QFT ON CURVED SPACETIMES & ITS APPLICATIONS IN COSMOLOGY. Anna Ijjas Columbia University
|
|
|
- Charla King
- 5 years ago
- Views:
Transcription
1 QFT ON CURVED SPACETIMES & ITS APPLICATIONS IN COSMOLOGY Anna Ijjas Columbia University
2 2 The cosmologist s dilemma WE HAVE NO FULL-BLOWN THEORY OF QUANTUM GRAVITY [YET] WE HAVE EXPERIMENTAL ACCESS TO ENERGIES WHERE EINSTEIN GRAVITY IS NOT ENOUGH [more later] two `schools: priority to QFT: cosmology is `EFT QFT enters on small scales only, background is driven by classical dynamics (may or may not be Einstein gravity) THIS TALK: A PRACTIONER S ACCOUNT FROM A PRAGMATIC PERSPECTIVE Save your philosophy questions for the discussion!
3 3 PLAN THE BACKGROUND Classical Friedman-Robertson-Walker dynamics QFT ON CURVED SPACE- TIME A VERY brief introduction INFLATION AND ETERNAL INFLATION What goes well and what goes very wrong. QFT ON CONTRACTING BACKGROUNDS When all goes well.
4 a r X i v : The classical background PATCH SIZE: R(t) ~ x R(t 0 ) 2 R(t 0 ) a(t 0 ) = vs. HORIZON SIZE: H - ~ e x H - (t 0 ) EQUATION OF STATE: e = (3/2)(+p/r ) RADIATION: e =2, a(t LSS ) = /000 DUST: e =3/2
5 B a r d e e n, S t e i n h a r d t, T u r n e r QFT on curved spacetime h ij: t e n s o r m o d e s a. k. a. gravitational waves classical eq. of motion: Fourier transform: with basis introduce conjugate momentum: CANONICAL QUNATIZATION p r o m o t e b o t h h kr a n d π kr t o o p e r a t o r s t h a t s a t i s f y e q u a l - t i m e c o m m u t a t i o n r e l a t i o n s s i n c e b o t h h kr & π kr hermitian: mode functions satisfy: where
6 <latexit sha_base64="djdskcnhl5f+dv08xzeokhg/t4=">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</latexit> <latexit sha_base64="djdskcnhl5f+dv08xzeokhg/t4=">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</latexit> <latexit sha_base64="djdskcnhl5f+dv08xzeokhg/t4=">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</latexit> <latexit sha_base64="djdskcnhl5f+dv08xzeokhg/t4=">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</latexit> <latexit sha_base64="cohi756pxnvhfjdbvja5j3u5lfa=">aaacfhicbvbns8naen3urq/oh69lbzbuetsbpvwiphctywmhg22227dpph7kqoix/ci3/fiwcvrx68+w/ctdo64obx3szzmzzy8evwna3uzibxhcki6xvlbxjfmzabfswssganrcrbplfm8jagingrvgyevicnf3bre43h5hupapvybgznyc9khc5jaalzzw8ws4le0cwe/e5lzoywfrk+aa76l5c6nrym/fuqplnlq2knqkejfaelneedc/8cjortqiwahveqbztxecmrakngmuljesjnraeqytaugcptx09fwg97tswdi6gobj9tfeykjlbogvu4mcptvtjel/3ntblqnbsrdoaew0vgibiiwrdipche4zbteubncjde3ytonkldqqzz0cpb0y7okua2cvezr43ltfjjgee2gxbspbhscaugkvedufsinterejoejbfj3fgytxamycw2+gpj8wev9z4k</latexit> <latexit sha_base64="cohi756pxnvhfjdbvja5j3u5lfa=">aaacfhicbvbns8naen3urq/oh69lbzbuetsbpvwiphctywmhg22227dpph7kqoix/ci3/fiwcvrx68+w/ctdo64obx3szzmzzy8evwna3uzibxhcki6xvlbxjfmzabfswssganrcrbplfm8jagingrvgyevicnf3bre43h5hupapvybgznyc9khc5jaalzzw8ws4le0cwe/e5lzoywfrk+aa76l5c6nrym/fuqplnlq2knqkejfaelneedc/8cjortqiwahveqbztxecmrakngmuljesjnraeqytaugcptx09fwg97tswdi6gobj9tfeykjlbogvu4mcptvtjel/3ntblqnbsrdoaew0vgibiiwrdipche4zbteubncjde3ytonkldqqzz0cpb0y7okua2cvezr43ltfjjgee2gxbspbhscaugkvedufsinterejoejbfj3fgytxamycw2+gpj8wev9z4k</latexit> <latexit