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Issues in Gravitational Clustering and Cosmology Issues in Gravitational Clustering and Cosmology A Thesis submitted to the UNIVERSITY OF PUNE for the degree of Doctor of Philosophy in Physics by JATUSH V. SHETH arXiv:astro-ph/0602433 18 Feb 2006 INTER-UNIVERSITY CENTRE FOR ASTRONOMY AND ASTROPHYSICS PUNE July 2004 Declaration CERTIFIED that the work incorporated in the thesis Issues in Gravitational Clus- tering and Cosmology submitted by Jatush V. Sheth was carried out by the cadidate under my supervision. Such material as has been obtained from other sources has been duly acknowledged in the thesis. Place: IUCAA, Pune Professor Varun Sahni Date : July, 2004 Thesis Supervisor ii To my parents..... Acknowledgments Carrying out a thesis-work is such an elaborate process ! Over years of hard work, one evolves both as a researcher as well as a person. Many a times, it is a journey in solitude; a journey into uncharted territories. It is a funful adventure to seek goals amidst uncertainties. To me, the experience of carrying out this thesis-work has been this, and much more. It is a pleasure to have reached this destination successfully. There are numerous people who have directly or indirectly helped me find my way, have nurtured my personal and/or academic growth. You all have been my fellow-travellers, friends and at times, my guiding light! Today I want to thank you all for being with me in this journey. It was during my course work that I developed a sense of fascination for large-scale structure. Through SURFGEN, I could give an objective meaning to this nameless, somewhat poetic sense of fascination. It is gladdening that this pursuit has served as a link to my further scientific explorations. Thanks Varun, for offering me to work on this challenging problem! You encouraged me to develop myself as an independent researcher; a quality which I am sure, I will cherish forever. You truly supervised my progress, corrected me when I went wrong and were always available in tough times, giving me a friendly shoulder when needed. Thanks for everything! It has been a rewarding experience to collaborate with Sergei Shandarin. I have learnt much from him. His unique insight into large-scale structure studies have often helped me give an objective meaning to my sense of wonder for cosmic structure. Through stories which one hears during graduate school, I had developed a sense iii iv of regard towards Sathya (B.S.Sathyaprakash) for his exceptional programming skills. My efforts to venture into C programming language and later to utilise it in writing SURFGEN, I think, were guided by Sathya's inspiring example of similar sort during his postdoctoral tenure here at IUCAA. It has been a learning experience to work with Sathya, Somnath Bharadwaj and Suketu Bhavsar. Working with Tolia (Anatoly Klypin) on a recent collaboration was similarly quite rewarding. He has been an elderly friend, from whom I have learnt to be careful in work, enthusiastic and hard-working. I would forever be grateful both to Sathya and Tolia for supporting my case while I was applying for jobs. Further, I want to thank my instructors, teachers and colleagues at IUCAA, whose lectures and seminars have been a source of much of my understanding of cosmology and astrophysics. Numerous friends have made my stay at IUCAA cherishable and those lonely months of struggle, bearable! Dinners and treks with Ranjeev-Rama will always re- main fresh in my memory. It always paid to discuss problems with Ranjeev. Jasjeet and Harvinder have been so caring! I have received much warmth and guidance from them. Thanks to both of them for being such wonderful friends! I warmly remember another wonderful couple, Archana and Shanki, who lent me a friendly ear, stood by me in tough times, and received me with understanding. I heartily recall great times I have had with Tarun Saini, Arun Thampan, Sunu, Srini, Niranjan, Suman Datta, Tirthankar, Anand Sankar, Ujjaini, Atul, Amrit, Arman, Sanjit, Amir, Humchand, Abhishek, Saumyadeep, Tapan, Sushmita and Gaurang. It is also a pleasure to recall many discussions with dear friends C.D.Ravikumar and Sudhanshu Barway. Similarly, I recall my friends from across the road Dharam, Poonam, Ayesha and Neeraj whose − friendship I have cherished! Special thanks to Dharam for providing me with thesis style files, and helping me out with many related problems. Thanks to the administrative staff at IUCAA for their support and cooperation in solving bureaucratic glitches as and when they arose. I would specially like to v acknowledge Chella, Rajesh Pardeshi, Lata Shankar, Ratna Rao, Neelima, Deepika, S.L.Gaekwad, Mr.Modak and Mr.Sahasrabuddhe. Neelima and her team (Hemant, Sandeep, Vijay and Shashikant) at the library were always very helpful. The compu- tational work in this thesis was carried out with the help of excellent computational facility provided by