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Non Gaussianity of primordial gravitational waves and cosmic density and velocity fields
Non Gaussianity of primordial gravitational waves and cosmic density and velocity fields
We study non-Gaussianity of primordial gravitational waves (GWs) generated during inflation, and of present day matter and galaxy density and velocity fields in the Universe. We show that non-Gaussianity of primordial GWs is a crucial test of their origin and can be used to constrain the energy density fraction of spectator gauge fields in the early Universe if the primordial GWs are sourced by a spectator sector. We consider a particular inflation model containing a scalar inflaton, and spectator axion and SU(2) gauge fields. The axion and the gauge fields are coupled to each other via a Chern-Simons like interaction. Because of this coupling, the gauge fields experience a tachyonic instability during inflation and get amplified. The SU(2) gauge fields have a tensor degree of freedom which linearly sources GWs that are helical, and can be strongly scale-dependent. Moreover, their amplitude can be much larger than vacuum fluctuations of the metric. In this thesis however, we focus on scale-independent GWs produced in this model. We study the bispectrum of these scale- independent GWs, and find that its production is dominated by the self-interaction of the gauge fields. The shape of the tensor bispectrum is approximately an equilateral shape for 3<=mQ<=4, where mQ is an effective dimensionless mass of the SU(2) field normalised by the Hubble expansion rate during inflation. The amplitude of non-Gaussianity of the tensor modes, characterised by the ratio Bh/Ph^2 , is inversely proportional to the energy density fraction of the gauge field. This ratio can be much greater than unity, whereas we show that the ratio from the vacuum fluctuation of the metric is of order unity. The bispectrum is effective at constraining large mQ regions of the parameter space, whereas the power spectrum constrains small mQ regions. The present-day cosmic density and velocity fields in the Universe are also highly non- Gaussian due to non-linear gravitational evolution. By assuming the matter and galaxy density distributions to be log-normal, and the velocity field to be linearly generated from the matter density field, we show that the pairwise line-of-sight velocity distribution of log-normal fields is non-Gaussian and looks qualitatively similar to that measured from N-body simulations. The moments of the pairwise velocity PDF can in principle be ana- lytically calculated for this simple setting, giving us a handle on modelling of the full PDF. We compare the redshift space monopole and quadrupole power spectrum for our mock catalogs, finding a good match with the Kaiser prediction on large scales. We present a public code to generate log-normal mock catalogs of galaxies in redshift space which can be used to study the cross-correlation between galaxy positions and weak lensing fields. Our code is also being used to study power spectrum and bispectrum covariance matrices in real and redshift space, which will be useful for upcoming galaxy surveys such as PFS and Euclid.
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Agrawal, Aniket
2018
English
Universitätsbibliothek der Ludwig-Maximilians-Universität München
Agrawal, Aniket (2018): Non Gaussianity of primordial gravitational waves and cosmic density and velocity fields. Dissertation, LMU München: Faculty of Physics
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Abstract

We study non-Gaussianity of primordial gravitational waves (GWs) generated during inflation, and of present day matter and galaxy density and velocity fields in the Universe. We show that non-Gaussianity of primordial GWs is a crucial test of their origin and can be used to constrain the energy density fraction of spectator gauge fields in the early Universe if the primordial GWs are sourced by a spectator sector. We consider a particular inflation model containing a scalar inflaton, and spectator axion and SU(2) gauge fields. The axion and the gauge fields are coupled to each other via a Chern-Simons like interaction. Because of this coupling, the gauge fields experience a tachyonic instability during inflation and get amplified. The SU(2) gauge fields have a tensor degree of freedom which linearly sources GWs that are helical, and can be strongly scale-dependent. Moreover, their amplitude can be much larger than vacuum fluctuations of the metric. In this thesis however, we focus on scale-independent GWs produced in this model. We study the bispectrum of these scale- independent GWs, and find that its production is dominated by the self-interaction of the gauge fields. The shape of the tensor bispectrum is approximately an equilateral shape for 3<=mQ<=4, where mQ is an effective dimensionless mass of the SU(2) field normalised by the Hubble expansion rate during inflation. The amplitude of non-Gaussianity of the tensor modes, characterised by the ratio Bh/Ph^2 , is inversely proportional to the energy density fraction of the gauge field. This ratio can be much greater than unity, whereas we show that the ratio from the vacuum fluctuation of the metric is of order unity. The bispectrum is effective at constraining large mQ regions of the parameter space, whereas the power spectrum constrains small mQ regions. The present-day cosmic density and velocity fields in the Universe are also highly non- Gaussian due to non-linear gravitational evolution. By assuming the matter and galaxy density distributions to be log-normal, and the velocity field to be linearly generated from the matter density field, we show that the pairwise line-of-sight velocity distribution of log-normal fields is non-Gaussian and looks qualitatively similar to that measured from N-body simulations. The moments of the pairwise velocity PDF can in principle be ana- lytically calculated for this simple setting, giving us a handle on modelling of the full PDF. We compare the redshift space monopole and quadrupole power spectrum for our mock catalogs, finding a good match with the Kaiser prediction on large scales. We present a public code to generate log-normal mock catalogs of galaxies in redshift space which can be used to study the cross-correlation between galaxy positions and weak lensing fields. Our code is also being used to study power spectrum and bispectrum covariance matrices in real and redshift space, which will be useful for upcoming galaxy surveys such as PFS and Euclid.