From Dark Energy to Dark Force Luca Amendola INAF/Osservatorio Astronomico di Roma

Dark energy-dark matter interactions Non-linear observational effects of DE Modified gravity Outline

What do we know about cosmic expansion ? Nucleosynthesis (z~10 9 ) CMB (z~1000) Standard candles (z~1) Perturbations (z~0-1000)

Four hypotheses on dark energy A) Lambda B) scalar field C) modified gravity D) non-linear effect

Scalar field It is more general Scalars are predicted by fundamental theories Compton wavelength = Hubble length V(  )  Observational requirements: A)Evolve slowly B)Light mass

An ultra-light scalar field Abundance Mass L.A. & R. Barbieri 2005

Evolution of background Flat space:

Tracking vs. attractors In a phase space, tracking is a curve, attractor is a point ΩγΩγ ΩKΩK ΩPΩP

The coupling But beside the potential there can be also a coupling…

Dark energy as scalar gravity Einstein frame Jordan frame

Dark energy as scalar gravity T  (m)  = CT (m)   T   = -CT (m)   coupled conservation laws : First basic property:    C 2 /G = scalar-to-tensor ratio

An extra gravity Newtonian limit: the scalar interaction generates an attractive extra-gravity Yukawa term

Local tests of gravity: λ<1 a.u. Only on baryons and on sublunar scales Adelberger et al α λ

Astrophysical tests of gravity: λ<1 Mpc Distribution of dark matter and baryons in galaxies and clusters (rotation curves, virial theorem, X-ray clusters,…) Gradwohl & Frieman 1992 α λ

Cosmological tests of gravity: λ>1/H 0 gravitational growth of structures: CMB, large scale structure

baryons very weakly Since α b =β b 2 <0.001, baryons must be very weakly coupled dark matter strongly Since α c =β c 2 <1.5, dark matter can be strongly coupled

T  (cdm)  = CT (cdm)   T   = -CT (cdm)   T  (bar)  = 0 T  (rad)  = 0 A species-dependent interaction

Dark energy and the equivalence principle cdm baryon cdm G * =G(1+4β 2 /3) G G baryon G

A 3D phase space

Phase spaces © A. Pasqui Ω rad ΩKΩK ΩPΩP

Two qualitatively different cases: weak coupling  strong coupling 

rad mat field rad mat field No coupling coupling  MDE   =   /9 a ~ t p p = 6/(4  2 +9)   = 0 a ~ t p p = 2/3  MDE: kinetic phase, indep. of potential! MDE: today Weak coupling: density trends

The equation of state w=p/  depends on  during  MDE and on  during tracking: w e = 4    past value (decelerated) w  =  present value (accelerated) Deceleration and acceleration Assume V  =   today rad mat field Dominated by kinetic energy β Dominated by potential energy α

 cl) WMAP and the coupling  Planck:  Scalar force 100 times weaker than gravity

strong coupling 

Dark energy Acceleration has to begin at z<1 Perturbations stop growing in an accelerated universe The present value of Ω m depends on the initial conditions Strongly coupled dark energy Acceleration begins at z > 1 Perturbations grow fast in an accelerated universe The present value of Ω m does not depend on the initial conditions

A Strong coupling and the coincidence problem …  < 1  > 1 today Weak: Strong:

High redshift supernovae at z > 1 L.A., M. Gasperini & F. Piazza: 2002 MNRAS, 2004 JCAP

Dream of a global attractor

Stationary models coupling slope bar stationary large β any μ baryon epoch ! baryondensity is the controllingfactor

Does it work ?

constraints from SN, constraints on omega constraints from ISW Does it work ? No ! L. A. & D. Tocchini-Valentini 2002

Second try Generalized coupled scalar field Lagrangian Under which condition one gets a stationary attractor Ω, w constant?

Theorem A stationary attractor is obtained if and only if Piazza & Tsujikawa 2004 L.A., M. Quartin, I. Waga, S. Tsujikawa 2006 For instance : dark energy with exp. pot. tachyon field dilatonic ghost condensate

Perturbations on Stationary attractors New perturbation equation in the Newtonian limit which can be written using only the observable quantities w,Ω L.A., S. Tsujikawa, M. Sami, 2005

Analytical solution Therefore we have an analytical solution for the growth of linear perturbations on any stationary attractor: In ordinary scalar field cosmology, m lies between 0 and 1. Now it can be larger than 1, negative or complex ! Two interesting regions: phantom (p ;X 0)

Phantom damping contour plot of Re(m) Theorem 1: a phantom field on a stationary attractor always produces a damping of the perturbations: Re(m)<0.