sha_base64="cohi756pxnvhfjdbvja5j3u5lfa=">aaacfhicbvbns8naen3urq/oh69lbzbuetsbpvwiphctywmhg22227dpph7kqoix/ci3/fiwcvrx68+w/ctdo64obx3szzmzzy8evwna3uzibxhcki6xvlbxjfmzabfswssganrcrbplfm8jagingrvgyevicnf3bre43h5hupapvybgznyc9khc5jaalzzw8ws4le0cwe/e5lzoywfrk+aa76l5c6nrym/fuqplnlq2knqkejfaelneedc/8cjortqiwahveqbztxecmrakngmuljesjnraeqytaugcptx09fwg97tswdi6gobj9tfeykjlbogvu4mcptvtjel/3ntblqnbsrdoaew0vgibiiwrdipche4zbteubncjde3ytonkldqqzz0cpb0y7okua2cvezr43ltfjjgee2gxbspbhscaugkvedufsinterejoejbfj3fgytxamycw2+gpj8wev9z4k</latexit> <latexit sha_base64="cohi756pxnvhfjdbvja5j3u5lfa=">aaacfhicbvbns8naen3urq/oh69lbzbuetsbpvwiphctywmhg22227dpph7kqoix/ci3/fiwcvrx68+w/ctdo64obx3szzmzzy8evwna3uzibxhcki6xvlbxjfmzabfswssganrcrbplfm8jagingrvgyevicnf3bre43h5hupapvybgznyc9khc5jaalzzw8ws4le0cwe/e5lzoywfrk+aa76l5c6nrym/fuqplnlq2knqkejfaelneedc/8cjortqiwahveqbztxecmrakngmuljesjnraeqytaugcptx09fwg97tswdi6gobj9tfeykjlbogvu4mcptvtjel/3ntblqnbsrdoaew0vgibiiwrdipche4zbteubncjde3ytonkldqqzz0cpb0y7okua2cvezr43ltfjjgee2gxbspbhscaugkvedufsinterejoejbfj3fgytxamycw2+gpj8wev9z4k</latexit> <latexit sha_base64="vwoby+nozi8oghhq4ogu5v3nd6k=">aaacanicbvbns8naen3urq/ot70slgetyupgnoreumxgrgfjpbnztmu3xy4oxfkkhjxr3jxoolvx+hnf+o2zufbhww83pthzp6fcq7asr6n0tlyyupaeb2ysbmvwpu7t2qjjouotqriez4rdhby+yab8e6qwqk8gvr+8orid9+yflxjl6bucq8iprjhnjkqes988bv9xjyn2acijso+f9jf3fi9zsmvwrzk2bf4ldkcoq0oqzx26q0cximvbbloravgpetirwkti44makpyqosz9nyjxjsxt38y42otbdhmpk4y8ft9pzgtsklr5ovoimbazxst8t+vm0f47uu8tjngmz0tcjobicgtqhdajamgrpoqkrm+fdmbkyscjq2iq7dnx4ktr2ubovt6unyyknmjper+ge2egmnvattzcdkhpez+gvvrlpxovxbnzmwktgmbop/sd4/aej8pdh</latexit> <latexit sha_base64="vwoby+nozi8oghhq4ogu5v3nd6k=">aaacanicbvbns8naen3urq/ot70slgetyupgnoreumxgrgfjpbnztmu3xy4oxfkkhjxr3jxoolvx+hnf+o2zufbhww83pthzp6fcq7asr6n0tlyyupaeb2ysbmvwpu7t2qjjouotqriez4rdhby+yab8e6qwqk8gvr+8orid9+yflxjl6bucq8iprjhnjkqes988bv9xjyn2acijso+f9jf3fi9zsmvwrzk2bf4ldkcoq0oqzx26q0cximvbbloravgpetirwkti44makpyqosz9nyjxjsxt38y42otbdhmpk4y8ft9pzgtsklr5ovoimbazxst8t+vm0f47uu8tjngmz0tcjobicgtqhdajamgrpoqkrm+fdmbkyscjq2iq7dnx4ktr2ubovt6unyyknmjper+ge2egmnvattzcdkhpez+gvvrlpxovxbnzmwktgmbop/sd4/aej8pdh</latexit> <latexit sha_base64="vwoby+nozi8oghhq4ogu5v3nd6k=">aaacanicbvbns8naen3urq/ot70slgetyupgnoreumxgrgfjpbnztmu3xy4oxfkkhjxr3jxoolvx+hnf+o2zufbhww83pthzp6fcq7asr6n0tlyyupaeb2ysbmvwpu7t2qjjouotqriez4rdhby+yab8e6qwqk8gvr+8orid9+yflxjl6bucq8iprjhnjkqes988bv9xjyn2acijso+f9jf3fi9zsmvwrzk2bf4ldkcoq0oqzx26q0cximvbbloravgpetirwkti44makpyqosz9nyjxjsxt38y42otbdhmpk4y8ft9pzgtsklr5ovoimbazxst8t+vm0f47uu8tjngmz0tcjobicgtqhdajamgrpoqkrm+fdmbkyscjq2iq7dnx4ktr2ubovt6unyyknmjper+ge2egmnvattzcdkhpez+gvvrlpxovxbnzmwktgmbop/sd4/aej8pdh</latexit> <latexit sha_base64="vwoby+nozi8oghhq4ogu5v3nd6k=">aaacanicbvbns8naen3urq/ot70slgetyupgnoreumxgrgfjpbnztmu3xy4oxfkkhjxr3jxoolvx+hnf+o2zufbhww83pthzp6fcq7asr6n0tlyyupaeb2ysbmvwpu7t2qjjouotqriez4rdhby+yab8e6qwqk8gvr+8orid9+yflxjl6bucq8iprjhnjkqes988bv9xjyn2acijso+f9jf3fi9zsmvwrzk2bf4ldkcoq0oqzx26q0cximvbbloravgpetirwkti44makpyqosz9nyjxjsxt38y42otbdhmpk4y8ft9pzgtsklr5ovoimbazxst8t+vm0f47uu8tjngmz0tcjobicgtqhdajamgrpoqkrm+fdmbkyscjq2iq7dnx4ktr2ubovt6unyyknmjper+ge2egmnvattzcdkhpez+gvvrlpxovxbnzmwktgmbop/sd4/aej8pdh</latexit> a r X i v : ; S t e i n h a r d t ; V i l e n k i n ; Guth Inflation and Eternal Inflation background evolution field picture V cl + p 2 φ = V ' 2 V, V 2 < within unit Hubble time: cl = H H V, 3H vs. p 2 H quantum runaway/eternal inflation/multiverse: HORIZON SIZE: H - ~ e x H - (t 0 ) p 2 Cl V 3/2 V, >
7 a r X i v : QFT on contracting backgrounds HORIZON SIZE: H - ~ e x H - (t 0 ) e 3 D(t 0 ) a(t 0 ) = V φ = V > 3 NO quantum runaway/ eternal inflation/ multiverse!
