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On the interactions between dark energy and dark matter

Jurgen Mifsud

Consortium for Fundamental Physics, School of Mathematics and Statistics The University of Sheffield In collaboration with Carsten van de Bruck Cosmology and fundamental physics with current and future ESO facilities 3rd Azores School on Observational Cosmology 5th Azores International Advanced School in Space Sciences Angra do Hero´ ısmo, A¸ cores, Portugal 27 August - 02 September 2017

28/08/17 Jurgen Mifsud On the interactions between dark energy and dark matter 28/08/17 1 / 7

Introduction

There is overwhelming observational evidence that the Universe is undergoing accelerated expansion. This late–time acceleration of the Universe must be driven by some unidentified energy source, generally referred to as dark energy (DE). The ΛCDM model is in an excellent agreement with these cosmological probes and its parameters have now been determined to a very good accuracy. From a theoretical viewpoint, this concordance cosmology is somewhat troubling:

the observed cosmological constant is surprisingly small Λobs. ∼

• 10−3eV

4 ∼

• 10−30MPl

4 , when compared with the theoretical expectation of Λtheory ∼ (TeV)4 ∼ 10−60M 4

Pl .

Rather than dealing directly with Λ, a number of alternative routes, such as quintessence, have been proposed which skirt around this thorny issue.

Jurgen Mifsud On the interactions between dark energy and dark matter 28/08/17 2 / 7

Introduction

There is overwhelming observational evidence that the Universe is undergoing accelerated expansion. This late–time acceleration of the Universe must be driven by some unidentified energy source, generally referred to as dark energy (DE). The ΛCDM model is in an excellent agreement with these cosmological probes and its parameters have now been determined to a very good accuracy. From a theoretical viewpoint, this concordance cosmology is somewhat troubling:

the observed cosmological constant is surprisingly small Λobs. ∼

• 10−3eV

4 ∼

• 10−30MPl

4 , when compared with the theoretical expectation of Λtheory ∼ (TeV)4 ∼ 10−60M 4

Pl .

Rather than dealing directly with Λ, a number of alternative routes, such as quintessence, have been proposed which skirt around this thorny issue.

Jurgen Mifsud On the interactions between dark energy and dark matter 28/08/17 2 / 7

Introduction

There is overwhelming observational evidence that the Universe is undergoing accelerated expansion. This late–time acceleration of the Universe must be driven by some unidentified energy source, generally referred to as dark energy (DE). The ΛCDM model is in an excellent agreement with these cosmological probes and its parameters have now been determined to a very good accuracy.

Jurgen Mifsud On the interactions between dark energy and dark matter 28/08/17 2 / 7

Introduction

There is overwhelming observational evidence that the Universe is undergoing accelerated expansion. This late–time acceleration of the Universe must be driven by some unidentified energy source, generally referred to as dark energy (DE). The ΛCDM model is in an excellent agreement with these cosmological probes and its parameters have now been determined to a very good accuracy. From a theoretical viewpoint, this concordance cosmology is somewhat troubling:

the observed cosmological constant is surprisingly small Λobs. ∼

• 10−3eV

4 ∼

• 10−30MPl

4 , when compared with the theoretical expectation of Λtheory ∼ (TeV)4 ∼ 10−60M 4

Pl .

Rather than dealing directly with Λ, a number of alternative routes, such as quintessence, have been proposed which skirt around this thorny issue.

Jurgen Mifsud On the interactions between dark energy and dark matter 28/08/17 2 / 7

Introduction

There is overwhelming observational evidence that the Universe is undergoing accelerated expansion. This late–time acceleration of the Universe must be driven by some unidentified energy source, generally referred to as dark energy (DE). The ΛCDM model is in an excellent agreement with these cosmological probes and its parameters have now been determined to a very good accuracy. From a theoretical viewpoint, this concordance cosmology is somewhat troubling:

the observed cosmological constant is surprisingly small Λobs. ∼

• 10−3eV

4 ∼

• 10−30MPl

4 , when compared with the theoretical expectation of Λtheory ∼ (TeV)4 ∼ 10−60M 4

Pl .

Rather than dealing directly with Λ, a number of alternative routes, such as quintessence, have been proposed which skirt around this thorny issue.

Jurgen Mifsud On the interactions between dark energy and dark matter 28/08/17 2 / 7

Theoretical Model

We consider the scalar–tensor theory described by the following action: S =

• d4x√−g

M2

Pl

2 R − 1 2gµν∂µφ ∂νφ − V (φ) + LSM

• +
• d4x
• −˜

g ˜ LDM (˜ gµν, ψ) , where κ2 ≡ M−2

Pl ≡ 8πG together with

R – Ricci scalar, φ – DE scalar field, V (φ) – potential of the scalar field, LSM – Lagrangian which includes a relativistic component r, and a baryon component b.

