Observational Constraints on Sudden Future Singularity Models

1
Observational Constraints on Sudden Future
Singularity Models

• Hoda Ghodsi Supervisor Dr Martin Hendry
• Glasgow University, UK
• Grassmannian Conference in Fundamental Cosmology
• Szczecin, Poland, September 2009

2
Outline

• Concordance Cosmology Overview
• Sudden Future Singularity Theory
• Observational Constraints
• Method
• Results
• Conclusions and Future Directions

3
Concordance Cosmology

• Cosmological observations of most importantly the
  Cosmic Microwave Background Radiation (CMBR), the
  Large Scale Structure and SNe Ia have helped
  establish a standard Concordance Cosmology with
  the following characteristics
• Evolution Accelerating expansion driven by a
  form of Dark Energy
• Geometry Flat
• Contents 74 Dark Energy, 22 Dark Matter, 4
  Baryonic Matter
• Age 13.7 Gyr old
• Fate Empty de-sitter type fate

Courtesy http//map.gsfc.nasa.gov/
Courtesy http//abyss.uoregon.edu/
4
Sudden Future Singularity Model

• Barrow (Class. Quantum Grav. 21, L79) discovered
  a new type of possible end to the Universe
  (assuming no equation of state) which violated
  the dominant energy condition only
• He called them Sudden Future Singularities
• Pressure singularities
• Barrow then constructed an example model which
  could accommodate an SFS with scale factor of the
  form
• 
  
• 
  ,

5
Sudden Future Singularity Model

• Occurrence regardless of curvature, homogeneity
  or isotropy of the universe
• Pressure behaviour satisfies observation current
  acceleration possible

Note that no explicit Dark Energy component has
been assumed to exist. Dabrowski calls the cause
some pressure driven dark energy .
log (pressure)
time
6
Observational Constraints

• SNIa redshift-magnitude relation
• Deceleration parameter
• The Location of the CMBR Acoustic Peaks
• Baryon Acoustic Oscillations
• Age of the Universe

7
SNIa redshift-magnitude relation
Luminosity distance is given by
where The distance
modulus is defined as

• Previously it was shown by Dabrowski et al.
  (2007) that the SFS SNIa redshift-magnitude
  relation matches observations and the Concordance
  model.
• Test redone with 182 SNe Ia as compiled by Riess
  et al. (2007) In the Gold data set ? same results
  were achieved.

Distance modulus vs. log(redshift) for the SFS
and Concordance models as compared with SNIa data
from Tonry et al. (2003) Gold sample and Astier
et al. (2006) SNLS sample. Graph from Dabrowski
et al. (2007).
8
Deceleration parameter
Concordance Model parameters
SFS Model
q(z)
Concordance Model
SFS Model parameters
z
9
CMBR acoustic peaks

• Shift parameter,
• Angular diameter distance to the last
  scattering surface (LSS) divided by Hubble
  horizon at the decoupling epoch
• The apparent size of the sound horizon at
  recombination
• Can be found using the formula
• Acoustic scale,
• Angular diameter distance to the LSS
  divided by sound horizon at the decoupling epoch
• Can be calculated using the formula
• The observed values of these parameters are
  taken from Komatsu et al. (2008)

Courtesy http//map.gsfc.nasa.gov/
10
Baryon Acoustic Oscillations

• Cosmological perturbations excite sound waves in
  the early universe photon-baryon plasma ?
  competition between gravity and radiation
  pressure. These oscillations leave their imprint
  on matter distribution now
• Natural standard ruler ? useful distance
  indicators now
• Can be used to constrain the quantity known as
  the distance parameter, , well
• Angular scale of oscillations
• Observed value taken from Komatsu et al. (2008)

Courtesy http//www.sdss3.org/
Courtesy http//cmb.as.arizona.edu/
11
Age of the Universe

• Using the standard Friedmann equation, the age of
  the Universe is calculated from
• 
  where and
• Corresponding age for the SFS model was
  calculated
• Observed value for the age from the globular
  cluster estimates as Krauss and Chaboyer (2003)
  present, i.e. no cosmology assumed
• Hubble constant from the HST Key Project as given
  by Freedman et al. (2001) which assumes only
  local cosmology
• Therefore Hubble constant constraint also included

12
Method

• Used statistics to fit model parameters to
  data
• Theoretically to obtain an SFS
  and a currently accelerating universe
• To comply with early universe requirements
• For , was used as the fraction of
  the time to an SFS elapsed
• 2d parameter space of search while
  keeping constant

13
Results
d
n
14
SN
A
R
All
Age
15
BAO
SNIa
CMBR
d
n
16
BAO
SNIa
d
CMBR
n
17
SNIa
BAO
d
CMBR
n
18
SNIa
BAO
d
CMBR
n
19
SNIa
BAO
d
CMBR
n
20
BAO
SNIa
CMBR
d
n
21
Results
BAO
SNIa
CMBR
d
n
22
Results
BAO
SNIa
CMBR
d
n
23
BAO
SNIa
CMBR
d
n
24
Conclusions and Future Directions

• The example SFS model (with kept constant)
  investigated has been shown not to be compatible
  with current data.
• With the data analysis tools set up we are
  planning to continue our research by working on
  other non-standard models like the GR averaging
  model proposed by Wiltshire (2007).