The early and late time acceleration of the Universe
The early and late time acceleration of the Universe Tomo Takahashi (Saga University) March 7, 2016 New Generation Quantum Theory -Particle Physics, Cosmology, and Chemistry- @Kyoto University The early
Quantum gravity and aspects of relativity
Quantum gravity and aspects of relativity Branislav Nikolic Institute for Theoretical Physics, University of Cologne Bonn-Cologne Graduate School in Physics and Astronomy who are we??? Gravitation and
Big Bounce and Inflation from Spin and Torsion Nikodem Popławski
Big Bounce and Inflation from Spin and Torsion Nikodem Popławski Colloquium, Department of Physics Queens College, City University of New York, Queens, NY, USA November 12, 2018 Cosmic Microwave Background
In the expanding Universe, a comoving volume element expands along with the cosmological flow, getting physically larger over time.
Cosmological models In the expanding Universe, a comoving volume element expands along with the cosmological flow, getting physically larger over time. The expansion is described by the scale factor R(t).
PHYM432 Relativity and Cosmology 17. Cosmology Robertson Walker Metric
PHYM432 Relativity and Cosmology 17. Cosmology Robertson Walker Metric Cosmology applies physics to the universe as a whole, describing it s origin, nature evolution and ultimate fate. While these questions
SEMICLASSICAL and QUANTUM BLACK HOLES
SEMICLASSICAL and QUANTUM BLACK HOLES Norma G. SANCHEZ DR CNRS, LERMA Observatoire de Paris Ecole Internationale Daniel Chalonge Héctor de Vega Open Session 19 MAI 2016 Observatoire de Paris Macroscopic
Oddities of the Universe
Oddities of the Universe Koushik Dutta Theory Division, Saha Institute Physics Department, IISER, Kolkata 4th November, 2016 1 Outline - Basics of General Relativity - Expanding FRW Universe - Problems
Contents. Part I The Big Bang and the Observable Universe
Contents Part I The Big Bang and the Observable Universe 1 A Historical Overview 3 1.1 The Big Cosmic Questions 3 1.2 Origins of Scientific Cosmology 4 1.3 Cosmology Today 7 2 Newton s Universe 13 2.1
Relativity SPECIAL, GENERAL, AND COSMOLOGICAL SECOND EDITION. Wolfgang Rindler. Professor of Physics The University of Texas at Dallas
Relativity SPECIAL, GENERAL, AND COSMOLOGICAL SECOND EDITION Wolfgang Rindler Professor of Physics The University of Texas at Dallas OXPORD UNIVERSITY PRESS Contents Introduction l 1 From absolute space
PROBLEM SET 6 EXTRA CREDIT PROBLEM SET
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.286: The Early Universe May 3, 2004 Prof. Alan Guth PROBLEM SET 6 EXTRA CREDIT PROBLEM SET CAN BE HANDED IN THROUGH: Thursday, May 13,
2.1 Basics of the Relativistic Cosmology: Global Geometry and the Dynamics of the Universe Part I
1 2.1 Basics of the Relativistic Cosmology: Global Geometry and the Dynamics of the Universe Part I 2 Special Relativity (1905) A fundamental change in viewing the physical space and time, now unified
Black hole formation in a contracting universe
Black hole formation in a contracting universe Jerome Quintin McGill University Montréal, Québec, Canada ITC Luncheon, Harvard CfA, Cambridge September 13, 2018 Based on work with Robert Brandenberger
Eternally Inflating Multiverse and Many Worlds in Quantum Mechanics: Same Concept?
