Transcript Dark Energy

Dark Energy and Extended
Gravity theories
Francesca Perrotta
(SISSA, Trieste)
Overview
• The case for Dark Energy and possible
approaches;
• “Quintessence’’ models properties;
• Extended Gravity Theories: effects on
cosmological background evolution (expansion
rate, R-boost) and perturbative effects (CMB,
weak lensing, clustering properties);
• Current constraints on G variations
The case for Dark Energy
In the old standard picture, Gravity is an attractive force,
decelerating the cosmic expansion by means of the mutual
attraction between matter particles and structures.
This scenario has been upset when distant Type 1A Supernovae
evidenced an accelerating expansion of the Universe
(Riess et al. 1998; Perlmutter et al. 1999).
CMB and LSS observations strengthen this view.
 Some type of “DARK ENERGY” must drive the
acceleration through a REPULSIVE gravitational force.
POSSIBLE APPROACHES:
i)
Add a new component with negative equation of
state (e.g. Quintessence fields);
ii) Geometrically modify Gravity, e.g. including  or
terms depending on the curvature;
iii) Add a new fundamental force coupling (Extended
theories of Gravity).
The cosmological constant 
1
8G
Rik  gik R  gik  4 Tik
2
c
If arising from the “zero point” quantum fluctuations of the
known forms of matter (“vacuum energy”), then
Imposing an ultraviolet cutoff at the Planck scale,
T00

c
/
G


10
GeV
vac
5
  10
47
while
2
GeV
76
4
4
 discrepancy of 123 orders of magnitude !
“Quintessence’’ models of DE
A classical, minimally-coupled scalar field evolves in a potential
V(f),while its energy density and pressure combine to produce a
negative equation of state w=p/ .
Unlike the cosmological constant, the Quintessence field
admits fluctuations f.
• Fine-tuning problem: in analogy with , the need to tune initial
values of fto get the observed energy density and equation of state;
• “Coincidence’’ problem: why m ~ f just today ?
 Search for ATTRACTOR SOLUTIONS (“tracking fields”)
e.g. Ratra-Peebles (1988) potential:
V
M
4 
f
Tracking solutions are defined in the background
(matter or rad.) dominated epoch. In the present
Quintessence-dominated era, the field has already
passed the tracking phase.
Analyzing the post-tracking regime, good trackers
(attractors with large basin of attraction) end
up with an e.o.s. too different from –1, ruled out
by observations of CMB, LSS, IA Supernovae
(Bludmann 2004).
wQ  0.98  0.12
(Spergel et al. 2003)
The fine-tunig problem is resumed (Bludman 2004)
Beyond General Relativity
• Can the Dark Energy be the signature of a
modification of Gravity?
• Hints from Quantum Gravity:  coupled to R to
allow for a mechanics of geometry, equivalent to a
new force in the classical limit (modify the
gravitational sector of the low energy Lagrangian)
• Prototype: Jordan-Brans-Dicke theory
Deserves further scrutiny as a testing ground of many aspects
of more general NMC theories
Generalized theories of Gravity
1
1 ;
L  f ( R,  )   ;  V ( )  Lfluid
2
2
R
coupling function
 F ( ) R
Explored classes:
8G
1
F ( ) 
  2
(“Extended Quintessence”)
8G
Perrotta F., Matarrese S., Baccigalupi C., Phys. Rev. D 61 (2000) 023507
Baccigalupi, Matarrese, Perrotta 2000;
• Modifications of the background evolution:
cosmic expansion, R-boost.
• Modifications of the perturbed quantities: CMB, clustering
properties, weak lensing…
Background effects
Friedmann equation:
1  2
1
HF 
2

