Final Report Summary - NEBRIC (Non-linear effects and backreaction in classical and quantum cosmology.)
Cosmology has gone through an amazing revolution during the last decade owing to the large amount of new precise observational data. These data strongly indicate the existence of two periods of accelerated expansion in the history of the Universe. One in the primordial universe, the so-called inflationary phase, and one at the present era. The link between data and models is made mostly by linear perturbation theory on a spatially homogeneous and isotropic Friedmann Universe. But beyond linear order many interesting effects appear, such as the non-Gaussianity, that should be present in the CMB, and backreaction (BR) effects. In particular, quantum BR of primordial fluctuations can significantly modify the dynamics of the early universe and its observational signatures, while classical BR of large scale structure (LSS) might contribute to the observed late time acceleration. The goal of my project was to quantify these non-linear effects more precisely. First, I wanted to connect the BR of the LSS to observations using a light-cone averaging prescription. Then, to evaluate BR effects from magnetic fields generated during inflation in a consistent way both using the effective equation for the cosmological backreaction and the data inside the backward light-cone of a physical observer. I also planned to obtain observational bounds on BR from the study of the effective equation of state it induces and from its effect on early phases of expansion, from preheating to CMB decoupling passing through the relativistic era that takes place before the Big-bang nucleosynthesis. A further objective was to consider alternative approach to the BR of the LSS. Namely, to investigate how a smooth expand Universe can be obtained from small, static inhomogeneous cells that are glued together. Finally, I wanted to investigate how non-Gaussianity (and other observables) can change as consequences of the loop corrections.
During the fellowship I finally faced the first three objectives of my research project. In particular, I have studied, to higher order in perturbation theory, the non-linear and relativistic physics necessary to extract information from large scale structure (LSS) surveys and CMB experiments. While, in the early universe context, I have studied the quantum backreaction of scalar and tensor perturbations.
The main results that I have achieved so far are the following.
In connection with the recent literature about the generation of cosmological seeds for the magnetic fields, observe in galaxies and clusters, during inflation, I have showed how the adiabatic renormalization of the two-point function of the magnetic field is not a viable way to generate inflationary magnetic field.
In a chaotic inflationary model, I have investigated the backreaction effects due to long wavelength scalar and tensor fluctuations on the effective Hubble factor and equation of state (with respect to different classes of observers). In particular, I showed how the observed dynamic for a test field observer can be rather different from the background one. In a large region of parameter space, the observed inflation stops much earlier with respect to the background one, and the measured equation of state has an inverted time evolution.
On the other hand, regarding the impact of classical inhomogeneities on late time cosmological observables, my main research achievements have led me to formulate new tools with applications in the field of relativistic cosmology, namely in the study of the non-linear and relativistic physics necessary to extract information from LSS surveys and CMB experiments.
As main results, I have showed how the impact of stochastic inhomogeneities on LSS cosmological observables can not be the responsible for the present acceleration of the Universe. Then I have obtained an exact solution of the Jacobi Map and the perturbative expressions, up to second order and the Poisson gauge, of different cosmological observables. Among them, the number of galaxy per solid ancle and redshift bin, the so-called galaxy number counts. Furthermore, I have investigated the bispectrum of the galaxy number counts in a setting that can be directly compared with observation of large scale structure surveys.
To conclude, I have shown how to take into consideration the impact of inhomogeneities on local measurement and how this alleviates the tension between different measurements of the Hubble parameter. The relative paper was selected as a PRL editors’ suggestion for its novelty and groundbreaking character.
During the fellowship I finally faced the first three objectives of my research project. In particular, I have studied, to higher order in perturbation theory, the non-linear and relativistic physics necessary to extract information from large scale structure (LSS) surveys and CMB experiments. While, in the early universe context, I have studied the quantum backreaction of scalar and tensor perturbations.
The main results that I have achieved so far are the following.
In connection with the recent literature about the generation of cosmological seeds for the magnetic fields, observe in galaxies and clusters, during inflation, I have showed how the adiabatic renormalization of the two-point function of the magnetic field is not a viable way to generate inflationary magnetic field.
In a chaotic inflationary model, I have investigated the backreaction effects due to long wavelength scalar and tensor fluctuations on the effective Hubble factor and equation of state (with respect to different classes of observers). In particular, I showed how the observed dynamic for a test field observer can be rather different from the background one. In a large region of parameter space, the observed inflation stops much earlier with respect to the background one, and the measured equation of state has an inverted time evolution.
On the other hand, regarding the impact of classical inhomogeneities on late time cosmological observables, my main research achievements have led me to formulate new tools with applications in the field of relativistic cosmology, namely in the study of the non-linear and relativistic physics necessary to extract information from LSS surveys and CMB experiments.
As main results, I have showed how the impact of stochastic inhomogeneities on LSS cosmological observables can not be the responsible for the present acceleration of the Universe. Then I have obtained an exact solution of the Jacobi Map and the perturbative expressions, up to second order and the Poisson gauge, of different cosmological observables. Among them, the number of galaxy per solid ancle and redshift bin, the so-called galaxy number counts. Furthermore, I have investigated the bispectrum of the galaxy number counts in a setting that can be directly compared with observation of large scale structure surveys.
To conclude, I have shown how to take into consideration the impact of inhomogeneities on local measurement and how this alleviates the tension between different measurements of the Hubble parameter. The relative paper was selected as a PRL editors’ suggestion for its novelty and groundbreaking character.