the computer centre. Sarah, Anjali, Manisha and Neelam have always helped me meet my computing needs. Thanks to you all! In tough times, it is difficult to maintain sanity. I am blessed with some of the most loving friends from whom I have received pure, selfless love and understanding. But for them, it would have been difficult to keep calm and remain balanced in toughest hours of my stay at IUCAA. Some of those whom I want to fondly recall at this happy hour are Jignesh and Umeshbhai; Naushad, Maitreya and Vikram. Thanks to you all for being with me. I am sure, we shall continue treading the same path, and shall always have each others' company to rejoice in! Mummy-Papa, I dedicate this thesis to you! You both are my ever-lasting source of inspiration and energy, my guiding light! But for your love and the faith you put in me, it would have been impossible for me to survive these long years of academic pursuit! It is difficult to say it in person, but let me steal this opportunity to say that this is the tribute I found most fitting for all your love, support and understanding! I wish and pray, I can offer you much more in days to come. My dear brother Chirag, my Bhabhi and my cute, little nephew Uddhava are too near to be thanked! They are but a part of my life. Today I am warmly thinking of them! IUCAA, Pune Jatush V.Sheth July, 2004 vi Abstract The present era marks a remarkable milestone in the history of cosmology. While val- ues of the cosmological parameters have been obtained to a great precision through measurement of microwave background anisotropies (e.g., COBE, BOOMERANG, WMAP) and type Ia supernovae, dedicated telescopes have been yielding informa- tion about the distribution of galaxies going back in time to when the Universe was only a fraction of its current age. These observations allow us to understand the history of the Universe. We have recently witnessed the culmination of one of the two most ambitious surveys the 2 degree Field Galaxy Redshift Survey (2dFGRS). It maps − out the 3 dimensional distribution of galaxies over 1500 steradians of the sky going − as deep as 600 Mpc∗. As a result we know the 3 dimensional locations of a quarter of − a million galaxies. Another even more ambitious survey, the Sloan Digital Sky Survey (SDSS) is underway, and when completed in a few more years, it would have covered a quarter of the sky and would give us positions of a million galaxies. Thus, the time is ripe enough to confront predictions for large-scale structure (here- after, LSS) arising from theoretical models, with observations. This thesis reports the development of a unique methodology which will help the cosmology community in comparing theoretical predictions of LSS with observations in a detailed and reliable manner. The LSS data from either numerical experiments or observations consist of a large ∗1Mpc 3 106light-years ' × vii viii number of galaxies distributed over a cosmic volume, with mean inter-galactic separa- tion of 5Mpc. Before comparing theory with observations, we first need to quantify ' the basic facts concerning LSS. The traditional way of doing this has been to utilise the two-point correlation function and its Fourier-space counterpart, the power spectrum. It turns out however that quantifying LSS using the 2 point correlation function alone − can result in a considerable information loss. For example, the correlation length-scale for galaxies is estimated to be 5Mpc, signifying that the galaxy-distribution is highly ' clustered compared to one that is random. But this information is of little help in understanding the existence of large-scale superclusters 50 100 Mpc in length as well − as large voids which exist in the universe which reflect the fact that the underlying density field is quite non-Gaussian. It is now widely believed that the non-Gaussian features in the LSS formed as a result of the gravitational clustering of a density field which was initially distributed in the manner of a Gaussian random field (hereafter, GRF). Evidence of Gaussian initial conditions come primarily from observations of cosmic microwave background (CMB). Gravitational clustering is characterised by the transfer of power from larger to smaller scales, which leads to phase coupling be- − tween different Fourier wavemodes. Although the two point correlation function is − sufficient to describe the properties of a GRF, the density field which we see in the Universe today is significantly non-Gaussian. To fully specify its statistical properties, one in principle requires to know the entire hierarchy of correlation functions. How- ever, the task of estimating n point correlation functions is highly cumbersome and − offers limited physical insight into the gravitational clustering process. Hence, the need for alternative statistics, which would be more effective in quantifying LSS, is highly essential.
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