5.4 Effect of cosmological parameters on the isocurvature CMB temperature power spectrum100
5.4.6 Spectral index n s
The CMB angular power spectrum can be written as Cℓ = 2
π Z ∞
0
k2PI(k)|Θℓ(k)|2dk, (5.67) wherePI(k)is the primordial power spectrum. The primordial power spectrum is proportional tokns wherek is the wavenumber andnsthe spectral density [41]. This can be written as
PI(k)∝ k
kp
ns
, (5.68)
wherekp is a constant. At the wavenumberk = kp, the power spectrum is independent of the spectral index. For other wavenumbers, ns will modify the slope of the CMB power spectrum, pivoting around some multipole ℓp ≃ kpτ0. This effect on the CMB spectrum is clearly seen in Figure 5.27 for the CI, BI NID and NIV modes. A value of ns < 1lowers the small scale anisotropy and boosts the large scale anisotropy with the opposite effect forns >1.
0.1 1 10 100 1000 10000 100000
0 400 800 1200 1600 2000
ns=0.5 1.
1.5
ℓ ℓ(ℓ+1)Cℓ/2π(µK2 )
(a) CI
0.001 0.01 0.1 1 10 100 1000
0 400 800 1200 1600 2000
ns=0.5 1.
1.5
ℓ ℓ(ℓ+1)Cℓ/2π(µK2 )
(b) BI
0 200 400 600 800 1000 1200 1400
0 400 800 1200 1600 2000
ns=0.5 1.
1.5
ℓ ℓ(ℓ+1)Cℓ/2π(µK2 )
(c) NID
0 500 1000 1500 2000 2500
0 400 800 1200 1600 2000
ns=0.5 1.
1.5
ℓ ℓ(ℓ+1)Cℓ/2π(µK2 )
(d) NIV
Figure 5.27: Spectral index dependence of the CMB power spectrum for isocurvature models.
This is for a flat ΛCDM universe withΩbh2 = 0.022, Ωch2 = 0.125 andh = 0.7, pivot scale kp = 0.05Mpc−1.
CHAPTER 6
Fundamental Uncertainty in the BAO Scale from Isocurvature Modes
6.1 Introduction
Large galaxy surveys fall squarely in the realm of astrophysics and traditionally we think of them as living almost independently of the physics of the early Universe. In this Letter we show that this assumption breaks down rather dramatically in the case of Baryon Acoustic Oscillations (BAO) (for a recent review see [12] ). BAO surveys are a key component of the global plan for the next two decades in cosmology because they are believed to provide a robust and powerful statistical standard ruler that can probe dark energy. They have shown to be robust to a variety of potential systematic effects which only become important at the1% level [155, 157]. However, here we show that there is a much more significant “systematic” arising from the possibility of isocurvature modes correlated with the dominant adiabatic perturbation which may have been generated during the early Universe.
To understand this systematic, consider the standard ruler provided by the distance that sound waves can propagate in the primordial plasma. The standard picture based on adiabatic pertur- bations suggests that the key scale is the sound horizon:
rs= Z tcmb
0
cs(1 +z)dt= Z ∞
zcmb
cs(z′) H(z′)dz′, wherecs(z) = 1/p
3 (1 +Rb(1 +z)−1)andRb = 31500ωb(Tcmb/2.7K)−4. The measurement of the late-time clustering of galaxies in the transverse direction probes the angular diameter dis- tance given bydA(z) = r⊥(1 +z)−1/∆Θ wherer⊥ is the intrinsic size of rs in the transverse direction and∆Θis the position of the peak in the angular correlation function, while the clus- tering on a scaler|| along the line of sight probes the Hubble parameter,H(z) = ∆z/r||.
Measurements of the angular diameter distance and Hubble parameter in a series of redshift bins using the BAO technique provide an effective probe of the properties of dark energy [23, 139, 155], with prospective constraints on the equation of state of dark energy,w0,and its evolution wa,as low as 0.02 and 0.04, respectively, for a future space-based spectroscopic mission (e.g., ADEPT [151]), with forecasts for current experiments (e.g., BOSS [149]) at the level of 0.03 and 0.1 respectively.
Systematic effects that affect the position and shape of the Baryon Acoustic Peak (BAP), such as nonlinearity and redshift-space distortions, have been studied and can be treated without a sig- nificant impact on dark energy constraints [155, 157]. The impact on the BAP from non-standard conditions in the early Universe such as changes in recombination, early dark energy or inhomo- geneous reionization, have been studied before [40]. Here we concentrate on the possibility that the initial conditions were not purely adiabatic. Adiabatic initial conditions are described by a net density perturbation such that the relative number densities of all cosmological species remain unperturbed. There is however another possible type of perturbation, termed isocurvature, char- acterized by variations in the particle number ratios such that the net curvature perturbation is zero [29]. We show that isocurvature modes alter the standard picture above and deform the char- acteristic BAP scale which manifests in the anisotropies in the cosmic microwave background
and the clustering of matter. We investigate the extent to which an admixture of isocurvature modes, small enough to be undetectable by PLANCK, degrades constraints on dark energy pa- rameters when allowed for, or bias the recovered values if not taken into account. Put more generally, we investigate the coupling of the primordial density perturbation to the constraints arising from our observations at late times, even with strong prior constraints on the isocurvature modes from CMB data. Constraints from WMAP 3 year data indicate that a 50% admixture of three isocurvature modes with the adiabatic mode is permitted [13], whereas forecasts for the PLANCK experiment indicate that arbitrary isocurvature mode admixtures will be constrained to below the 10% level [31].
What are the possible origins of isocurvature modes? The simplest possibility perhaps is multiple field inflation [119, 137], with the curvaton mechanism as a special case [113]. The resulting isocurvature perturbation is a leading candidate to explain any primordial non-Gaussianity and can, in certain cases, explain the observed asymmetry in the CMB [52]. While the simplest, adiabatic models of inflation are currently preferred [177], it is possible that some isocurvature contamination will be uncovered in future experiments and indeed this would be very fortuitous since it would provide new handles on the physics of the very early Universe. In this chapter we argue that allowing for the possibility of isocurvature modes is crucial in future BAO surveys and that as a reward, such surveys can provide a powerful lens on the early Universe.