Mustapha Ishak (U.T. Dallas)1 Dark Energy or Apparent Acceleration Due to a Relativistic Cosmological Model More Complex than FLRW? Prof. Mustapha Ishak

Mustapha Ishak (U.T. Dallas) 1

Dark Energy or Apparent Acceleration Due to a

Relativistic Cosmological Model More Complex than FLRW?

Prof. Mustapha IshakCosmology and Relativity Group

Department of PhysicsThe University of Texas at Dallas

Collaborators: J. Richardson, D. Garred, D. Wittington, A. Nwankwo, R. Sussman

Ishak et al. Phys. Rev. D 78, 123531 (2008) arXiv:0708.2943 [astro-ph]


Cosmology & Relativity at University of Texas at Dallas


Contributions to research on cosmic acceleration and related questions

" Probing Cosmic Acceleration Beyond the Equation of State: Distinguishing between Dark Energy and Modified Gravity Models" Mustapha Ishak, Amol Upadhye, David N. Spergel. Preprint available at astro-ph/0507184. Published in Physical Review D, 74, 043513 (2006).

“Remarks on the formulation of the cosmological constant/dark energy questions.” Mustapha Ishak. Published in Foundations of Physics Journal, Volume 37, Number 10, (2007) 1470-1498. Paper available at the Los Alamos Archive Server as astro-ph/0504416

""Probing decisive answers to dark energy questions from cosmic complementarity and lensing tomography" Mustapha Ishak (2005). Published in Monthly Notices of the Royal Astronomical Society, V363, issue 2, p469 (2005). Paper available at astro-ph/0501594.

"Dynamical dark energy: Current constraints and forecasts" Amol Upadhye, Mustapha Ishak, Paul J. Steinhardt (2004). Published in Physical Review D, 72, 063501 (2005). Preprint available at astro-ph/0411803.

“The Contribution of the Cosmological Constant to the Relativistic Bending pf light Revisited.” Wolfgang Rindler and Mustapha Ishak. Published in Physical Review D, 76, 043006 (2007). Paper available at the Los Alamos Archive Server as [astro-ph] arXiv: 0709.2948

“Light Deflection, Lensing, and Time Delays from Gravitational Potentials and Fermat's Principle in the Presence of a Cosmological Constant.” Mustapha Ishak. Submitted to Physical Review D Journal (2008). Preprint available at the Los Alamos Archive Server as [astro-ph] arXiv:0801.3514

“A New Independent Limit on the Cosmological Constant/Dark Energy from the Relativistic Bending of Light by Galaxies and Clusters of Galaxies”. Mustapha Ishak, Wolfgang Rindler, Jason Dossett, Jacob Moldenhauer, Chris Allison. Submitted to Monthly Notices of the Royal Astronomy Society (2008). Preprint available at the Los Alamos Archive Server as [astro-ph] arXiv:0710.4726

“Dark Energy or Apparent Acceleration Due to a Relativistic Cosmological Model More Complex than FLRW?” Mustapha Ishak, James Richardson, Delilah Whittington, David Garred. Physical Review D Journal (2007). Preprint available at the Los Alamos Archive Server as [astro-ph] arXiv:0708.2943


Cosmic Acceleration and the Dark Side

Several possible explanations have been discussed in thousands of scientific publications:

A dark energy component/cosmological constant

A modification to general relativity at cosmological scales

Averaging and backreaction effects

Apparent acceleration due to the fact that we live in a relativistic cosmological model more complex than FLRW


May General Relativity Be With You (Jedi Einstein)

GR history is full of surprises: starting from the prediction of a non-static expanding universe which already encountered some resistance

May the force be with you (Jedi Yoda)

Today: Dark Side times (Dark Energy, Dark Matter,

Cosmological constant, Modified Gravity models…)


Cosmic Acceleration and the Dark Side

Several possible explanations have been discussed in thousands of scientific publications:

A dark energy component/cosmological constant

A modification to general relativity at cosmological scales

Averaging and backreaction effects

Apparent acceleration due to the fact that we live in a relativistic cosmological model more complex than FLRW


Do we have the right model in hands?

