Dark Energy Theory Overview Ed Copeland -- Nottingham University 1. Issues with pure Lambda 2. Models of Dark Energy 3. Modified Gravity approaches 4. Testing for and parameterising Dark Energy Dark Side of the Universe - Bergen - July 26th 2016 1 M. Betoule et al.: Joint cosmological analysis of the SNLS and SDSS SNe Ia. 46 The Universe is sample σcoh low-z 0.12 HST accelerating and C 44 SDSS-II 0.11 β yet we still really SNLS 0.08 − have little idea 1 42 HST 0.11 X what is causing ↵ SNLS σ Table 9. Values of coh used in the cosmological fits. Those val- + 40 this acceleration. ues correspond to the weighted mean per survey of the values ) G ( SDSS shown in Figure 7, except for HST sample for which we use the 38 Is it a average value of all samples. They do not depend on a specific M − cosmological B choice of cosmological model (see the discussion in §5.5). ? 36 m constant, an Low-z = 34 evolving scalar µ 0.2 field, evidence of modifications of 0.4 . General CDM 0 2 ⇤ 0.0 0.15 µ Relativity on . − 0 2 − large scales or µ 0.4 − 2 1 0 something yet to 10− 10− 10 coh 0.1 z be dreamt up ? σ Betoule et al 2014 2 Fig. 8. Top: Hubble diagram of the combined sample. The dis- tance modulus redshift relation of the best-fit ⇤CDM cosmol- 0.05 1 1 ogy for a fixed H0 = 70 km s− Mpc− is shown as the black line. Bottom: Residuals from the best-fit ⇤CDM cosmology as a function of redshift. The weighted average of the residuals in 0 0 0.5 1 logarithmic redshift bins of width ∆z/z 0.24 are shown as black dots. ⇠ redshift σ Fig. 7. Values of coh determined for seven subsamples of the 6.1. ⇤CDM fit of the Hubble diagram Hubble residuals: low-zz < 0.03 and z > 0.03 (blue), SDSS z < 0.2 and z > 0.2 (green), SNLS z < 0.5 and z > 0.5 (orange), Using the distance estimator given in Eq. (4), we fit a ⇤CDM and HST (red). cosmology to supernovae measurements by minimizing the fol- lowing function: 2 1 χ = (µˆ µ (z; ⌦ ))†C− (µˆ µ (z; ⌦ )) (15) may a↵ect our results including survey-dependent errors in es- − ⇤CDM m − ⇤CDM m timating the measurement uncertainty, survey dependent errors with C the covariance matrix of µˆ described in Sect. 5.5 and in calibration, and a redshift dependent tension in the SALT2 µ⇤CDM(z; ⌦m) = 5 log10(dL(z; ⌦m)/10pc) computed for a fixed model which might arise because di↵erent redshifts sample dif- 1 1 13 fiducial value of H0 = 70 km s− Mpc− , assuming an unper- ferent wavelength ranges of the model. In addition, the fit value turbed Friedmann-Lemaître-Robertson-Walker geometry, which of σcoh in the first redshift bin depends on the assumed value 1 is an acceptable approximation (Ben-Dayan et al. 2013). The of the peculiar velocity dispersion (here 150km s− ) which is · free parameters in the fit are ⌦m and the four nuisance param- somewhat uncertain. 1 eters ↵, β, MB and ∆M from Eq. (4). The Hubble diagram for We follow the approach of C11 which is to use one value of the JLA sample and the ⇤CDM fit are shown in Fig. 8. We find σ coh per survey. We consider the weighted mean per survey of a best fit value for ⌦m of 0.295 0.034. The fit parameters are the values shown in Figure 7. Those values are listed in Table 9 given in the first row of Table 10.± and are consistent with previous analysis based on the SALT2 For consistency checks, we fit our full sample excluding sys- method (Conley et al. 2011; Campbell et al. 2013). tematic uncertainties and we fit subsamples labeled according to the data included: SDSS+SNLS, lowz+SDSS and lowz+SNLS. Confidence contours for ⌦m and the nuisance parameters ↵, β 6. ⇤CDM constraints from SNe Ia alone and ∆M are given in Fig. 9 for the JLA and the lowz+SNLS sample fits. The correlation between ⌦m and any of the nuisance The SN Ia sample presented in this paper covers the redshift parameters is less than 10% for the JLA sample. range 0.01 < z < 1.2. This lever-arm is sufficient to provide The ⇤CDM model is already well constrained by the SNLS a stringent constraint on a single parameter driving the evolu- and low-z data thanks to their large redshift lever-arm. However, tion of the expansion rate. In particular, in a flat universe with the addition of the numerous and well-calibrated SDSS-II data a cosmological constant (hereafter ⇤CDM), SNe Ia alone pro- to the C11 sample is interesting in several respects. Most impor- vide an accurate measurement of the reduced matter density tantly, cross-calibrated accurately with the SNLS, the SDSS-II ⌦m. However, SNe alone can only measure ratios of distances, data provide an alternative low-z anchor to the Hubble diagram, which are independent of the value of the Hubble constant today 1 1 with better understood systematic uncertainties. This redundant (H0 = 100h km s− Mpc− ). In this section we discuss ⇤CDM parameter constraints from SNe Ia alone. We also detail the rel- 13 This value is assumed purely for convenience and using another ative influence of each incremental change relative to the C11 value would not a↵ect the cosmological fit (beyond changing accord- 1 analysis. ingly the recovered value of MB). 