The Degeneracy of Dark Energy and Curvature

Transcription

1 The Degeneracy of Dark Energy and Curvature Department of Physics and Astronomy, UWC, Cape Town Department of MAM, UCT, Cape Town PhD student: Amadeus Witzemann Collaborators: Philip Bull, HIRAX coll. Supervisors: Mario Santos Chris Clarkson Amanda Weltman May 5th, 2017

2 Introduction Why worry about curvature? Inflation predicts small curvature. Current constraints are strong: Ω k However... Relaxing assumptions on dark energy weakens the curvature constraints. How well can we constrain curvature if we assume nothing about dark energy?

3 Introduction Dark energy models A general dark energy model, with redshift dependent equation of state p DE /ρ DE = w(z) is hard to constrain, because w(z) can exactly mimic Ω k. ( ) H(z) 2 = Ω m (1 + z) 3 + Ω k (1 + z) 2 H 0 + Ω DE exp ( z 1 + w(z ) z dz ) (1)

4 Curvature Degeneracy HIRAX HIRAX ν 600 MHz ν 400 MHz dν 0.4 MHz Survey area 2100 sq. deg. Picture taken from a slide from Jon Sievers Tsys 50 mk aperture m integration time 1 year z

5 HIRAX HIRAX f BAO constraints:

6 HIRAX HIRAX D and H forecasts. The relative error is 1%:

7 Piecewise Constant Parametrization of EOS A piecewise constant parametrization of the EOS We want our dark energy model to reproduce (almost) all of the possible degeneracies with curvature: Ω DE (z) = Ω DE exp ( z 1 + w(z ) z dz ), (2)

8 Piecewise Constant Parametrization of EOS Likelihood calculation for the MCMC lnlike = 1 2 N (ξ i µ i ) T COV 1 (z i )(ξ i µ i ) i=1 with the fiducial values for D A and H in redshift bin i, ( ) Di 0 µ i :=, 0 H i and the values calculated with Θ, the step in the MCMC, ( ) DA (z ξ i := i, Θ) 0. 0 H(z i, Θ)

9 Piecewise Constant Parametrization of EOS Flat priors lnprob = lnprior + lnlike, where lnprior are the following flat priors: 3 w i 2 0 Ω k + Ω m Ω k h 1

10 Piecewise Constant Parametrization of EOS N = 10 Figure: Best fit (blue) and outlier (orange) in an MCMC chain

11 Piecewise Constant Parametrization of EOS N = 80 Figure: Best fit (blue) and outlier (orange) in an MCMC chain

12 Piecewise Constant Parametrization of EOS Illustration: Using only H(z)

13 Piecewise Constant Parametrization of EOS Illustration: Combining D A and H

14 Piecewise Constant Parametrization of EOS Convergence of σ(ω k ) for N Figure: σ(ω k ) broadly converges for a mock survey.

15 Results Preliminary results DE model Planck SDSS HIRAX w const w 0 w a n.a Piecewise constant n.a Table: Constraints on Ω k for different dark energy models and analysis methods. For the piecewise constant dark energy model 80 bins are used for SDSS and HIRAX. In both cases Planck data for the CMB distance is included. Constraints marked with are derived using Planck priors.

16 Discussion In a nutshell We did an MCMC analysis with a piecewise constant equation of state of dark energy on SDSS and Fisher forecasted H(z) and D A (z) measurements of HIRAX. For a low redshift experiment like SDSS, the curvature constraints worsen by a factor of HIRAX performs much better, σ(ω k ) only increases by a factor of 20. A good understanding of dark energy is crucial for constraining curvature.

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18 References Planck Collaboration: Planck 2015 results. XIII. Cosmological parameters Astronomy & Astrophysics manuscript, 2016 L. Knox: On Precision Measurement of the Mean Curvature Phys.Rev.D73:023503,2006 R. Hlozek, M. Corts, C. Clarkson, B. Bassett: Non-parametric Dark Energy Degeneracies General Relativity and Gravitation, Volume 40, Issue 2-3, pp (2008) R. Sung, M. Smith, C. Clarkson, P. G. Ferreira: Constraining the Geometry of the Universe Independently of Dark Energy with Baryon Acoustic Oscillations TBD P. Bull, P. G. Ferreira, P. Patel, M. G. Santos: Late-time cosmology with 21cm intensity mapping experiments ApJ 803, 21 (2015)

19 References SDSS collaboration: The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample arxiv: [astro-ph.co] L. Newburgh et. al.: HIRAX: A Probe of Dark Energy and Radio Transients