From Dark Energy to Dark Force Luca Amendola

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

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

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

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

What do we know about cosmic expansion ? Nucleosynthesis (z~109) CMB (z~1000) Standard candles

What do we know about cosmic expansion ? Nucleosynthesis (z~109) 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)

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

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

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

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

Evolution of background Flat space:

Evolution of background Flat space:

Tracking vs. attractors In a phase space, tracking is a curve, attractor is a

Tracking vs. attractors In a phase space, tracking is a curve, attractor is a point Ωγ ΩP ΩK

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

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 Einstein frame Jordan frame

Dark energy as scalar gravity T (m) = CT(m) T = -CT(m) coupled conservation

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

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

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

Local tests of gravity: λ<1 a. u. α Only on baryons and on sublunar scales λ Adelberger et al. 2002

Astrophysical tests of gravity: λ<1 Mpc Distribution of dark matter and baryons in galaxies

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

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

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

Since αb=βb 2<0. 001, baryons must be very weakly coupled Since αc=βc 2<1. 5,

Since αb=βb 2<0. 001, baryons must be very weakly coupled Since αc=βc 2<1. 5, dark matter can be strongly coupled

A species-dependent interaction T (cdm) = CT(cdm) T = -CT(cdm) T (bar) = 0

A species-dependent interaction T (cdm) = CT(cdm) T = -CT(cdm) T (bar) = 0 T (rad) = 0

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

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

A 3 D phase space

A 3 D phase space

Phase spaces Ωrad ΩP ΩK © A. Pasqui

Phase spaces Ωrad ΩP ΩK © A. Pasqui

Two qualitatively different cases: weak coupling strong coupling

Two qualitatively different cases: weak coupling strong coupling

to da y Weak coupling: density trends No coupling MDE: = 0 mat a

to da y Weak coupling: density trends No coupling MDE: = 0 mat a ~ tp p = 2/3 coupling MDE: rad field rad = /9 a ~ tp p = 6/(4 2+9) kinetic phase, indep. of potential! mat MDE field

Deceleration and acceleration to da y Assume V ) = -a rad Dominated by

Deceleration and acceleration to da y Assume V ) = -a rad Dominated by kinetic energy β mat Dominated by potential energy α field The equation of state w=p/r depends on during MDE and on a during tracking: we = 4 / : past value (decelerated) w = - / a+ ) : present value (accelerated)

WMAP and the coupling cl) Planck: Scalar force 100 times weaker than gravity

WMAP and the coupling cl) Planck: Scalar force 100 times weaker than gravity

strong coupling

strong coupling

Dark energy • Acceleration has to begin at z<1 • Perturbations stop growing in

Dark energy • Acceleration has to begin at z<1 • Perturbations stop growing in an accelerated universe • The present value of Ωm 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 Ωm does not depend on the initial conditions

to da y A Strong coupling and the coincidence problem… Weak: < 1 Strong:

to da y A Strong coupling and the coincidence problem… Weak: < 1 Strong: > 1

High redshift supernovae at z > 1 L. A. , M. Gasperini & F.

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

Dream of a global attractor

Dream of a global attractor

Stationary models large β any μ slope stationary baryon epoch ! coupling baryon density

Stationary models large β any μ slope stationary baryon epoch ! coupling baryon density is the controlling factor

Does it work ?

Does it work ?

Does it work ? No ! constraints from SN, constraints on omega constraints from

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

Second try Generalized coupled scalar field Lagrangian Under which condition one gets a stationary

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

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

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

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) and non-phantom (p; X>0)

Phantom damping contour plot of Re(m) Theorem 1: a phantom field on a stationary

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? Poisson equation Theorem 2: the gravitational potential is constant (i. e.

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

A No-Go theorem • • L. A. , M. Quartin, I. Waga, S. Tsujikawa

A No-Go theorem • • L. A. , M. Quartin, I. Waga, S. Tsujikawa 2006 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 ? ? ?

Background expansion Linear perturbations What’s next ?

Background expansion Linear perturbations What’s next ?

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

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

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

Interactions • Two effects: DM mass is varying, G is different for baryons and DM mb mc

N-body recipe • • • Flag particles either as CDM (c) or baryons (b)

N-body recipe • • • Flag particles either as CDM (c) or baryons (b) in proportions according to present value Give identical initial conditions Evolve them according their Newtonian equation: at each step we calculate two gravitational potentials and evolve the c particle mass Reach a predetermined variance Evaluate clustering separately for c and b particles 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 PRD 69, 2004

N-body simulations Λ β=0. 15 © A. Maccio’ β=0. 25

N-body simulations Λ β=0. 15 © A. Maccio’ β=0. 25

N-body simulations β=0. 15 β=0. 25 © A. Maccio’

N-body simulations β=0. 15 β=0. 25 © A. Maccio’

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

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

A scalar gravity friction • • • The extra friction term drives the halo

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

Non-linearity: Higher order perturbation theory Linear Newtonian perturbations A field initially Gaussian remains Gaussian:

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

Non-linear Newtonian perturbations A field initially Gaussian develops a non-Gaussianity: the skewness S 3

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

Non-linear scalar-Newtonian perturbations the skewness S 3 is a constant (L. A. & C.

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

Skewness as a test of DE coupling Sloan DSS: Predicted error on S 3

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

Modified 3 D gravity A) Lambda B) scalar field Higher order gravity ! C)

Modified 3 D gravity A) Lambda B) scalar field Higher order gravity ! C) modified gravity D) non linear effect Simplest case: 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

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 Extra-dim. Degrees of freedom

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

The simplest case A) Lambda is equivalent to coupled dark energy B) scalar field

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

da y R+1/R model B) scalar field to A) Lambda rad mat C) modified

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

n R+R model A) Lambda B) scalar field C) modified gravity D) non linear

n R+R 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+Rn model A) Lambda B) scalar field C) modified

Distance to last scattering in R+Rn 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 we find

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

Anti-gravity has many side-effects…

Anti-gravity has many side-effects…