Constraints on scalar and tensor perturbations in phenomenological and two-field inflation models: Bayesian evidences for primordial isocurvature and tensor modes

TL;DR

This paper constrains models of primordial perturbations with adiabatic and isocurvature components using CMB, supernova, and LSS data, finding strong support for purely adiabatic initial conditions and setting limits on isocurvature and tensor contributions.

Contribution

It provides the first comprehensive Bayesian evidence comparison between adiabatic and mixed perturbation models using combined cosmological data.

Findings

Upper limits on isocurvature fractions are around 6-7% with CMB data.

Tensor-to-scalar ratio constrained to r<0.26, unaffected by isocurvature modes.

Bayesian evidence favors the pure adiabatic model over mixed models.

Abstract

We constrain cosmological models where the primordial perturbations have both an adiabatic and a (possibly correlated) cold dark matter (CDM) or baryon isocurvature component. We use both a phenomenological approach, where the primordial power spectra are parametrized with amplitudes and spectral indices, and a slow-roll two-field inflation approach where slow-roll parameters are used as primary parameters. In the phenomenological case, with CMB data, the upper limit to the CDM isocurvature fraction is \alpha<6.4% at k=0.002Mpc^{-1} and 15.4% at k=0.01Mpc^{-1}. The median 95% range for the non-adiabatic contribution to the CMB temperature variance is -0.030<\alpha_T<0.049. Including the supernova (or large-scale structure, LSS) data, these limits become: \alpha<7.0%, 13.7%, and -0.048<\alpha_T< 0.042 (or \alpha<10.2%, 16.0%, and -0.071<\alpha_T<0.024). The CMB constraint on the tensor-to-scalar ratio, r<0.26 at k=0.01Mpc^{-1}, is not affected by the nonadiabatic modes. In the slow-roll two-field inflation approach, the spectral indices are constrained close to 1. This leads to tighter limits on the isocurvature fraction, with the CMB data \alpha<2.6% at k=0.01Mpc^{-1}, but the constraint on \alpha_T is not much affected, -0.058<\alpha_T<0.045. Including SN (or LSS) data, these limits become: \alpha< 3.2% and -0.056<\alpha_T<0.030 (or \alpha<3.4% and -0.063<\alpha_T<-0.008). When all spectral indices are close to each other the isocurvature fraction is somewhat degenerate with the tensor-to-scalar ratio. In addition to the generally correlated models, we study also special cases where the perturbation modes are uncorrelated or fully (anti)correlated. We calculate Bayesian evidences (model probabilities) in 21 different cases for our nonadiabatic models and for the corresponding adiabatic models, and find that in all cases the data support the pure adiabatic model.