15 Brief reminder why the cosmological constant is regarded as a problem? R = p g ⇢ The CC gravitates in General L − 16⇡G − vac Relativity: ✓ ◆ G = 8⇡G⇢ g µ⌫ − vac µ⌫ Now: ⇢obs ⇢theory vac ⌧ vac Just as well because anything much bigger than we have and the universe would have looked a lot different to what it does look like. In fact structures would not have formed in it. 3 Estimate what the vacuum energy should be : ⇢theory ⇢bare vac ⇠ vac + zero point energies of each particle + contributions from phase transitions in the early universe 4 zero point energies of each particle For many fields (i.e. leptons, quarks, gauge fields etc...): Λi 3 4 1 2 2 d k giΛi < ⇥> = gi k + m 3 2 2 0 (2π) 16π fields ⇥ ⇤ fields where gi are the dof of the field (+ for bosons, - for fermions). 5 contributions from phase transitions in the early universe ∆V (200 GeV)4 ewk ⇠ ∆V (0.3GeV)4 QCD ⇠ 6 Quantum Gravity cut-off (1018 GeV)4 fine tuning to 120 decimal places − SUSY cut-off (TeV)4 fine tuning to 60 decimal places − EWK phase transition (200GeV)4 fine tuning to 56 decimal places − QCD phase transition (0.3GeV)4 − fine tuning to 44 decimal places Muon (100MeV)4 − electron (1 MeV)4 fine tuning to 36 decimal places − (meV)4 Observed value of the effective cosmological − constant today ! 7 a˙ 2 8π k Λ Friedmann with Λ: H 2 ≡ = Gρ − + a2 3 a2 3 a(t) depends on matter. € w=1/3 – Rad dom: w=0 – Mat dom: w=-1– Vac dom P w(a) = w +(1 a)w Typical parameterisation ⌘ ⇢ 0 − a Friedmann with evolving dark energy: z 2 2 4 3 2 1 + w(z) H (z)=H Ω (1 + z) + Ω (1 + z) + Ω (1 + z) + Ω exp 3 dz 0 r m k de 1 + z ⇤0 ⇥⇥ 8 Planck Collaboration: Planck Cosmological Parameters Planck Collaboration: Planck Cosmological Parameters Fig. 32. The 2D joint posterior distribution betweenNe↵ and Yp with both parameters varying freely, determined from the Planck+WP+highL likelihood. The colour of each sample in Fig. 33. The 2D joint posterior distribution between Ne↵ and ✓s Markov chain indicates the associated value of ✓d/✓s. The Ne↵- from the LCDM+Ne↵+Yp (red) and LCDM+Ne↵ (blue) models, + + Fig.Yp relation 32. The from 2D the joint BBN posterior theory is distribution shown by the between dashedNe curve.↵ and using Planck WL HighL data. YThep with vertical both line parameters shows the varying standard freely, value determinedNe↵ = 3.046. from The the Planckregion+ withWPY+phighL> 0.294 likelihood. is highlighted The colour in gray of delineating each sample the re- in Fig. 33. The 2D joint posterior distribution between Ne↵ and ✓s Markovgion of the chain plot indicates exceeding the the associated 2σ upper value limit of of✓ thed/✓ recents. The mea-Ne↵- 6.5.from Dark the LCDM Energy+N Constraintse↵+Yp (red) and LCDM+Ne↵ (blue) models, Ysurementp relation of from initial the Solar BBN helium theory is abundance shown by (Serenelli the dashed & curve. Basu, using Planck+WL+HighL data. The2010 vertical). line shows the standard value N = 3.046. The A major challenge for cosmology is to elucidate the nature of the e↵ dark energy driving the accelerated expansion of the Universe. region with Yp > 0.294 is highlighted in gray delineating the re- gion of the plot exceeding the 2σ upper limit of the recent mea- 6.5.The Darkmost Energy prosaic Constraintsexplanation is that dark energy is a cosmo- logical constant. An alternative is dynamicalPlanck dark Collaboration: energy mod- Planck Cosmological Parameters surementis thus an of approximate initial Solar degeneracy helium abundance between these(Serenelli two &parame- Basu, 2010). elsA major (Wetterich challenge, 1988 for; Ratra cosmology & Peebles is to, elucidate1988), usually the nature based of the on ters. It can be partially broken by the phase shift of the acoustic adark scalar energy field.