H 
 a  fluid  2   V  3 2 
3F 
2a
a 
2
H  Geff
1

F ( )
 Changing effective G changes cosmic expansion rate.
Klein-Gordon:
1
  2H   ( a 2 F, R  2a 2V, )
2
The R-term originates a ``boost’’ in the field dynamics
R-boost
Since R diverges as a -3 as a 0 (if non-relativistic species are
present), an “effective” potential is generated in the KG equation,
boosting the dynamics of fat early times. (Baccigalupi et al.2000)
 EQ admits tracking trajectories AND they are good trackers
(large basin of attraction).
Approaching without fine-tuning
Matarrese S., Baccigalupi C., Perrotta F., 2004
W0= -0.999, TEQ for different initial K,V
Even if w-1, R boost enlarges the allowed range of initial energy
densities
Perturbations effects
• Clustering properties: scalar field perturbations
may interact with matter perturbations in EQ
models. Perrotta F., Baccigalupi 2002; Perrotta et al. 2003
• Weak lensing : variations of G induce corrections
in distance calculations; perturbations gain a new
d.o.f., the anisotropic stress Acquaviva V., Baccigalupi C., Perrotta F., 2004
• CMB effects (ISW, projection, lensing,
bispectrum)
Modifications to the Poisson equation (Perrotta et al. 2004):
Possible effects on collapsed structures?
Weak lensing in Generalized Gravity theories
(Acquaviva, Baccigalupi, Perrotta 2004).
The lensing signal is affected by the Dark Energy both at the
background and perturbation level.
BACKGROUND effects: modification of the measures of
distances (time-varying G).
PERTURBATIONS: in Generalized theories, the anisotropic
stress is non-vanishing, contrarily to the “ordinary Quintessence”
models, and  is sourced by .
Pk / Pk  128G
2
Dark Energy and CMB
Projection effects:
H 
H ,dec
d dec
Affects the location of acoustic peaks
Integrated Sachs-Wolfe (ISW) effect:
( z ) 
2
1
( z )  const.
3 1  w( z )
Enhanced in DE models
Part of the CMB normalization at low multipoles is due to the ISW
ISW and Projection effects on CMB
w  1
multipoles
w   0 .5
CMB and Extended Quintessence
1
G
F
For l < 10,
Integrated Sachs-Wolfe effect:
C

G 
   2 0
 12 1 
C
 Gdec 
Projection:
l
l

F
F
These corrections will depend on the value and sign of the
coupling constant 
CMB and Dark Energy
• ISW not detectable, because of Cosmic Variance;
• Projection effects show degeneracy with variations
of Wm, H0, K, … but still the basic effect on which
CMB constraints on dark energy are based so far;
• EQ: the possibility of testing EQ scenarios is
related to the actual value of the coupling constant

HOW BIG IS  ?
Constraints on a time-varying G
1  2JBD  4 


8Geff 
F ( )  2JBD  3 
JBD 
Jordan-Brans-Dicke parameter:
F
F '2
Recent solar-system experiments (Cassini spacecraft) give
a lower bound:
JBD  40,000
(Bertotti et al. 2004)
This can be translated, in a model-dependent way, into a constraint
on the time variation of G. E.g., In a Brans-Dicke theory in a
matter dominated universe,
14
| Gt / G || Ft / F | 10
1
yr
HOWEVER, a time–dependent G alters the Hubble length
at matter-radiation equality, which is a scale imprinted on the
power spectrum. CMB and large-scale structure experiments
can provide complementary constraints, on different scales
(Liddle, Mazumdar, Barrow 1998).
(Acquaviva V., Baccigalupi C., Leach S., Liddle A.R., Perrotta F., 2004)
Solar system experiments probe scales different from the
ones probed by the CMB: we should expect different constraints
on  and 

The coupling parameter 1/ in scalar-tensor
theories may be larger than locally is
Conclusions
• Generalized theories of Gravity have advantages
with respect to “ordinary” Quintessence and .
Fine-tuning can be alleviated
• Possible effects on structure formation and
gravitational collapse
• Possible signatures from CMB and weak lensing
• Coupling constants may be larger than expected