Eternally Inflating Multiverse and Many Worlds in Quantum Mechanics: Same Concept? Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720, USA Theoretical
Introduction to Inflation
Introduction to Inflation Miguel Campos MPI für Kernphysik & Heidelberg Universität September 23, 2014 Index (Brief) historic background The Cosmological Principle Big-bang puzzles Flatness Horizons Monopoles
Cosmology: An Introduction. Eung Jin Chun
Cosmology: An Introduction Eung Jin Chun Cosmology Hot Big Bang + Inflation. Theory of the evolution of the Universe described by General relativity (spacetime) Thermodynamics, Particle/nuclear physics
Big Bounce and Inflation from Spin and Torsion Nikodem Popławski
Big Bounce and Inflation from Spin and Torsion Nikodem Popławski Institute for Theory and Computation Luncheon Harvard-Smithsonian Center for Astrophysics September 29, 2016 Cosmic Microwave Background
VU lecture Introduction to Particle Physics. Thomas Gajdosik, FI & VU. Big Bang (model)
Big Bang (model) What can be seen / measured? basically only light _ (and a few particles: e ±, p, p, ν x ) in different wave lengths: microwave to γ-rays in different intensities (measured in magnitudes)
The Universe: What We Know and What we Don t. Fundamental Physics Cosmology Elementary Particle Physics
The Universe: What We Know and What we Don t Fundamental Physics Cosmology Elementary Particle Physics 1 Cosmology Study of the universe at the largest scale How big is the universe? Where What Are did
Relativity, Gravitation, and Cosmology
Relativity, Gravitation, and Cosmology A basic introduction TA-PEI CHENG University of Missouri St. Louis OXFORD UNIVERSITY PRESS Contents Parti RELATIVITY Metric Description of Spacetime 1 Introduction
Preface. Out for no reason this universe came to be Out of a place to be, this universe filled itself Rumi vii
Preface Out for no reason this universe came to be Out of a place to be, this universe filled itself Rumi 1207 1273 Many cultures throughout the history including the Greeks, ancient Egyptians, Indians,
The History and Philosophy of Astronomy
Astronomy 350L (Spring 2005) The History and Philosophy of Astronomy (Lecture 27: Modern Developments II: Inflation) Instructor: Volker Bromm TA: Amanda Bauer The University of Texas at Austin Big Bang
Shortcomings of the inflationary paradigm
Shortcomings of the inflationary paradigm Looking at the Planck results, Steinhardt et all say:! 1) chaotic inflation with V = O(1) does not work! 2) the only remaining models are the ones with V
The Conventional Big Bang Theory What it is: The theory that the universe as we know it began billion years ago. (Latest estimate: 13:8±0:05 bil
The Conventional Big Bang Theory What it is: The theory that the universe as we know it began 13-15 billion years ago. (Latest estimate: 13:8±0:05 billion years!) The initial state was a hot, dense, uniform
You may not start to read the questions printed on the subsequent pages until instructed to do so by the Invigilator.
MATHEMATICAL TRIPOS Part III Friday 8 June 2001 1.30 to 4.30 PAPER 41 PHYSICAL COSMOLOGY Answer any THREE questions. The questions carry equal weight. You may not start to read the questions printed on
GENERAL RELATIVISTIC SINGULARITY-FREE COSMOLOGICAL MODEL
GENERAL RELATIVISTIC SINGULARITY-FREE COSMOLOGICAL MODEL arxiv:0904.3141v2 [physics.gen-ph] 16 Aug 2009 Marcelo Samuel Berman 1 1 Instituto Albert Einstein / Latinamerica - Av. Candido Hartmann, 575 -
Lecture 1 General relativity and cosmology. Kerson Huang MIT & IAS, NTU
A Superfluid Universe Lecture 1 General relativity and cosmology Kerson Huang MIT & IAS, NTU Lecture 1. General relativity and cosmology Mathematics and physics Big bang Dark energy Dark matter Robertson-Walker
Cosmic Censorship Conjecture and Topological Censorship
Cosmic Censorship Conjecture and Topological Censorship 21 settembre 2009 Cosmic Censorship Conjecture 40 years ago in the Rivista Nuovo Cimento Sir Roger Penrose posed one of most important unsolved problems
EFT Beyond the Horizon: Stochastic Inflation and How Primordial Quantum Fluctuations Go Classical
EFT Beyond the Horizon: Stochastic Inflation and How Primordial Quantum Fluctuations Go Classical C. P. Burgess, R.H., Gianmassimo Tasinato, Matt Williams, arxiv:1408.5002 Status and Future of Inflation
Emergent Universe by Tunneling. Pedro Labraña, ICC, Universidad de Barcelona and Facultad de Ciencias, Universidad del Bío-Bío, Chile.
Emergent Universe by Tunneling Pedro Labraña, ICC, Universidad de Barcelona and Facultad de Ciencias, Universidad del Bío-Bío, Chile. The Emergent Universe scenario Is Eternal Inflation, past eternal?
