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 non-linear 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 wavenumbers, we show how the current upper bound sigma_mu(z=1) < 0.12on 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 alpha = d n_s / d ln k and running of running beta = 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 beta(k_0)=0.036-0.42 alpha(k_0) and a realistic estimate disfavors any enhancement above the line beta(k_0)=0.022-0.44 alpha(k_0).

5 pages, 3 figures, published version

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• $R^2\log R$ quantum corrections and the inflationary observables
• Correlation function of the luminosity distances
• CMB Spectral Distortion Constraints on Thermal Inflation
• Effects of thermal inflation on small scale density perturbations
• Constraints on small-scale cosmological fluctuations from SNe lensing dispersion
• CMB Spectral $\mu$-Distortion of Multiple Inflation Scenario
• More on Emergent Dark Energy from Unparticles
• Small-scale Effects of Thermal Inflation on Halo Abundance at High-$z$, Galaxy Substructure Abundance and 21-cm Power Spectrum
• Lensing dispersion of SNIa and small scales of the primordial power spectrum
• Diagnosing multiplicative error by lensing magnification of type Ia supernovae