1.20
1.15

0.75

1.10
1.05

0.50

1.00

TTEE+lensing+ACA+BSHR
TTEE+lensing+CA+BSHRTTEE+BSHR0.250.01zreio

4 , V (φ) = V 4 e−λκφC(φ) = e2ακφ , D(φ) = DM
00.00
0.0

σ80.04

1.25

1.00

0.06

0.84
0.80

0.275 0.300 0.325 0.350Ωm0.070.05

J. Mifsud

TTEE+lensing+ACA+BSHR

Disformal Coupling

0.85

0.75

TTEE+lensing+CA+BSHR

TTEE+BSHE

TTEE+lensing+ACA+BSHE
TTEE+lensing+ACA+BSHR
TTEE+lensing+CA+BSHE
TTEE+lensing+CA+BSHR
TTEE+BSHE
TTEE+BSHR

0.90

σ8

TTEE+lensing+ACA+BSHR

DM / meV −10.95

TTEE+lensing+CA+BSHE

Conformal Coupling

0.4

0.81.20.95
0.90
0.85

1.6

λ
[Phys. Rev. D97 (2018) 023506]

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Parameter Constraints - H0 from GW170817
0.10 Planck + H(z)CC + BAO+ H0GW+ H0R

7276

0.08
α0.06
0.04
0.02
0.00

6064

68

H0 / km s −1 Mpc −1[MNRAS 487 (2019) 900]
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1Introduction

2

Theoretical Framework3

Growth History

4

The ISW Effect5Parameter Constraints

6Conclusion

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Conclusion
Interacting DE models give an enhanced growth on the small–scales,
particularly in the disformal case.
A disformal dark sector coupling leads to intermediate–scale damped
oscillations in the matter growth rate function; a unique signature ofthe disformal coupling.
The conformal coupling is found to be tightly constrained with CMB
data, although the disformal coupling is able to evade this probe.
A better understanding of the non–linear cosmic evolution of
perturbations should be able to shed light on the still hidden featuresof these coupled quintessence models.
Other distinctive signatures of dark sector interactions might beindirectly detected through observations of the tidal tails of a
disrupting satellite galaxy.
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Thank You

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