Chapter 9. Perturbations in the Universe
Chapter 9 Perturbations in the Universe In this chapter the theory of linear perturbations in the universe are studied. 9.1 Differential Equations of Linear Perturbation in the Universe A covariant, linear,
Entanglement and the Bekenstein-Hawking entropy
Entanglement and the Bekenstein-Hawking entropy Eugenio Bianchi relativity.phys.lsu.edu/ilqgs International Loop Quantum Gravity Seminar Black hole entropy Bekenstein-Hawking 1974 Process: matter falling
Introduction to Cosmology
Introduction to Cosmology João G. Rosa joao.rosa@ua.pt http://gravitation.web.ua.pt/cosmo LECTURE 2 - Newtonian cosmology I As a first approach to the Hot Big Bang model, in this lecture we will consider
MATHEMATICAL TRIPOS Part III PAPER 53 COSMOLOGY
MATHEMATICAL TRIPOS Part III Wednesday, 8 June, 2011 9:00 am to 12:00 pm PAPER 53 COSMOLOGY Attempt no more than THREE questions. There are FOUR questions in total. The questions carry equal weight. STATIONERY
Graceful exit from inflation for minimally coupled Bianchi A scalar field models
Graceful exit from inflation for minimally coupled Bianchi A scalar field models Florian Beyer Reference: F.B. and Leon Escobar (2013), CQG, 30(19), p.195020. University of Otago, Dunedin, New Zealand
The Cosmological Principle
Cosmological Models John O Byrne School of Physics University of Sydney Using diagrams and pp slides from Seeds Foundations of Astronomy and the Supernova Cosmology Project http://www-supernova.lbl.gov
4 Evolution of density perturbations
Spring term 2014: Dark Matter lecture 3/9 Torsten Bringmann (torsten.bringmann@fys.uio.no) reading: Weinberg, chapters 5-8 4 Evolution of density perturbations 4.1 Statistical description The cosmological
A Critique of Modern Cosmology
A Critique of Modern Cosmology [Transparencies of the talk delivered at Valencia in June 2006 by Jayant V. Narlikar, Inter-University Centre for Astronomy and Astrophysics, Pune, India] The Pythagoreans
The State of the Multiverse: The String Landscape, the Cosmological Constant, and the Arrow of Time
The State of the Multiverse: The String Landscape, the Cosmological Constant, and the Arrow of Time Raphael Bousso Center for Theoretical Physics University of California, Berkeley Stephen Hawking: 70th
Cosmology holography the brain and the quantum vacuum. Antonio Alfonso-Faus. Departamento de Aerotécnia. Madrid Technical University (UPM), Spain
Cosmology holography the brain and the quantum vacuum Antonio Alfonso-Faus Departamento de Aerotécnia Madrid Technical University (UPM), Spain February, 2011. E-mail: aalfonsofaus@yahoo.es Abstract: Cosmology,
Origin of the Universe
Origin of the Universe Shortcomings of the Big Bang Model There is tremendous evidence in favor of the Big Bang Cosmic Microwave Background Radiation Abundance of Deuterium, Helium, Lithium, all cooked
INFLATIONARY COSMOLOGY. and the ACCELERATING UNIVERSE. Alan Guth, MIT
INFLATIONARY COSMOLOGY and the ACCELERATING UNIVERSE Alan Guth, MIT An Open World of Physics Talks and Discussion by Friends of Fred Goldhaber Harriman Hall, SUNY Stony Brook, October 7, 2001 OUTLINE The
Patrick Peter. Institut d Astrophysique de Paris Institut Lagrange de Paris. Evidences for inflation constraints on alternatives
Patrick Peter Institut d Astrophysique de Paris Institut Lagrange de Paris Evidences for inflation constraints on alternatives Thanks to Jérôme Martin For his help Planck 2015 almost scale invariant quantum
Arvind Borde / MTH 675, Unit 20: Cosmology
Arvind Borde / MTH 675, Unit 20: Cosmology 1. Review (1) What do we do when we do GR? We try to solve Einstein s equation. (2) What is Einstein s equation? and R ab = e[ 1 2 ged ( a g bd + b g ad d g ab
The Theory of Inflationary Perturbations
The Theory of Inflationary Perturbations Jérôme Martin Institut d Astrophysique de Paris (IAP) Indian Institute of Technology, Chennai 03/02/2012 1 Introduction Outline A brief description of inflation
Hawking & the Universe
Hawking & the Universe This is a supplement to the lecture given on Jan 26, 2015, by Dr. Mounib El Eid, Physics department, AUB. It may motivate the reader to explore some of the presented issues. There
PHYM432 Relativity and Cosmology fall Introduction. Dr. David K. Sing
PHYM432 Relativity and Cosmology fall 2012 1. Introduction Dr. David K. Sing 1 PHYM432 General Relativity and Cosmology Fall 2012-2013 Instructor: Dr. David K Sing Office: Physics building room 514 Email