We can’t explain ~70% (or~95%) of the observed dynamics

Certainly, one should praise the achievements of the FLRW model, however, one should also allow himself/herself to ask and explore some necessary questions

Observations of the expansion rate of Supernovae can have different interpretations in FLRW versus an Inhomogeneous model

Do we live in a complex and subtle general relativistic cosmological model?

Is the FLRW model limiting our ability to interpret observations?

Well motivated questions in view of the non-linearity of GR, and the unsolved averaging problem in cosmology (see other talks)


Apparent acceleration seen from

an under-dense region An apparent acceleration is possible if we live in an under-dense

region of the universe

Apparent acceleration can result from the Hubble parameter, H0, being larger inside the under-dense region than outside of that region

In FLRW, H(t) is a function of time only but in inhomogeneous models H(t,r) is a function of time and space

Supernova observations imply a larger H0 at low redshifts then at higher redshifts

In FLRW models this implies acceleration while in inhomogeneous models different values of H are possible without acceleration


Apparent acceleration using the Szekeres-

Szafron inhomogeneous models

Several interesting papers explored the question using the Lemaitre-Tolman-Bondi (LTB) models

However, because of the spherical symmetry of LTB, the results can be viewed as a proof of concept unless we sacrifice the cosmological/Copernican principle (but see some recent discussions, e.g. Celerier et al, 06/2009)

It is desirable to explore the question of apparent acceleration using more general models than LTB

Derived by Szekeres (1975) with no-symmetries (no killing vector fields) with a dust source. Generalized to perfect fluids by Szafron (1977). Studied by a number of authors.

Regarded as good models to study our inhomogeneous universe (GFR Ellis; A. Krasinski)

Have a flexible geometrical structure that can fit cosmological constraints and observations at various scales


The approach is consistent with the

Copernican Principle It is perhaps worth clarifying that we are not proposing the

Szekeres model as the true model of the universe but rather investigating the possibility of an apparent acceleration in an inhomogeneous universe

In this scenario, apparent acceleration is due to the fact that we happen to live in one of the many under-dense regions of the universe.

No need to be close to the center of the under-dense region. In fact, there is no exact definition of a center in these models since not spherically symmetric

So this is not all that inconsistent with the Copernican Principle (or the cosmological principle)


Apparent acceleration using the Szekeres-Szafron inhomogeneous models

The Szekeres metric in Krasinski & Hellaby coordinates

Have several sub-cases We explored one of them but plan to look into the other

cases as well hyperbolic (k(r)<0), parabolic (k(r)=0), and elliptic

(k(r)>0) The function E(r,p,q) and the constant ε=0,+1,or -1 also

define further sub-cases and mapping of various hyper-surfaces.

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Observations in inhomogeneous models and the null geodesic equations

The null geodesic equations describe the motion of light rays arriving to us from astronomical objects

It is necessary to solve these equations it in order to derive observable functions, such as the luminosity-distance to supernovae

This equation is easily solved in the FLRW but not in the Szekeres models, and here we employ an analytical and numerical approach to the problem


Observations in inhomogeneous models and the null geodesic equations (not radial)

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Observations in inhomogeneous models and the null geodesic equations: numerical integration

We introduced the redshift in the equations

The system can be regarded as a second order ODE system with the parameters given by the Einstein Field Equations

Further, we used the Runge-Kutta method with the following vectors in order to separate the 4 second order ODEs to 8 first order ODEs


Hubble diagram for the Szekeres models

The luminosity-distance is found numerically using

It dependends on r, p, and q (or similarly on r, theta, and phi)

Next, the magnitude is given by

We used Supernova Combined Data Set as in Davis et al 2007, Wood-Vasey et al 2007, and Riess et al 2007.

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R t rd z z

E r p q

10( ) 5log ( ) 25Lm z M d


Results: Ishak et al. Phys. Rev. D 78, 123531 (2008) arXiv:0708.2943 [astro-ph]

The data is 94 Supernova (up to $1+z=1.449$) from Davis et al 2007, Wood-Vasey et al 2007, and Riess et al 2007

The Szekeres model fits the data with a chi^2=112. This is close to the chi^2=105 of the LCDM concordance FLRW model.

