Unified Dark Matter Models

1
Unified Dark Matter Models

• Daniele Bertacca
• Dipartimento di Fisica Galileo Galilei,
• Via Marzolo 8, 35131 Padova, Italy
• E-mail daniele.bertacca_at_pd.infn.it

2
Credits

• 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

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Observational 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)
4
Theoretical 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.
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In 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.

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In 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.

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• Advantages over DM DE (?CDM)
• - There is a single fluid that behaves both
  as DM and DE.

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• 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.

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• 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.

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• 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.

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• 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

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• 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) .

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(1) Adiabatic UDM fluid

• - Pp(?) effective speed of sound is the same
  as the adiabatic speed of sound very strong
  fine tuning .

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(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
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(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).

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(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.

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(2) Non Adiabatic UDM

• In this case the effective speed of sound cs2
  differs from the adiabatic one.

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(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!
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(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)

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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.

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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.

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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).

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UDM Lagrangian L(f,X) f(f)g(X)-V(f)

• We seek a Lagrangian that reproduces the
  background evolution of ?CDM.

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UDM 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

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UDM 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

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UDM 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).

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In 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.
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In 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.
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In 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.
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Conclusions

• I focus UDM models alternative to understand the
  nature of the Dark Matter and Dark Energy
  components of the Universe.

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Conclusions

• 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.

32
Conclusions

• 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.

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Conclusions

• 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).

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Conclusions

• 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

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The 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
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• 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.