The dark matter sector and new forces mediated by dark energy Carsten van de Bruck University of Sheffield work in progress with Anthony Brookfield and Lisa Hall

Scalar fields coupled to matter (Brans, Dicke (1961); Wetterich (1988,1995); Amendola (1999);...; Brax, vdB, Davis, Rhodes (2003)) Typical form of action: S = R d 4 x p ¡ g £ 2 · 1 ¹ º @ Á V ( ) ¤ + m a t ª ; A R : i c s a l r ª a : M t e r ¯ l d s A ( Á ) : C o u p l i n g f c t s , m a e b ¯ d !

) Geodesic equation: ® = + ¡ = ® 2 x ¹ ¿ + ¡ º ¸ = ® @ Á ¡ ¹ º ¸ : C h r i s t o ® e l - S y m b ® = @ l n m ( Á ) Scalar field transmits new force between particles ! )

Klein-Gordon-Equation: (e.g. Wetterich (1995); Amendola (1999);...; Brax, vdB, Davis, Rhodes (2003)) Ä Á + 3 H _ @ V l n m ( ) ½ ¡ p = Coupling terms: _ ½ + 3 H ( p ) = @ l n m Á ¡ Examples: CDM, neutrinos,...

Ususal assumptions about dark sector: One dark matter candidate Weakly interacting particles Dark matter interacts not with dark energy. This view has been challenged recently (coupled quintessence) Neutrinos: usually decoupled from dark energy; recently also challenged (mass-varying neutrinos)

Considered here: More complex dark matter sector; not only one species. Both could behave as CDM. But they could also behave like mixed dark matter (MDM): one cold species (needed for structure formation) and one species which had non-negligible pressure for some time during cosmic history (HDM, e.g. neutrinos). Couple both to dark energy sector (not with the same strength) → New force between these species!

Evolution of density contrast (in Fourier space): ¢ i = ½ Species i Ä ¢ i + H = 4 ¼ P j G N ( 1 2 ¯ k a m Á ) ½ G N = e w t o n s c a k = w a v e n u m b r

Effective gravitational constant between species: ( i j ) e f N = 1 + 2 ¯ k a m Á where k = 2 ¼ ¸ m 2 Á = d V If couplings have opposite sign, Geff can be smaller than GN (between these species).

Three cases: V ( Á ) = e Case β1 β2 CDM only (λ = 1.2) 4 0.1 -1.5 1 e ¡ ¸ Case β1 β2 CDM only (λ = 1.2) 4 0.1 -1.5 1 MDM (λ = 2) 5.8 (neutrinos) -0.1(CDM) ­ c h 2 = : 1 ­ º h 2 = : 7

Case 1 (CDM only):

Case 2 (CDM only):

Case 3 (MDM):

Background evolution: Multi-fluid can mimic a single fluid with effective coupling: ¯ e ® = P i ( ½ ¡ 3 p ) Effective coupling is not constant. Observer assuming one fluid would deduce time-varying coupling. Effective coupling is the weighted coupling.

Evolution of effective coupling: Case 1 Case 3 Case 2

Effective coupling can go through zero Effective coupling can go through zero! This happens if the couplings have opposite signs. So, in matter dominated epoch, the background evolution behaves like if there is one uncoupled fluid. In case 3, the neutrino mass is growing in time (as in recent work by Amendola, Baldi & Wetterich). This degeneracy is broken at perturbative level: perturbations receive contributions from a) perturbation of number density and b) perturbation of mass (through scalar field). m i = e ¯ Á

Heuristically: Field follows minimum @ V e f Á = + P ¯ i ( ½ ¡ 3 p ) ¼ This holds for „quintessential“ potentials. ¯ e ® = P i ( ½ ¡ 3 p ) ¼ So: Requires couplings with opposite signs.

Apparent equation of state: Usually assumed: This is not the case here! „Absorb“ that into the evolution of dark energy. This results in an „apparent equation of state“: ½ m / a ¡ 3 m p a r t i c l e = f ( Á ) w a p = Á 1 ¡ x x = ¡ ½ ( ) m a 3 Á ³ f 1 ) (Das et al 2006)

Evolution of apparent equation of state: Case 2 Case 1 Case 3

CMB power spectrum (Case 1)

CMB power spectrum (Case 2)

CMB power spectrum (Case 3)

Power specra (Case 1) β = βeff β = 0

Power spectra (Case 2)

Power spectra (Case 3)

Future directions: Compare theory (3 cases) to data (CMB + LSS) (expect β<0.1). Even if background is mimicked by single fluid with vanishing coupling, studying the matter power spectrum may reveal small couplings. Explore large coupling case in more detail: chameleon scenarios based on multiple couplings (Brax, vdB, Davis, Hall). What about effective equation of state in these model? Include baryons in the analysis! No reason to believe that baryons are decoupled! Field dependent couplings: can observed properties of particles be fixed by such mechanism (c.f. Damour & Polyakov („Least coupling principle“ (1994)))?