Unified Dark Matter Models Daniele Bertacca Dipartimento di Fisica “Galileo Galilei”, Via Marzolo 8, Padova, Italy The Unity of the Universe 29th June - 1st July 2009

–D. Bertacca, S. Matarrese, M. Pietroni, Unified Dark Matter in Scalar Field Cosmologies. Mod. Phys. Lett. A22: ,2007 e-Print:astro-ph/ v3 – D. Bertacca, N. Bartolo, ISW effect in Unified Dark Matter Scalar Field Cosmologies: An analytical approach. JCAP 0711:026,2007 e-Print: arXiv: v3 [astro-ph] –D.Bertacca, N.Bartolo, S. Matarrese, Haloes of Unified Dark Matter. JCAP 05(2008)005 e-Print: arXiv: v2 [astro-ph] – D.Bertacca, N.Bartolo, A.Diaferio, S.Matarrese, How Unified Dark Matter in Scalar Field can cluster. JCAP 0810:023,2008 e-Print: arXiv: v3 [astro-ph] – S.Camera, D.Bertacca, A.Diaferio, N.Bartolo, S.Matarrese, Weak lensing signal in Unified Dark Matter models. e-Print: arXiv: Credits

Observational Evidence The confidence regions coming from SN I a, CMB and BAO. The flat Universe without Λ is ruled out. The compilation of cosmological data sets the need for a dark energy dominated Universe with Ω M ≈ 0.274, Ω DE ≈ Combination of SNe with BAO (Eisenstein et. al., 2005) CMB (WMAP-5 year data, 2008) (Marek Kowalski 2008)

Theoretical Motivations I focus on Unified Models of Dark Matter and Dark Energy (UDM) Alternative to understand the nature of the Dark Matter and Dark Energy components of the Universe.

In UDM models there are two simple but distinctive aspects: 1.The fluid which triggers the accelerated expansion at late times is also the one which has to cluster in order to produce the structures.

In UDM models there are two simple but distinctive aspects: 1.The fluid which triggers the accelerated expansion at late times is also the one which has to cluster in order to produce the structures. 2.From the last scattering to the present epoch, the energy density of the Universe is dominated by a single dark fluid, the gravitational potential evolution is determined by the background and perturbation evolution of a single component.

Advantages over DM + DE (ΛCDM): - There is a single fluid that behaves both as DM and DE.

Advantages over DM + DE (ΛCDM): - There is a single fluid that behaves both as DM and DE. Disadvantages over DM + DE (ΛCDM): - Success of UDM models strongly depend on the effective speed of sound.

Advantages over DM + DE (ΛCDM): - There is a single fluid that behaves both as DM and DE. Disadvantages over DM + DE (ΛCDM): - Success of UDM models strongly depend on the effective speed of sound.  When the speed of sound very small Constraint satisfied for: CMB anisotropies The formation of the structures in the Universe.

Advantages over DM + DE (ΛCDM): - There is a single fluid that behaves both as DM and DE. Disadvantages over DM + DE (ΛCDM): - Success of UDM models strongly depend on the effective speed of sound.  When the speed of sound very small  Otherwise : Constraint satisfied for: CMB anisotropies The formation of the structures in the Universe. Corresponds to the appearance of a non zero Jeans length.

Advantages over DM + DE (ΛCDM): - There is a single fluid that behaves both as DM and DE. Disadvantages over DM + DE (ΛCDM): - Success of UDM models strongly depend on the effective speed of sound.  When the speed of sound very small  Otherwise : Constraint satisfied for: CMB anisotropies The formation of the structures in the Universe. Corresponds to the appearance of a non zero Jeans length. Oscillating behavior of the dark fluid perturbations below the Jeans length Strong time dependence of the gravitational potential

Advantages over DM + DE (ΛCDM): - There is a single fluid that behaves both as DM and DE. Disadvantages over DM + DE (ΛCDM): - Success of UDM models strongly depend on the effective speed of sound c s 2.  When the speed of sound very small  Otherwise : Constraint satisfied for: CMB anisotropies The formation of the structures in the Universe. Corresponds to the appearance of a non zero Jeans length. Oscillating behavior of the dark fluid perturbations below the Jeans length Strong time dependence of the gravitational potential When c s becomes large at late times, strong deviations from the usual ISW effect of ΛCDM models (Bertacca & Bartolo 2007).

(1) Adiabatic UDM fluid - P=p(ρ): effective speed of sound is the same as the adiabatic speed of sound: very strong fine tuning.

(1) Adiabatic UDM fluid - P=p(ρ): effective speed of sound is the same as the adiabatic speed of sound: very strong fine tuning. In this models, imposing a constraint on the speed of sound c s 2, in the same time, we obtain a very strong fine tuning on the equation state, w

(1) Adiabatic UDM fluid - P=p(ρ): effective speed of sound is the same as the adiabatic speed of sound: very strong fine tuning. -Chaplygin and generalized Chaplygin Gas (Kamenshchik et al. 2001; Bilic et al. 2002; Bento et al. 2002) ΛCDM recovered for α ≈ 0. For |α| ≥ 10 −5 ruled out by observation (Sandvik et al 2004).