Introduction to Cosmology
1 Introduction to Cosmology Mast Maula Centre for Theoretical Physics Jamia Millia Islamia New Delhi - 110025. Collaborators: Nutty Professor, Free Ride Mast Maula (CTP, JMI) Introduction to Cosmology
Stable bouncing universe in Hořava-Lifshitz Gravity
Stable bouncing universe in Hořava-Lifshitz Gravity (Waseda Univ.) Collaborate with Yosuke MISONOH (Waseda Univ.) & Shoichiro MIYASHITA (Waseda Univ.) Based on Phys. Rev. D95 044044 (2017) 1 Inflation
Dynamics of the Universe
Dynamics of the Universe 1 Contents 1 A Brief Summary of Observational Facts 3 2 The Friedmann-Robertson-Walker Universe 3 3 Critical Density 7 4 Dark Matter and Dark Energy 8 5 Early Universe and Critical
Physics 133: Extragalactic Astronomy and Cosmology
Physics 133: Extragalactic Astronomy and Cosmology Week 2 Spring 2018 Previously: Empirical foundations of the Big Bang theory. II: Hubble s Law ==> Expanding Universe CMB Radiation ==> Universe was hot
Connecting Quarks to the Cosmos
Connecting Quarks to the Cosmos Institute for Nuclear Theory 29 June to 10 July 2009 Inflationary Cosmology II Michael S. Turner Kavli Institute for Cosmological Physics The University of Chicago Michael
Inflation and the origin of structure David Wands Institute of Cosmology and Gravitation University of Portsmouth
Cody Astronomical Society 7 th December 2011 Inflation and the origin of structure David Wands Institute of Cosmology and Gravitation University of Portsmouth outline of my talk: large-structure in the
SPACETIME FROM ENTANGLEMENT - journal club notes -
SPACETIME FROM ENTANGLEMENT - journal club notes - Chris Heinrich 1 Outline 1. Introduction Big picture: Want a quantum theory of gravity Best understanding of quantum gravity so far arises through AdS/CFT
The State of the Universe [2010] There is only data and the interpretation of data (green text = assumptions)
![The State of the Universe [2010] There is only data and the interpretation of data (green text = assumptions)](/thumbs/89/97484015.jpg "The State of the Universe [2010] There is only data and the interpretation of data (green text = assumptions)")
The State of the Universe [2010] There is only data and the interpretation of data (green text = assumptions) Current thinking in cosmology says that the universe is filled with dark matter and dark energy.
CMB Polarization in Einstein-Aether Theory
CMB Polarization in Einstein-Aether Theory Masahiro Nakashima (The Univ. of Tokyo, RESCEU) With Tsutomu Kobayashi (RESCEU) COSMO/CosPa 2010 Introduction Two Big Mysteries of Cosmology Dark Energy & Dark
PROBLEM SET 10 (The Last!)
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.286: The Early Universe December 8, 2016 Prof. Alan Guth PROBLEM SET 10 (The Last!) DUE DATE: Wednesday, December 14, 2016, at 4:00 pm.
The Big Bang: Fact or Fiction?
A new perspective on Einstein s universe The Big Bang: Fact or Fiction? Cormac O Raifeartaigh and Brendan Mcann (WIT) Werner Nahm (DIAS) and Simon Mitton (Univ. of Cambridge) Cosmology: the study of the
Inflationary Massive Gravity
New perspectives on cosmology APCTP, 15 Feb., 017 Inflationary Massive Gravity Misao Sasaki Yukawa Institute for Theoretical Physics, Kyoto University C. Lin & MS, PLB 75, 84 (016) [arxiv:1504.01373 ]
A Field Theory approach to important Cosmological Issues including Dark Energy and the. Energy -Anupam Singh, L.N.M. I.I.T.
A Field Theory approach to important Cosmological Issues including Dark Energy and the gravitational collapse of Dark Energy -Anupam Singh, L.N.M. I.I.T. Outline Introduction and Motivation Field Theory:
The Standard Big Bang What it is: Theory that the universe as we know it began billion years ago. (Latest estimate: 13:82 ± 0:05 billion years!)
The Standard Big Bang What it is: Theory that the universe as we know it began 13-14 billion years ago. (Latest estimate: 13:82 ± 0:05 billion years!) Initial state was a hot, dense, uniform soup of particles
COSMOLOGY The Origin and Evolution of Cosmic Structure
COSMOLOGY The Origin and Evolution of Cosmic Structure Peter COLES Astronomy Unit, Queen Mary & Westfield College, University of London, United Kingdom Francesco LUCCHIN Dipartimento di Astronomia, Universita
Physics 314 (Survey of Astronomy) Exam 3
Physics 314 (Survey of Astronomy) Exam 3 Please show all significant steps clearly in all problems. Please give clear, legible, and reasonably complete (although brief) responses to qualitative questions.
