Title: Unified Dark Matter Models
1Unified Dark Matter Models
- Daniele Bertacca
- Dipartimento di Fisica Galileo Galilei,
- Via Marzolo 8, 35131 Padova, Italy
- E-mail daniele.bertacca_at_pd.infn.it
2Credits
-
- D. Bertacca, S. Matarrese, M. Pietroni, Unified
Dark Matter in Scalar Field Cosmologies. - Mod. Phys. Lett. A222893-2907,2007
e-Printastro-ph/0703259v3 - D. Bertacca, N. Bartolo, ISW effect in Unified
Dark Matter Scalar Field Cosmologies An
analytical approach. - JCAP 0711026,2007 e-Print arXiv0707.4247v3
astro-ph - D.Bertacca, N.Bartolo, S. Matarrese, Haloes of
Unified Dark Matter. - JCAP 05(2008)005 e-Print arXiv0712.0486v2
astro-ph - D.Bertacca, N.Bartolo, A.Diaferio, S.Matarrese,
How Unified Dark Matter in Scalar Field can
cluster. JCAP 0810023,2008 e-Print
arXiv0807.1020v3 astro-ph - S.Camera, D.Bertacca, A.Diaferio, N.Bartolo,
S.Matarrese, Weak lensing signal in Unified Dark
Matter models. e-Print arXiv0902.4204
3Observational Evidence
- The confidence regions coming from SN Ia, CMB and
BAO. - The flat Universe without ? is ruled out.
- The compilation of cosmological data sets the
need for a dark energy dominated Universe with
OM 0.274, ODE 0.726 .
Combination of SNe with BAO (Eisenstein et. al.,
2005) CMB (WMAP-5 year data, 2008) (Marek
Kowalski 2008)
4Theoretical 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.
5In UDM models there are two simple but
distinctive aspects
- The fluid which triggers the accelerated
expansion at late times is also the one which has
to cluster in order to produce the structures.
6In UDM models there are two simple but
distinctive aspects
- The fluid which triggers the accelerated
expansion at late times is also the one which has
to cluster in order to produce the structures. - 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.
7- Advantages over DM DE (?CDM)
- - There is a single fluid that behaves both
as DM and DE. -
8- Advantages over DM DE (?CDM)
- - There is a single fluid that behaves both
as DM and DE. - Disadvantages over DM DE (?CDM)
- - Success of UDM models strongly depend on
the effective - speed of sound.
-
9- Advantages over DM DE (?CDM)
- - There is a single fluid that behaves both
as DM and DE. - Disadvantages over DM DE (?CDM)
- - 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.
10- Advantages over DM DE (?CDM)
- - There is a single fluid that behaves both
as DM and DE. - Disadvantages over DM DE (?CDM)
- - 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.
11- Advantages over DM DE (?CDM)
- - There is a single fluid that behaves both
as DM and DE. - Disadvantages over DM DE (?CDM)
- - 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
12- Advantages over DM DE (?CDM)
- - There is a single fluid that behaves both
as DM and DE. - Disadvantages over DM DE (?CDM)
- - Success of UDM models strongly depend on
the effective - speed of sound cs2.
- 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 cs becomes large at late times, strong
deviations from the usual ISW effect of ?CDM
models (Bertacca Bartolo 2007) .
13(1) Adiabatic UDM fluid
- - Pp(?) effective speed of sound is the same
as the adiabatic speed of sound very strong
fine tuning .
14(1) Adiabatic UDM fluid
- - Pp(?) 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 cs2, in the same time, we obtain a
very strong fine tuning on the equation state, w
15(1) Adiabatic UDM fluid
- - Pp(?) 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) -
-
- ?CDM recovered for a 0.
- For a 10-5 ruled out by observation
(Sandvik et al 2004).
16(1) Adiabatic UDM fluid
- - Pp(?) 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) -
-
- ?CDM recovered for a 0.
- For a 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 -
-
- ?CDM recovered for a 0.
17(2) Non Adiabatic UDM
- In this case the effective speed of sound cs2
differs from the adiabatic one.
18(2) Non Adiabatic UDM
- In this case the effective speed of sound cs2
differs from the adiabatic one. - e.g., scalar field Lagrangian with standard
kinetic term, cs21 (Quintessence good for dark
energy, not for UDM models) - Ex seeking a Lagrangian that reproduces the
background evolution of ?CDM, i.e. when p -?
Bertacca, Matarrese, Pietroni (2007). -
In conflict with cosmological structure formation!
