Sourced scalar fluctuations in bouncing cosmology

Abstract

We calculate the scalar power spectrum generated by sourced fluctuations due to coupling between the scalar field, which holds most of the energy density of the universe, and a gauge field for a general FLRW metric. For this purpose we calculate the curvature perturbation to second order in the presence of gauge fields, and show that the gauge fields behave like an additional potential term. We then apply the analysis to the case of slow-contraction. Due to the interaction between the scalar field and gauge fields additional 'sourced' tensor and scalar spectra are generated. The resulting spectra are chiral, slightly blue and arbitrarily close to scale invariance. The only difference between the tensor and scalar spectra is the coupling constant with an O(1) numerical coefficient, and some momentum space polarization vectors. As a result the tilt of the spectra are the same. For the nearly scale invariant case, the momentum integration gives the same leading contribution. Hence, r 1 where the deviation from unity is controlled by the deviation from scale invariance, and is not in agreement with CMB observations. Deviating considerably from near scale invariance, and considering a bluer tilt with n T > 0.12, the model cannot account for CMB observations, but can be detected by LIGO and/or LISA in the future.

Sourced fluctuations in generic slow contraction

“…where K T , K S are the integrals over momentum given by JT λ ( k, τ ) JT λ ( k, τ ) and JS λ ( k, τ ) JS λ ( k, τ ) , where JT λ ( k, τ ) and JS λ ( k, τ ) are J T λ ( k, τ ) and J T λ ( k, τ ) without the time dependent factors a(τ ) and C(τ ) 2 (τ ). The scale dependence of K T , K S are same as that of momentum integrals f T and f S defined in [22,23].…”

“…Introducing such gauge fields can source second order inhomogeneities that dominate over the blue tilted first order perturbations. Following [22,23,41] equation (3.1) is modified by a source term:…”

Lectures on classical and quantum cosmology

“…However debatable they are, these models offer a prediction of the SGWB that can be compared with present or near-future observational data. Other models that could produce a detactable signal but that have not been studied yet in detail are the pre-big-bang scenario [143,144] and bouncing models with a slow contracting phase [145][146][147].…”

The Grand Canonical Multiverse and the Small Cosmological Constant

“…This single Universe is a superposition of multiple different eigenstates with energy levels, rather than the physical existence of many universes. Hence, the Multiverse by itself does allow to make nontrivial predictions without the need of a measure or anthropics, leaving Inflation with other problems such as the Big Bang singularity [23][24][25][26][27][28][29] , gradual ruling out of models and obviously the warm pool of quantum gravity conjectures [30][31][32][33][34].…”