Non-Gaussianity of Inflationary Gravitational Waves from the Field Equation

We demonstrate equivalence of the in-in formalism and Green's function method for calculating the bispectrum of primordial gravitational waves generated by vacuum fluctuations of the metric. The tree-level bispectrum from the field equation, $B_h$, agrees with the results obtained previously using the in-in formalism exactly. Characterising non-Gaussianity of the fluctuations using the ratio $B_h/P^2_h$ in the equilateral configuration, where $P_h$ is the power spectrum of scale-invariant gravitational waves, we show that it is much weaker than in models with spectator gauge fields. We also calculate the tree-level bispectrum of two right-handed and one left-handed gravitational wave using Green's function, reproducing the results from in-in formalism, and show that it can be as large as the bispectrum of three right-handed gravitational waves.Comment: 17 pages, 2 figures; comments welcom

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

Large Tensor Non-Gaussianity from Axion-Gauge Fields Dynamics

We show that an inflation model in which a spectator axion field is coupled to an SU(2) gauge field produces a large three-point function (bispectrum) of primordial gravitational waves, $B_{h}$, on the scales relevant to the cosmic microwave background experiments. The amplitude of the bispectrum at the equilateral configuration is characterized by $B_{h}/P_h^2=\mathcal{O}(10)\times \Omega_A^{-1}$, where $\Omega_A$ is a fraction of the energy density in the gauge field and $P_h$ is the power spectrum of gravitational waves produced by the gauge field.Comment: 6 pages, 2 figures; matches version accepted by PR

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

Tensor Non-Gaussianity from Axion-Gauge-Fields Dynamics : Parameter Search

We calculate the bispectrum of scale-invariant tensor modes sourced by spectator SU(2) gauge fields during inflation in a model containing a scalar inflaton, a pseudoscalar axion and SU(2) gauge fields. A large bispectrum is generated in this model at tree-level as the gauge fields contain a tensor degree of freedom, and its production is dominated by self-coupling of the gauge fields. This is a unique feature of non-Abelian gauge theory. The shape of the tensor bispectrum is approximately an equilateral shape for $3\lesssim m_Q\lesssim 4$, where $m_Q$ 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 $B_h/P^2_h$, is inversely proportional to the energy density fraction of the gauge field. This ratio can be much greater than unity, whereas the ratio from the vacuum fluctuation of the metric is of order unity. The bispectrum is effective at constraining large $m_Q$ regions of the parameter space, whereas the power spectrum constrains small $m_Q$ regions.Comment: 34 pages, 15 figures; comments welcome; extended range of parameter values for cosine, matches version accepted by JCA

Generating Log-normal Mock Catalog of Galaxies in Redshift Space

We present a public code to generate a mock galaxy catalog in redshift space assuming a log-normal probability density function (PDF) of galaxy and matter density fields. We draw galaxies by Poisson-sampling the log-normal field, and calculate the velocity field from the linearised continuity equation of matter fields, assuming zero vorticity. This procedure yields a PDF of the pairwise velocity fields that is qualitatively similar to that of N-body simulations. We check fidelity of the catalog, showing that the measured two-point correlation function and power spectrum in real space agree with the input precisely. We find that a linear bias relation in the power spectrum does not guarantee a linear bias relation in the density contrasts, leading to a cross-correlation coefficient of matter and galaxies deviating from unity on small scales. We also find that linearising the Jacobian of the real-to-redshift space mapping provides a poor model for the two-point statistics in redshift space. That is, non-linear redshift-space distortion is dominated by non-linearity in the Jacobian. The power spectrum in redshift space shows a damping on small scales that is qualitatively similar to that of the well-known Fingers-of-God (FoG) effect due to random velocities, except that the log-normal mock does not include random velocities. This damping is a consequence of non-linearity in the Jacobian, and thus attributing the damping of the power spectrum solely to FoG, as commonly done in the literature, is misleading.Comment: 38 pages, 16 figures, code publicly available as "lognormal_galaxies" at http://wwwmpa.mpa-garching.mpg.de/~komatsu/codes.html Matches published version : added figures and explanatory comment

A review on determinants and barriers affecting the transition from curative care to palliative care in patients suffering from terminal cancer

The integration of palliative care into comprehensive cancer care has become increasingly recognized as an essential aspect of cancer treatment. Palliative care can improve patient outcomes, symptom management, and overall satisfaction with care. However, despite the benefits of palliative care, several barriers exist that prevent its widespread implementation, including lack of awareness and understanding of palliative care, lack of access to palliative care services, and stigma associated with palliative care. The decision to transition from curative to palliative care is complex and influenced by several factors, including patient preferences, disease stage, and prognosis, symptom burden, comorbidities, and social support. Effective communication between healthcare providers, patients, and families is essential in ensuring that patients are informed about their options and can make informed decisions about their care. This literature review aims to explore the factors that influence the decision to transition to palliative care and to identify the barriers to the implementation of palliative care in cancer patients. The review also discusses strategies to overcome these barriers and highlights the importance of integrating palliative care into cancer care from the time of cancer diagnosis.