Inflation and the Primordial Perturbation Spectrum
PORTILLO 1 Inflation and the Primordial Perturbation Spectrum Stephen K N PORTILLO Introduction The theory of cosmic inflation is the leading hypothesis for the origin of structure in the universe. It
COSMIC INFLATION AND THE REHEATING OF THE UNIVERSE
COSMIC INFLATION AND THE REHEATING OF THE UNIVERSE Francisco Torrentí - IFT/UAM Valencia Students Seminars - December 2014 Contents 1. The Friedmann equations 2. Inflation 2.1. The problems of hot Big
arxiv:astro-ph/ v3 18 Apr 2005
Phantom Thermodynamics Revisited A. Kwang-Hua CHU P.O. Box 30-15, Shanghai 200030, PR China arxiv:astro-ph/0412704v3 18 Apr 2005 Abstract Although generalized Chaplygin phantom models do not show any big
From inflation to the CMB to today s universe. I - How it all begins
From inflation to the CMB to today s universe I - How it all begins Raul Abramo Physics Institute - University of São Paulo abramo@fma.if.usp.br redshift Very brief cosmic history 10 9 200 s BBN 1 MeV
Closed Universes, de Sitter Space and Inflation
Closed Universes, de Sitter Space and Inflation Chris Doran Cavendish Laboratory Based on astro-ph/0307311 by Lasenby and Doran The Cosmological Constant Dark energy responsible for around 70% of the total
Propagation of Gravitational Waves in a FRW Universe. What a Cosmological Gravitational Wave may look like
Propagation of Gravitational Waves in a FRW Universe in other words What a Cosmological Gravitational Wave may look like by Kostas Kleidis (kleidis@astro.auth.gr) INTRODUCTION & MOTIVATION What are we
Cosmology Winter School 5/12/2011! Jean-Philippe UZAN!
Cosmology Winter School 5/12/2011! Lecture 1:! Cosmological models! Jean-Philippe UZAN! Cosmological models! We work in the framework of general relativity so that the Universe is described by a spacetime
Tutorial II Newtonian Cosmology; Hubble Expansion
Tutorial II Newtonian Cosmology; Hubble Expansion Exercise I: Newtonian Cosmology In 1934 i.e. way after Friedman derived his equations- Milne and Mc- Crea showed that relations of the Friedman form can
Lecture 14: Cosmological Principles
Lecture 14: Cosmological Principles The basic Cosmological Principles The geometry of the Universe The scale factor R and curvature constant k Comoving coordinates Einstein s initial solutions 3/28/11
A glimpse on Cosmology: Mathematics meets the Data
Naples 09 Seminar A glimpse on Cosmology: Mathematics meets the Data by 10 November 2009 Monica Capone 1 Toward a unified epistemology of Sciences...As we know, There are known knowns. There are things
Redshift-Distance Relationships
Redshift-Distance Relationships George Jones April 4, 0. Distances in Cosmology This note considers two conceptually important definitions of cosmological distances, look-back distance and proper distance.
12. Relativistic Cosmology I. Simple Solutions to the Einstein Equations
12. Relativistic Cosmology I. Simple Solutions to the Einstein Equations 1. Minkowski space Initial assumptions:! no matter (T µν = 0)! no gravitation (R σ µνρ = 0; i.e., zero curvature) Not realistic!
Return to cosmology. Is inflation in trouble? Are we cycling back to cycles? And then what happens to the 2 nd law?
Return to cosmology Is inflation in trouble? Are we cycling back to cycles? And then what happens to the 2 nd law? We saw inflation correctly predict: 1. Flatness of universe 2. Homogeneity of universe
Einstein-Cartan Gravity in Particle Physics and Cosmology
Einstein-Cartan Gravity in Particle Physics and Cosmology Nikodem J. Popławski Department of Mathematics and Physics University of New Haven West Haven, CT, USA Department of Physics Seminar Indian Institute
Dilaton and IR-Driven Inflation
Dilaton and IR-Driven Inflation Chong-Sun Chu National Center for Theoretical Science NCTS and National Tsing-Hua University, Taiwan Third KIAS-NCTS Joint Workshop High 1 Feb 1, 2016 1506.02848 in collaboration
Applications of Bohmian mechanics in quantum gravity
Applications of Bohmian mechanics in quantum gravity Ward Struyve LMU, Munich, Germany Outline: Why do we need a quantum theory for gravity? What is the quantum theory for gravity? Problems with quantum
Cosmic Strings. May 2, Safa Motesharrei University of Maryland
Safa Motesharrei University of Maryland May 2, 2007 String Theory!! Cosmology Outline Why? What is a Topological Defect? Examples of Cosmological Defects Brief History Importance to String Theory Geometry
The universe or nothing: The heat death of the universe and it s ultimate fate
The universe or nothing: The heat death of the universe and it s ultimate fate I.A. Aly * * Independent Researcher and theorist July 20, 2017 Abstract This paper overviews my hypothesis of the ultimate
Quantum Mechanics in the de Sitter Spacetime and Inflationary Scenario
J. Astrophys. Astr. (1985) 6, 239 246 Quantum Mechanics in the de Sitter Spacetime and Inflationary Scenario Τ. Padmanabhan Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005 Received
Welcome to Physics 43!