Jurgen Mifsud On the interactions between dark energy and dark matter 28/08/17 3 / 7

Theoretical Model

We consider the scalar–tensor theory described by the following action: S =

• d4x√−g

M2

Pl

2 R − 1 2gµν∂µφ ∂νφ − V (φ) + LSM

• +
• d4x
• −˜

g ˜ LDM (˜ gµν, ψ) , Particle quanta of the DM fields ψ, propagate on geodesics defined by the metric ˜ gµν = C(φ)gµν + D(φ) ∂µφ ∂νφ , C(φ) – conformal coupling

this is the well–known conformal transformation which characterises the Brans–Dicke class of scalar–tensor theories.

D(φ) – disformal coupling

this appears in the Einstein frame formulation of any covariant theory involving an invariant other than R.

Jurgen Mifsud On the interactions between dark energy and dark matter 28/08/17 3 / 7

Theoretical Model – Background Evolution

In the standard flat FRW metric with conformal time τ, and scale factor a(τ), the Friedmann equations are given by H2 = κ2 3 a2 (ρφ + ρb + ρr + ρc) , H′ = −κ2 6 a2 (ρφ + 3pφ + ρb + 2ρr + ρc) ,

z 0.5 1 1.5 2 a3ρc 0.99 1 1.01 1.02 1.03 1.04 1.05

Uncoupled Conformal Disformal Mixed

where coupled DM is denoted by a subscript c, and H = a′/a. The modified Klein–Gordon equation simplifies to φ′′ + 2Hφ′ + a2V,φ = a2Q , and the fluid conservation equations reduce to ρ′

r + 4Hρr = 0,

ρ′

b + 3Hρb = 0,

ρ′

c + 3Hρc = −Qφ′,

with the coupling function Q = − a2C,φ + D,φφ′2 − 2D C,φ

C φ′2 + a2V,φ + 3Hφ′

2

• a2C + D
• a2ρc − φ′2

ρc .

Jurgen Mifsud On the interactions between dark energy and dark matter 28/08/17 4 / 7

Theoretical Model – Evolution of Perturbations

The matter growth rate function: fm = d ln δm d ln a = δ′

m

Hδm , with

δm = ρbδb+ρcδc

ρb+ρc

– matter density contrast δb – baryon density contrast δc – coupled DM density contrast

On subhorizon scales DM experiences Heff H =1 − 1 H Q ρc φ′ , Geff G =1 + 2 κ2 Q2 ρ2

c

.

k

• h Mpc−1

10 -6 10 -5 10 -4 10 -3 0.01 0.1 1

fm (k, z∗)

0.715 0.72 0.725 0.73 0.735 0.74 0.745 0.75 0.755 0.76

z∗ = 0.50 z∗ = 0.52 z∗ = 0.54 z∗ = 0.56

k

• h Mpc−1

10 -6 10 -5 10 -4 10 -3 0.01 0.1 1

fm (k, z∗)

0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78

Jurgen Mifsud On the interactions between dark energy and dark matter 28/08/17 5 / 7

Parameter Constraints

C(φ) = e2ακφ, D(φ) = D4

M, V (φ) = V 4 0 e−λκφ

Conformal Coupling

0.000 0.025 0.050 0.075 0.100

α

0.0 0.2 0.4 0.6 0.8 1.0

P/Pmax

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

0.0 0.3 0.6 0.9 1.2 λ 0.00 0.02 0.04 0.06 0.08 α TTEE+lensing+ACA+BSHR TTEE+lensing+CA+BSHR TTEE+BSHR TT+BSHR

Disformal & Mixed Couplings

0.0 0.4 0.8 1.2 1.6 λ 0.00 0.25 0.50 0.75 1.00 DM/meV−1 TTEE+lensing +ACA+BSHR TTEE+lensing +CA+BSHR TTEE+BSHR TT+BSHR

0.0 0.4 0.8 1.2 λ 0.0 0.1 0.2 0.3 0.4 α TTEE+lensing +CA+BSHE conformal TTEE+lensing +CA+BSHE (DMV0 = 1) TTEE+lensing +CA+BSHE mixed

Jurgen Mifsud On the interactions between dark energy and dark matter 28/08/17 6 / 7

Conclusions

The cosmological characteristics of the conformal and disformal couplings were discussed. A disformal coupling leads to intermediate–scales time–dependent damped oscillations in the matter growth rate function. The conformal coupling is tightly constrained with the CMB, although the disformal coupling is able to evade this probe. These interacting DE models enhance the growth of small–scale perturbations, thus do not alleviate the claimed LSS tension. Forthcoming data of the LSS, CMB, and their cross-correlations should be able to place tighter constraints on DE couplings.

Jurgen Mifsud On the interactions between dark energy and dark matter 28/08/17 7 / 7

Thank You

Jurgen Mifsud On the interactions between dark energy and dark matter 28/08/17 7 / 7