Does it work? Theorem 2: the gravitational potential is constant (i.e. no ISW) for Poisson equation Still quite off the SN constraints !!

A No-Go theorem Take a general p(X,U) Require a sequence of decel. matter era followed by acceleration Theorem: no function p(X,U) expandable in a finite polynomial can achieve a standard sequence matter+scaling acceleration ! END OF THE SCALING DREAM ??? L.A., M. Quartin, I. Waga, S. Tsujikawa 2006

Background expansion Linear perturbations What’s next ?

Non-linearity 1) N-Body simulations 2) Higher-order perturbation theory

Interactions Two effects: DM mass is varying, G is different for baryons and DM mbmb mcmc

N-body recipe Flag particles either as CDM (c) or baryons (b) in proportions according to present value Flag particles either as CDM (c) or baryons (b) in proportions according to present value Give identical initial conditions Give identical initial conditions Evolve them according the their Newtonian equation: at each step we calculate two gravitational potentials and evolve the c particle mass Evolve them according the their Newtonian equation: at each step we calculate two gravitational potentials and evolve the c particle mass Reach a predetermined variance Reach a predetermined variance Evaluate clustering separately for c and b particles Evaluate clustering separately for c and b particles Modified Adaptive Refinement Tree code (Kravtsov et al. 1997, Mainini et al, Maccio’ et al. 2003) Modified Adaptive Refinement Tree code (Kravtsov et al. 1997, Mainini et al, Maccio’ et al. 2003) Collab. with S. Bonometto, A. Maccio’, C. Quercellini, R. Mainini PRD69, 2004

N-body simulations © A. Maccio’ Λ β=0.15 β=0.25

N-body simulations © A. Maccio’ β=0.15 β=0.25

N-body simulations: halo profiles β dependent behaviour towards the halo center. Higher β: smaller r c

A scalar gravity friction The extra friction term drives the halo steepening The extra friction term drives the halo steepening How to invert its effect ? How to invert its effect ? Which cosmology ? Which cosmology ?

Linear Newtonian perturbations A field initially Gaussian remains Gaussian: the skewness S 3 is zero Non-linearity: Higher order perturbation theory

Non-linear Newtonian perturbations A field initially Gaussian develops a non-Gaussianity: the skewness S 3 is a constant value Independent of Ω, of eq. of state, etc.: S 3 is a probe of gravitational instability, not of cosmology (Peebles 1981)

Non-linear scalar-Newtonian perturbations the skewness S 3 is a constant therefore S 3 is also a probe of dark energy interaction (L.A. & C. Quercellini, PRL 2004)

Skewness as a test of DE coupling Sloan DSS: Predicted error on S 3 less than 10%

Modified 3D gravity A) Lambda B) scalar field C) modified gravity D) non linear effect Simplest case: Higher order gravity ! Turner, Carroll, Capozziello, Odintsov… L.A., S. Capozziello, F. Occhionero, 1992

Modified N-dim gravity A) Lambda B) scalar field C) modified gravity D) non linear effect Simplest case:

Aspects of the same physics A) Lambda B) scalar field C) modified gravity D) non linear effect Extra-dim. Degrees of freedom Higher order gravity Coupled scalar field Scalar-tensor gravity

The simplest case A) Lambda B) scalar field C) modified gravity D) non linear effect is equivalent to coupled dark energy But with strong coupling !

R+1/R model R+1/R model A) Lambda B) scalar field C) modified gravity D) non linear effect rad mat field rad mat field  MDE today

R+R n model R+R n model A) Lambda B) scalar field C) modified gravity D) non linear effect L.A., S. Tsujikawa, D. Polarski 2006

Distance to last scattering in R+R n model A) Lambda B) scalar field C) modified gravity D) non linear effect

General f(R, Ricci, Riemann) A) Lambda B) scalar field C) modified gravity D) non linear effect we find again the same past behavior: so probably most of these models are ruled out.

Anti-gravity has many side-effects…