Because of the possible systematic uncertainties in the supernova data, it is not clear that the difference between the two chi^2 and fits is significant. And we did not explore all the Szekeres models

The Szekeres model used is also consistent with the requirement of spatial flatness at CMB scales.


Conclusions and

future work

The Szekeres model fits current supernova data almost as well as the LCDM model and are also consistent with the spatial flatness required by the CMB

Approach can be consistent with the Copernican Principle

While the LCDM model requires a cosmological constant, the Szekeres inhomogeneous model does not

Although more work remains, our preliminary results encourage further investigation of the possibility of apparent acceleration using inhomogeneous models

Much more work needs to be done: We are exploring a list of items/issues in ongoing research

We plan to investigate comparisons of the Szekeres-Szafron models and possibly other inhomogeneous models with CMB and large-scale structure observables

In a more general context, we have plans to advance the comparisons between observations and inhomogeneous models


In a golden era of cosmology, “We know a lot about our universe but we understand very little”

Contents of the universe:

Baryons: 4%

Dark matter: 23%

Dark energy: 73%

Massive neutrinos: 0.1%

Spatial curvature: very close to 0


Cosmology & Relativity at University of Texas at Dallas


This is how the Wilkinson Microwave Anisotropy Probe (WMAP) sees the CMB


Contributions to research on cosmic acceleration and related questions

" Probing Cosmic Acceleration Beyond the Equation of State: Distinguishing between Dark Energy and Modified Gravity Models" Mustapha Ishak, Amol Upadhye, David N. Spergel. Preprint available at astro-ph/0507184. Published in Physical Review D, 74, 043513 (2006).

“Remarks on the formulation of the cosmological constant/dark energy questions.” Mustapha Ishak. Published in Foundations of Physics Journal, Volume 37, Number 10, (2007) 1470-1498. Paper available at the Los Alamos Archive Server as astro-ph/0504416

""Probing decisive answers to dark energy questions from cosmic complementarity and lensing tomography" Mustapha Ishak (2005). Published in Monthly Notices of the Royal Astronomical Society, V363, issue 2, p469 (2005). Paper available at astro-ph/0501594.

"Dynamical dark energy: Current constraints and forecasts" Amol Upadhye, Mustapha Ishak, Paul J. Steinhardt (2004). Published in Physical Review D, 72, 063501 (2005). Preprint available at astro-ph/0411803.

“The Contribution of the Cosmological Constant to the Relativistic Bending pf light Revisited.” Wolfgang Rindler and Mustapha Ishak. Published in Physical Review D, 76, 043006 (2007). Paper available at the Los Alamos Archive Server as [astro-ph] arXiv: 0709.2948

“Light Deflection, Lensing, and Time Delays from Gravitational Potentials and Fermat's Principle in the Presence of a Cosmological Constant.” Mustapha Ishak. Submitted to Physical Review D Journal (2008). Preprint available at the Los Alamos Archive Server as [astro-ph] arXiv:0801.3514

“A New Independent Limit on the Cosmological Constant/Dark Energy from the Relativistic Bending of Light by Galaxies and Clusters of Galaxies”. Mustapha Ishak, Wolfgang Rindler, Jason Dossett, Jacob Moldenhauer, Chris Allison. Submitted to Monthly Notices of the Royal Astronomy Society (2008). Preprint available at the Los Alamos Archive Server as [astro-ph] arXiv:0710.4726

“Dark Energy or Apparent Acceleration Due to a Relativistic Cosmological Model More Complex than FLRW?” Mustapha Ishak, James Richardson, Delilah Whittington, David Garred. Physical Review D Journal (2007). Preprint available at the Los Alamos Archive Server as [astro-ph] arXiv:0708.2943

Documents

Mustapha Ishak (U.T. Dallas)1 Dark Energy or Apparent Acceleration Due to a Relativistic Cosmological Model More Complex than FLRW? Prof. Mustapha Ishak