On the interactions between dark energy and dark matter Jurgen - PowerPoint PPT Presentation

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 3 rd Azores School on Observational Cosmology 5 th 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 � 4 ∼ � 4 , � 10 − 3 eV � 10 − 30 M Pl Λ obs. ∼ when compared with the theoretical expectation of Λ theory ∼ ( TeV ) 4 ∼ 10 − 60 M 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 � 4 ∼ � 4 , � 10 − 3 eV � 10 − 30 M Pl Λ obs. ∼ when compared with the theoretical expectation of Λ theory ∼ ( TeV ) 4 ∼ 10 − 60 M 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 � 4 ∼ � 4 , � 10 − 3 eV � 10 − 30 M Pl Λ obs. ∼ when compared with the theoretical expectation of Λ theory ∼ ( TeV ) 4 ∼ 10 − 60 M 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 � 4 ∼ � 4 , � 10 − 3 eV � 10 − 30 M Pl Λ obs. ∼ when compared with the theoretical expectation of Λ theory ∼ ( TeV ) 4 ∼ 10 − 60 M 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: � M 2 d 4 x √− g � � 2 R − 1 Pl 2 g µν ∂ µ φ ∂ ν φ − V ( φ ) + L SM S = � g ˜ d 4 x � + − ˜ L DM (˜ g µν , ψ ) , where κ 2 ≡ M − 2 Pl ≡ 8 πG together with R – Ricci scalar, φ – DE scalar field, V ( φ ) – potential of the scalar field, L SM – 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: � M 2 d 4 x √− g � � 2 R − 1 Pl 2 g µν ∂ µ φ ∂ ν φ − V ( φ ) + L SM S = � g ˜ d 4 x � + − ˜ L DM (˜ g µν , ψ ) , Particle quanta of the DM fields ψ , propagate on geodesics defined by the metric ˜ g µν = C ( φ ) g µν + D ( φ ) ∂ µ φ ∂ ν φ , 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 1.05 In the standard flat FRW metric with Uncoupled Conformal 1.04 Disformal conformal time τ , and scale factor a ( τ ) , the Mixed 1.03 Friedmann equations are given by a 3 ρ c 1.02 κ 2 3 a 2 ( ρ φ + ρ b + ρ r + ρ c ) , H 2 1.01 = 1 − κ 2 6 a 2 ( ρ φ + 3 p φ + ρ b + 2 ρ r + ρ c ) , 0.99 0 0.5 1 1.5 2 H ′ = z where coupled DM is denoted by a subscript c , and H = a ′ /a . The modified Klein–Gordon equation simplifies to φ ′′ + 2 H φ ′ + a 2 V ,φ = a 2 Q , and the fluid conservation equations reduce to ρ ′ ρ ′ ρ ′ c + 3 H ρ c = − Qφ ′ , r + 4 H ρ r = 0 , b + 3 H ρ b = 0 , with the coupling function � C ,φ a 2 C ,φ + D ,φ φ ′ 2 − 2 D C φ ′ 2 + a 2 V ,φ + 3 H φ ′ � Q = − ρ c . � � a 2 ρ c − φ ′ 2 �� a 2 C + D 2 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: 0.76 z ∗ = 0 . 50 z ∗ = 0 . 52 z ∗ = 0 . 54 z ∗ = 0 . 56 0.755 f m = d ln δ m δ ′ m 0.75 d ln a = , H δ m 0.745 f m ( k, z ∗ ) 0.74 with 0.735 0.73 δ m = ρ b δ b + ρ c δ c – matter ρ b + ρ c 0.725 density contrast 0.72 0.715 δ b – baryon density contrast 10 -6 10 -5 10 -4 10 -3 0.01 0.1 1 � h Mpc − 1 � δ c – coupled DM density k contrast 0.78 On subhorizon scales DM 0.77 experiences 0.76 f m ( k, z ∗ ) 0.75 H eff =1 − 1 Q φ ′ , 0.74 ρ c H H 0.73 Q 2 G eff =1 + 2 0.72 . κ 2 ρ 2 0.71 G c 10 -6 10 -5 10 -4 10 -3 0.01 0.1 1 � h Mpc − 1 � k Jurgen Mifsud On the interactions between dark energy and dark matter 28/08/17 5 / 7

Parameter Constraints C ( φ ) = e 2 ακφ , D ( φ ) = D 4 M , V ( φ ) = V 4 0 e − λκφ TTEE+lensing+ACA+BSHE TTEE+lensing+ACA+BSHR TTEE+lensing+FCA+BSHR TTEE+lensing+FCA+BSHE TTEE+lensing+CA+BSHE TTEE+lensing+CA+BSHR TTEE+lensing+ACA+BSHR TTEE+lensing+CA+BSHR TTEE+BSHR TT+BSHR Conformal Coupling Disformal & Mixed Couplings TTEE+lensing 1.00 1.0 +ACA+BSHE TTEE+lensing +ACA+BSHR 0.8 0.75 TTEE+lensing +FCA+BSHE D M / meV − 1 P/P max 0.6 TTEE+lensing +FCA+BSHR 0.50 TTEE+lensing 0.4 TTEE+lensing +CA+BSHE +ACA+BSHR TTEE+lensing TTEE+lensing 0.25 +CA+BSHR +CA+BSHR 0.2 TTEE+BSHR TT+BSHR 0.0 0.00 0.0 0.4 0.8 1.2 1.6 0.000 0.025 TTEE+lensing+ACA+BSHR TTEE+lensing+CA+BSHR 0.050 TTEE+BSHR TT+BSHR 0.075 0.100 λ α 2017-04-11_305999_ 2017-04-14_289000_ 2017-03-12_235000_ TTEE+lensing TTEE+lensing+ACA+BSHR 0.08 +CA+BSHE TTEE+lensing+CA+BSHR conformal 0.4 TTEE+BSHR TTEE+lensing +CA+BSHE TT+BSHR ( D M V 0 = 1) 0.06 TTEE+lensing 0.3 +CA+BSHE mixed α α 0.04 0.2 0.02 0.1 0.00 0.0 0.0 0.3 0.6 0.9 1.2 0.0 0.4 0.8 1.2 λ λ Jurgen Mifsud On the interactions between dark energy and dark matter 28/08/17 6 / 7