Constraining the primordial power spectrum from SNIa lensing dispersion

Abstract

The (absence of detecting) lensing dispersion of supernovae type Ia (SNIa) can be used as a novel and extremely efficient probe of cosmology. In this preliminary example we analyze its consequences for the primordial power spectrum. The main setback is the knowledge of the power spectrum in the nonlinear regime, 1 Mpc −1 ≲ k ≲ 10 2 -10 3 Mpc −1 up to redshift of about unity. By using the lensing dispersion and conservative estimates in this regime of wave numbers, we show how the current upper bound σ μ ðz ≤ 1Þ < 0.12 on existing data gives strong indirect constraints on the primordial power spectrum. The probe extends our handle on the spectrum to a total of 12-15 inflation e-folds. These constraints are so strong that they are already ruling out a large portion of the parameter space allowed by PLANCK for running α ≡ dn s =d ln k and running of running β ≡ d 2 n s =d ln k 2 . The bounds follow a linear relation to a very good accuracy. A conservative bound disfavors any enhancement above the line βðk 0 Þ ¼ 0.036-0.42αðk 0 Þ and a realistic estimate disfavors any enhancement above the line βðk 0 Þ ¼ 0.022-0.44αðk 0 Þ.

Constraints on small-scale cosmological fluctuations from SNe lensing dispersion

“…The model is characterized by the matter density Ωm = 0.3134, the baryon density Ω b = 0.0486, the cosmological constant density ΩΛ = 0.6866, the amplitude and the spectral index of primordial curvature power spectrum As = 2.20×10 −9 , ns = 0.96, and the Hubble expansion rate today H0 = 67.3 km s −1 Mpc −1 . We have verified that varying the other cosmological parameters does not change the conclusions beyond the quoted error bars (see Ben-Dayan & Kalaydzhyan 2014).…”

“…The main limitation of the analysis in Ben- Dayan & Kalaydzhyan (2014) and Ben-Dayan (2014), was the knowledge of the non-linear power spectrum k 1hMpc…”

3D simulations with boosted primordial power spectra and ultracompact minihalos

“…It is in any case interesting to ask how the dark matter substructure would change if the initial small scale perturbations were larger than expected. Other papers which constrain the power spectrum on small scales include [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. In particular, we note that CMB spectral distortion constraints provide an upper bound on the primordial power spectrum on about the same scales as UCMHs, which are about an order of magnitude weaker than the currently claimed constraints but independent of the DM model [20].…”

CMB spectral distortion constraints on thermal inflation

“…we have used Eqs (14),(24). and(31). The case of a pure power law primordial spectrum corresponds to taking N ea → −∞, in which case N * e → ∞ and Eq.…”