19(2) Non Adiabatic UDM
- In this case the effective speed of sound cs2
differs from the adiabatic one. - e.g., scalar field Lagrangian with standard
kinetic term, cs21 (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 (cs2 )
(Bertacca, Bartolo,
Diaferio Matarrese, JCAP 0810023, 2008)
20 UDM with Lagrangian L(f,X)
- Scalar field , p and ?
given by - pL(f,X), ?2X?L(f,X)/?X-L(f,X) ,
cs2p,X /?,X - construct Lagrangians to obtain Unified Dark
Matter Models.
21 UDM with Lagrangian L(f,X)
- Scalar field , p and ?
given by - pL(f,X), ?2X?L(f,X)/?X-L(f,X) ,
cs2p,X /?,X - construct Lagrangians to obtain Unified Dark
Matter Models. - We consider L(f,X) f(f)g(X)-V(f). Then
w(f,X) and cs2(X) - i.e. we can separately construct the
equation of state w and - the speed of sound cs2.
22 UDM with Lagrangian L(f,X)
- Scalar field , p and ?
given by - pL(f,X), ?2X?L(f,X)/?X-L(f,X) ,
cs2p,X /?,X - construct Lagrangians to obtain Unified Dark
Matter Models. - We consider L(f,X) f(f)g(X)-V(f). Then
w(f,X) and cs2(X) - i.e. we can separately construct the
equation of state w and - the speed of sound cs2.
- This feature does not occur when we consider
Lagrangians with - purely kinetic term (Ex, adiabatic fluid
pp(?)), Lagrangians - L f(f)g(X) or L g(X)-V(f).
23UDM Lagrangian L(f,X) f(f)g(X)-V(f)
- We seek a Lagrangian that reproduces the
background evolution of ?CDM. -
24UDM Lagrangian L(f,X) f(f)g(X)-V(f)
- We seek a Lagrangian that reproduces the
background evolution of ?CDM. - Assuming that the kinetic term is of the Infield
type -
25UDM Lagrangian L(f,X) f(f)g(X)-V(f)
- We seek a Lagrangian that reproduces the
background evolution of ?CDM. - Assuming that the kinetic term is of the Infield
type - Imposing that
-
26UDM Lagrangian L(f,X) f(f)g(X)-V(f)
- We seek a Lagrangian that reproduces the
background evolution of ?CDM. - Assuming that the kinetic term is of the Infield
type - Imposing that
- We can derive X(a), f(a), during various epochs,
and, finally, we can construct the functional
form of f(f) and V(f). -
27In the Figure we show the normalized potentials
Fk(a) Fk (0) for ?CDM (solid) and UDM
(dot-dashed). The lower panel shows potentials at
k 0.001 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 c82 10-6 10-4 10-2 from top
to bottom, respectively. At small c82 , ?CDM and
UDM curves are indistinguishable.
28In the Figure we show linear power spectrum of
UDM models for c82 10-8 10-6 10-4 10-2 10-1
from top to bottom, respectively. At small, i.e.
c8 2 10-8 10-6, ?CDM 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.
29In the Figure we show CMB, of UDM models for c82
10-4 10-2 10-1 0.5 from bottom to top,
respectively. For c8 2 10-4 , ?CDM 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.
30Conclusions
- I focus UDM models alternative to understand the
nature of the Dark Matter and Dark Energy
components of the Universe.
31Conclusions
- I focus UDM models alternative to understand the
nature of the Dark Matter and Dark Energy
components of the Universe. - Starting from LL(f,X), we have proposed a
technique to construct models where the effective
speed of sound is small enough that the scalar
field can cluster.
32Conclusions
- I focus UDM models alternative to understand the
nature of the Dark Matter and Dark Energy
components of the Universe. - Starting from LL(f,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 c82 10-6
for sources located at low redshifts.
33Conclusions
- I focus UDM models alternative to understand the
nature of the Dark Matter and Dark Energy
components of the Universe. - Starting from LL(f,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 c82 10-6
for sources located at low redshifts. - In Bertacca, Bartolo, Matarrese (2007), we have
investigated static spherically symmetric
solutions (dark halos) of Einsteins equations
for a scalar field with non-canonical kinetic
term (see also Armendariz-Picon Lim 2005).
34Conclusions
- I focus UDM models alternative to understand the
nature of the Dark Matter and Dark Energy
components of the Universe. - Starting from LL(f,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 c82 10-6
for sources located at low redshifts. - In Bertacca, Bartolo, Matarrese (2007), we have
investigated static spherically symmetric
solutions (dark halos) of Einsteins 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.
35-
- 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
36The role of the (effective) speed of sound cs in
UDM Models Defining an effective Jeans length
, we obtain The
result of this general trend is that the possible
appearance of cs ? 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
37- The role of the (effective) speed of sound cs
- 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 cs 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 cs becomes large at late times,
this leads to strong deviations from the usual
ISW effect of ?CDM 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 ?CDM 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 l3
up to . - This value of lISW 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.