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Aspects of Dark Energy 
         and  
  Cosmic  Curvature

      Patrice M. OKOUMA
       UCT/AIMS/SAAO
A Fundamental Uncertainty in
    The BAO Scale from Isocurvature Modes
   Physics Letters B. 696 (2011), pp. 433­437

The sensitivity of BAO Dark Energy Constraints to 
      General Isocurvature Perturbations 
                  arXiv:1111.2572v1

   Work(s) With C. Zunckel, S. Muya­Kasanda, 
            K. Moodley  (UKZN, SA) ;
     B.A. BASSETT (AIMS/UCT/SAAO, SA)
Motivation

   our current understanding of Baryon Acoustic Oscillations (BAO)
   relies on a set of restrictive assumptions about the initial conditions.



   Question : Assuming more general initial conditions, 

                 by how much could this assumption alter/bias 
                 our understanding of DE via the BAO scale  ? 
Initial Conditions              space



                             Adiabatic (curvature) perturbations




Isocurvature (entropy) perturbations




                              space
“ Fingerprints ” 
         on 
Large Scale Structure 
Eisenstein et al. (2005)




     r0

      In adiabatic mode :


                                         r0




     r0  =  Standard ruler 
Fisher formalism applied to galaxy power spectrum
If likelihood function of band powers of galaxy power spectrum is Gaussian 




                                (Tegmark et al. 1997; Seo & Eisenstein 2003)
Fisher formalism applied 
to galaxy power spectrum – cont'd



                    + Isocurvature parameters

  Gaussian Likelihood

   Minimum error on parameter         =
FoM alterations for stage III­IV ­like survey parameters




                                           1.5, 1.2
Bias in DE params. estimates for stage III­IV ­like survey parameters




                          7σ (10σ) incorrect measurement of Wo 
                                        and as much as
                    23σ (12σ) for Wa if ignoring isocurvature modes 
  
 
BAO are a firm prediction of CDM models 
and one key­topic of the science programme for SKA; 

Even  for  isocurvature  amplitudes  undetectable  by  PLANCK,  the 
presence of multiple isocurvature modes could lead to biases in the 
DE  parameters  that  exceed  7  sigma  on  average,  if  the  analysis  is 
done assuming isocurvature initial conditions;
 
Accounting  for  all  isocurvature  modes  corrects  for  this  bias  but 
degrades the DE figure of merit by at least 50% in the case of the 
BOSS experiment;

BAO  data  also  provide  much  stronger  constraints  on  the  nature  of 
the primordial perturbations than from the CMB alone.
In adiabatic mode :
r0



       r0  =  Standard ruler 
The curvature­dark energy
(geometric) degeneracy through 
           the CMB


   Work with Y. Fantaye (SISSA, Italy) 
& B. A. BASSETT (AIMS/UCT/SAAO, SA)
OUTLINE


Curvature, lnflation?  

What is the Geometric Degeneracy?

Some results 

Summary 
Motivation
The current model of Inflation predicts that spatial
  sections of space­time (the Universe) are flat;


  Current datasets are consistent with this paradigm 
   IF the dark energy is a cosmological constant;
  

   We study the impact of allowing for a general
  evolution of the dark energy on the geometry of
  the Universe and extract some new constraints on
  cosmological parameters.
Curvature ?
                                                     R


                R

            X
                                 (radius of) Curvature = 1/R  ­­­­­­­­­­­>  0


(radius of) Curvature = 1/R             K = 1




                               K = ­1
                     




 Curvature density parameter       
                               K = 0
Inflation : a solution to some Big Bang puzzles




          Larson et al. (2011)




                                 AIMS 2012     18
What is the 
  curvature­dark energy
(geometric) Degeneracy?
D. Larson et al. (2010)
                               21
                          l1



                               AIMS 2012  
The Basic Geometric Degeneracy :




                                                




Okouma et al., 2012. In prep
    K = 
Ωk and Wde effects can cancel each other 
    1
                                                   Using WMAP7 data only, 
­­­­­­>same angular power spectrum for 
K = ­1                                             IF   WDE = ­1,  Then  
                                                   IF
         different sets of these parameters.
                                                                   Larson et al., 2011
K = 0
The general geometric degeneracy
The curvature­dark energy
(geometric) degeneracy through the 
               CMB 
Bayes Theorem:                          

Metropolis­Hastings algorithm for the sampling of the posterior pdf 
­­­> Random walk in parameter space using a modified CosmoMC
Data: WMAP7­yr , Supernovae, BBN, HST (+ ACT data)




                                                                 B. Bassett stat. lectures
                                           5 chains of 300 000   steps each ran
Some Results
Okouma et al., 2012. In prep
Oohh Look !

                                                 Okouma et al., 2012. In prep
                         Okouma et al., 2011. In prep

    using CAMB

H0 = 71 (km/s)/Mpc,
Ok = 0.15



H0 = 56.36 (km/s)/Mpc,
Ok = ­0.06                    AIMS 2012                               27
?




Okouma et al., 2012. In prep
Okouma et al., 2012. In prep
Large open models with dynamical DE which fit the 
first  CMB  peak  do  exist,  but  the  strong  Integrated 
Sachs­Wolfe  (ISW)  effect  in  such  models  means 
that  low  multipoles  of  the  CMB  power  spectrum  is 
very poorly fit, hence these models are discarded. 

The  vast  ~  30­dimensional  parameter  volume 
explored is an additional limitation. 
X


√

        A  significantly  non­phantom  (Wde  >  ­1)  leads  to  a 
        strong  reduction  in  the  volume  of  possible  curved 
        models; 
 

    
        A  general  dynamical  dark  energy  model  adds  nothing 
        significant in terms of  allowing for curved models;


    
        Strong constraints on cosmic curvature remain despite 
        the  extra  dark  energy  freedom.  However,  these 
        constraints  now  come  from  a  mixture  of  dynamical 
        constraints (ISW effect) and distance measurements.
Okouma et al., 2012. In prep
Okouma et al., 2012. In prep




          J­Q Xia & M. Viel , 2009
Okouma et al., 2012. In prep
Okouma et al., 2012. In prep
Komatsu et al., 2008 
Okouma et al., 2012. In prep
Prospects with Growth Information
Summary  

 
    A general dynamical dark energy model adds nothing
    significant in terms of  allowing for curved models;


    Strong constraints on cosmic curvature remain despite
    the extra dark energy freedom. 

    However,  these  constraints  now  come  from  a  mixture  of 
    dynamical constraints (Integrated Sachs­Wolfe effect) and 
    distance measurements.
Thank you
      for 
your attention
Aspects of Dark Energy and Cosmic Curvature

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