(1) Adiabatic UDM fluid - P=p(ρ): effective speed of sound is the same as the adiabatic speed of sound: very strong fine tuning. -Chaplygin and generalized Chaplygin Gas (Kamenshchik et al. 2001; Bilic et al. 2002; Bento et al. 2002) ΛCDM recovered for α ≈ 0. For |α| ≥ 10 −5 ruled out by observation (Sandvik et al 2004). - Dark perfect fluid with two-parameter barotropic equation of state (Balbi et al 2007, Quercellini et al 2007) UDM with constant speed of sound ΛCDM recovered for α ≈ 0. Constraints from the matter power spectrum data, α <10 -7 (Pietrobon et al 2008).

(2) Non Adiabatic UDM In this case the effective speed of sound c s 2 differs from the adiabatic one.

(2) Non Adiabatic UDM In this case the effective speed of sound c s 2 differs from the adiabatic one. – e.g., scalar field Lagrangian with standard kinetic term, c s 2 =1 (Quintessence: good for dark energy, not for UDM models) Ex: seeking a Lagrangian that reproduces the background evolution of ΛCDM, i.e. when p ≈ -Λ [Bertacca, Matarrese, Pietroni (2007)]. In conflict with cosmological structure formation!

(2) Non Adiabatic UDM In this case the effective speed of sound c s 2 differs from the adiabatic one. – e.g., scalar field Lagrangian with standard kinetic term, c s 2 =1 (Quintessence: good for dark energy, not for UDM models) Scalar field Lagrangian with non standard kinetic term: k-essence We can obtain at the same time the proper background evolution (w) and the right structure formation (c s 2 ) (Bertacca, Bartolo, Diaferio & Matarrese, JCAP 0810:023, 2008)

Scalar field, p and ρ given by p=L(φ,X), ρ=2X∂L(φ,X)/∂X-L(φ,X), c s 2 =p,X /ρ,X construct Lagrangians to obtain Unified Dark Matter Models. UDM with Lagrangian L(φ,X)

Scalar field, p and ρ given by p=L(φ,X), ρ=2X∂L(φ,X)/∂X-L(φ,X), c s 2 =p,X /ρ,X construct Lagrangians to obtain Unified Dark Matter Models. We consider L(φ,X) = f(φ)g(X)-V(φ). Then w(φ,X) and c s 2 (X) i.e. we can separately construct the equation of state w and the speed of sound c s 2. UDM with Lagrangian L(φ,X)

Scalar field, p and ρ given by p=L(φ,X), ρ=2X∂L(φ,X)/∂X-L(φ,X), c s 2 =p,X /ρ,X construct Lagrangians to obtain Unified Dark Matter Models. We consider L(φ,X) = f(φ)g(X)-V(φ). Then w(φ,X) and c s 2 (X) i.e. we can separately construct the equation of state w and the speed of sound c s 2. This feature does not occur when we consider Lagrangians with purely kinetic term (Ex, adiabatic fluid p=p(ρ) ), Lagrangians L = f(φ)g(X) or L = g(X)-V(φ). UDM with Lagrangian L(φ,X)

UDM Lagrangian L(φ,X) = f(φ)g(X)-V(φ) We seek a Lagrangian that reproduces the background evolution of ΛCDM.

UDM Lagrangian L(φ,X) = f(φ)g(X)-V(φ) We seek a Lagrangian that reproduces the background evolution of ΛCDM. Assuming that the kinetic term is of the Infield type

UDM Lagrangian L(φ,X) = f(φ)g(X)-V(φ) We seek a Lagrangian that reproduces the background evolution of ΛCDM. Assuming that the kinetic term is of the Infield type Imposing that

UDM Lagrangian L(φ,X) = f(φ)g(X)-V(φ) We seek a Lagrangian that reproduces the background evolution of ΛCDM. Assuming that the kinetic term is of the Infield type Imposing that We can derive X(a), φ(a), during various epochs, and, finally, we can construct the functional form of f(φ) and V(φ).

In the Figure we show the normalized potentials Φ k (a) Φ k (0) for ΛCDM (solid) and UDM (dot-dashed). The lower panel shows potentials at k = h Mpc -1, the medium panel at k =0.01 h Mpc -1 and the upper panel at k = 0.1 h Mpc -1. UDM curves are for c ∞ 2 = ; ; from top to bottom, respectively. At small c ∞ 2, ΛCDM and UDM curves are indistinguishable.