Welcome to Physics 43! Classical Mechanics! Study of the motion of objects and mechanical systems that are large relative to atoms and move at speeds much slower than the speed of light. You can t get
Stephen Blaha, Ph.D. M PubHsMtw
Quantum Big Bang Cosmology: Complex Space-time General Relativity, Quantum Coordinates,"Dodecahedral Universe, Inflation, and New Spin 0, 1 / 2,1 & 2 Tachyons & Imagyons Stephen Blaha, Ph.D. M PubHsMtw
MASAHIDE YAMAGUCHI. Quantum generation of density perturbations in the early Universe. (Tokyo Institute of Technology)
Quantum generation of density perturbations in the early Universe MASAHIDE YAMAGUCHI (Tokyo Institute of Technology) 03/07/16@Symposium: New Generation Quantum Theory -Particle Physics, Cosmology, and
arxiv:gr-qc/ v3 17 Jul 2003
REGULAR INFLATIONARY COSMOLOGY AND GAUGE THEORIES OF GRAVITATION A. V. Minkevich 1 Department of Theoretical Physics, Belarussian State University, av. F. Skoriny 4, 0050, Minsk, Belarus, phone: +37517095114,
THE PRIMORDIAL UNIVERSE IN A NEW TIME SCALE
THE PRIMORDIAL UNIVERSE IN A NEW TIME SCALE Francis MATHE. 44 La Clairière, 7880 BULLION, France E-MAIL: FRMATHE@aol.com 1 - INTRODUCTION Using some reasonable hypothesis, General Relativity leads to a
Research Center for the Early Universe (RESCEU) Department of Physics. Jun ichi Yokoyama
Research Center for the Early Universe (RESCEU) Department of Physics Jun ichi Yokoyama time size Today 13.8Gyr Why is Our Universe Big, dark energy Old, and full of structures? galaxy formation All of
Physical Conclusions of Experimental Physics Versus Metaphysical Assumptions of Theoretical Physics Theoretical physicists create assumptions for
Physical Conclusions of Experimental Physics Versus Metaphysical Assumptions of Theoretical Physics Theoretical physicists create assumptions for their theories to explain the results of measurements made
arxiv:gr-qc/ v1 15 Apr 1997
Indeterministic Quantum Gravity and Cosmology VII. Dynamical Passage through Singularities: Black Hole and Naked Singularity, Big Crunch and Big Bang Vladimir S. MASHKEVICH 1 arxiv:gr-qc/9704038v1 15 Apr
Crossing the Event Horizon Presented by Nassim Haramein
Crossing the Event Horizon Presented by Nassim Haramein Part 1: The Untold Physics Chapter 5: Concept of Black Holes In order to understand the concept of atoms, planets, galaxies and stars as all having
Third Year: General Relativity and Cosmology. 1 Problem Sheet 1 - Newtonian Gravity and the Equivalence Principle
Third Year: General Relativity and Cosmology 2011/2012 Problem Sheets (Version 2) Prof. Pedro Ferreira: p.ferreira1@physics.ox.ac.uk 1 Problem Sheet 1 - Newtonian Gravity and the Equivalence Principle
Cosmic Inflation Tutorial
Cosmic Inflation Tutorial Andreas Albrecht Center for Quantum Mathematics and Physics (QMAP) and Department of Physics UC Davis Simons Workshop on Quantum Information in Cosmology Niels Bohr Institute
Kinetic Theory of Dark Energy within General Relativity
Kinetic Theory of Dark Energy within General Relativity Author: Nikola Perkovic* percestyler@gmail.com University of Novi Sad, Faculty of Sciences, Institute of Physics and Mathematics Abstract: This paper
Lecture 7(cont d):our Universe
Lecture 7(cont d):our Universe 1. Traditional Cosmological tests Theta-z Galaxy counts Tolman Surface Brightness test 2. Modern tests HST Key Project (H o ) Nucleosynthesis (Ω b ) BBN+Clusters (Ω M ) SN1a
The cosmological constant puzzle
The cosmological constant puzzle Steven Bass Cosmological constant puzzle: Accelerating Universe: believed to be driven by energy of nothing (vacuum) Vacuum energy density (cosmological constant or dark
Structure. Subodh Patil NBIA Nov Formation in the Universe From the Big Bang to the Big Rip?
Structure Subodh Patil NBIA Nov 19 2018 Formation in the Universe From the Big Bang to the Big Rip? Physicists like to think in terms of characteristic scales the `typical size of something or some process.
Lecture 05. Cosmology. Part I
Cosmology Part I What is Cosmology Cosmology is the study of the universe as a whole It asks the biggest questions in nature What is the content of the universe: Today? Long ago? In the far future? How
Mimetic Cosmology. Alexander Vikman. New Perspectives on Cosmology Institute of Physics of the Czech Academy of Sciences
New Perspectives on Cosmology Mimetic Cosmology Alexander Vikman Institute of Physics of the Czech Academy of Sciences 07.01.2016 This talk is mostly based on arxiv: 1512.09118, K. Hammer, A. Vikman arxiv:
Scott A. Hughes, MIT SSI, 28 July The basic concepts and properties of black holes in general relativity
The basic concepts and properties of black holes in general relativity For the duration of this talk ħ=0 Heuristic idea: object with gravity so strong that light cannot escape Key concepts from general
Black Hole Cosmology in Gravity with Torsion Nikodem Popławski
Black Hole Cosmology in Gravity with Torsion Nikodem Popławski Department of Mathematics and Physics Seminar University of New Haven October 20, 2016 Cosmic Microwave Background Big Bang Licensed under