In the Figure we show linear power spectrum of UDM models for c ∞ 2 = ; ; ; ; from top to bottom, respectively. At small, i.e. c ∞ 2 = ; 10 -6, ΛCDM and UDM curves are indistinguishable and we obtain results that are in excellent agreement with the real data the power spectrum. The evolution of scalar perturbations is made by O.Piattella using the CAMB code.

In the Figure we show CMB, of UDM models for c ∞ 2 = ; ; ; 0.5 from bottom to top, respectively. For c ∞ 2 = 10 -4, ΛCDM and UDM curves are indistinguishable obtaining results that are in excellent agreement with the 5 year WMAP release. The evolution of scalar perturbations is made by O.Piattella using the CAMB code.

Conclusions I focus UDM models: alternative to understand the nature of the Dark Matter and Dark Energy components of the Universe.

Conclusions I focus UDM models: alternative to understand the nature of the Dark Matter and Dark Energy components of the Universe. Starting from L=L(φ,X), we have proposed a technique to construct models where the effective speed of sound is small enough that the scalar field can cluster.

Conclusions I focus UDM models: alternative to understand the nature of the Dark Matter and Dark Energy components of the Universe. Starting from L=L(φ,X), we have proposed a technique to construct models where the effective speed of sound is small enough that the scalar field can cluster. In Camera, Bertacca, Diaferio, Bartolo, Matarrese (2009) We have studied the weak lensing cosmic convergence signal power-spectrum. Weak lensing is more sensitive to the variations of c ∞ 2 ≥ for sources located at low redshifts.

Conclusions I focus UDM models: alternative to understand the nature of the Dark Matter and Dark Energy components of the Universe. Starting from L=L(φ,X), we have proposed a technique to construct models where the effective speed of sound is small enough that the scalar field can cluster. In Camera, Bertacca, Diaferio, Bartolo, Matarrese (2009) We have studied the weak lensing cosmic convergence signal power-spectrum. Weak lensing is more sensitive to the variations of c ∞ 2 ≥ for sources located at low redshifts. In Bertacca, Bartolo, Matarrese (2007), we have investigated static spherically symmetric solutions (“dark halos”) of Einstein’s equations for a scalar field with non-canonical kinetic term (see also Armendariz-Picon & Lim 2005).

Conclusions I focus UDM models: alternative to understand the nature of the Dark Matter and Dark Energy components of the Universe. Starting from L=L(φ,X), we have proposed a technique to construct models where the effective speed of sound is small enough that the scalar field can cluster. In Camera, Bertacca, Diaferio, Bartolo, Matarrese (2009) We have studied the weak lensing cosmic convergence signal power-spectrum. Weak lensing is more sensitive to the variations of c ∞ 2 ≥ for sources located at low redshifts. In Bertacca, Bartolo, Matarrese (2007), we have investigated static spherically symmetric solutions (“dark halos”) of Einstein’s equations for a scalar field with non-canonical kinetic term (see also Armendariz-Picon & Lim 2005). Future works: Unified DM/DE Models on non-linear theory structure formation in UDM models With Bartolo and Corasaniti, I am studying the constraints on power spectrum from current observation of large-scale structure of the universe With Piattella, Bruni and Pietrobon, I am studying a new class of UDM models with adiabatic equations of state.

Considering small inhomogeneities of the scalar field [Garriga & Mukhanov (1999)] and assuming that the metric in the longitudinal (Newtonian) gauge where and, and with (effective) speed of sound c s

The role of the (effective) speed of sound c s in UDM Models Defining an effective Jeans length, we obtain The result of this general trend is that the possible appearance of c s ≠ 0 corresponds to the appearance of a non zero Jeans length. It makes the oscillating behavior of the dark fluid perturbations below the Jeans length immediately visible through a strong time dependence of the gravitational potential (Bertacca & Bartolo 2007). One can verify that the scalar field fluctuations oscillate and decay in time as

The role of the (effective) speed of sound c s : Integrated Sachs-Wolfe effect in UDM Models. Therefore the speed of sound plays a major role in the evolution of the scalar field perturbations and in the growth of the over-densities. If c s is significantly different from zero it can alter the evolution of density of linear and non-linear perturbations [(Hu 1998) and (Giannakis & Hu 2005)]. Finally, when c s becomes large at late times, this leads to strong deviations from the usual ISW effect of ΛCDM models (Bertacca & Bartolo 2007). Indeed performing an analytical study of the ISW effect we obtain that When i.e. we find a similar slope as the one in the ΛCDM models (Kofman & Starobinsky 1985). In this case ISW is dictated by the background evolution, which causes the time decay of the gravitational potential when the negative pressure starts to dominate. When in the there are terms that are proportional to the speed of sound and they grow as l increases. There is a more dangerous term which makes the power spectrum scale as l 3 up to. This value of l I SW depends on modes that enter within the horizon during the radiation dominated epoch: Meszaros effect. This is effect that the matter fluctuations suffer until the full matter domination epoch.