Loop Quantum Cosmology holonomy corrections to inflationary models

Size: px
Start display at page:

Download "Loop Quantum Cosmology holonomy corrections to inflationary models"

Transcription

1 Michał Artymowski Loop Quantum Cosmology holonomy corrections to inflationary models University of Warsaw With collaboration with L. Szulc and Z. Lalak Pennstate Michał Artymowski, University of Warsaw

2 Outline Phenomenology of loop corrections Introduction to cosmology and inflation Background evolution in the FRW cosmology with the holonomy loop correction Evolution of the scalar metric perturbations Effective comoving sonic horizon Power spectrum of the initial energy density perturbations Michał Artymowski, University of Warsaw

3 Clasical cosmology and inflation Let us consider the FRW Universe with k=0. From Einstein equations one obtains Friedmann equations a&& H = = - ( + 3P) H = - ( + P) 3 a 6 & To solve these equations we need to know the barotropic parameter ω, where P=ω, or we need to know the equation of motion for matter fields Inflation appears when a && > a 0 and the most popular scenarios assume ω We need P rather unnatural equation of state! Ht Then a( t) e and the comoving Hubble horizon deeases rapidly ah Michał Artymowski, University of Warsaw

4 Inflaton field The most popular model: The early Universe is dominated by the scalar field φ = φ& + V(φ) P = φ& - V(φ) to get ω we need φ << V(φ) & φ && + 3Hφ & + V = 0 Equation of motion for the inflaton Michał Artymowski, University of Warsaw

5 Initial perturbations Now we work with the inflaton field φ(t) and its perturbation δφ(x,t) ( t) P( t) P ( o) ( o) r ( t) + δ( x, t) r ( t) + δp( x, t) g g oo ij r r ( t) goo( t) + δgoo( x, t) = -( + Φ( x, t)) r r ( t) g ( t) + δg ( x, t) = a ( - Ψ( x, t))δ ij ij ij δg μν = δt μν We do not have any anisotropic pressure. Δ... 3H Ψ+ 3H Ψ + δ Ψ+ 4 H Ψ+ a Ψ = - Φ = Ψ ( 3H + H& ) Ψ = δp After Fourier transformation we have Ψ+ (4 + 3c ) H Ψ+[H+ 3H (+ c ) - k c / a ]Ψ = s s s For kcs<<ah we have the solution Ψ const Perturbations are frozen outside the comoving sonic horizon Michał Artymowski, University of Warsaw

6 Power spectra For the strong slow rollapproximation... δφ evolves like the masless scalar field δφ+ 3Hδφ+ k δφ/a = 0 Conformal time: a(η)dη=dt Ht For a( t) e we obtain η = - ah ηh δφ = e ik i kη - k - η From the equation of motion for δφ(k,η) we get ( ) Then we define the Power spectrum of δφ by ( k,η) = H k η + 4π And finally ( ) H = Ψ + δφ φ& δφ In slow roll approximation 3 k δφ ( k,η) = δφ( k, η) π Mukhanov Sasaki variable. This is something like 4 H 4π φ& V 4π we can not measure that! Michał Artymowski, University of Warsaw ε δ

7 The loop correction and Ashtekar variables. Ashtekar variables in the FRW Universe: c = γ a p = a { p} c, = The hamiltonian 3 N H = p c + H gives us Friedmann equations mat γ γ 3 The parallel transport around the loop changes the vector. If we would shrink the loop to the smallest possible size we would get the elementary correction Michał Artymowski, University of Warsaw

8 Quantum of length By considering the loop quantum gravity modifications to the c sin(cl j / p) l p j l j, where is the quantum of length. The holonomy loop correction does not changes p! c we get l j l pl(j(j + )) / 4 This is an extremely important variable! No specific value of j chosen by nature! j = 3,,, Mpl = Critical (maximal) energy density of the Universe γ l j(j+ ) j For and big values of j we have ~ /j 8πG = Michał Artymowski, University of Warsaw

9 Friedmann equations. H Friedmann equations H 3 = = ( + P) / 0 normal FRW Effective variables P 3 3 = = P Michał Artymowski, University of Warsaw

10 Perturbations in LQC ds = N dt + p(d x) We can write Hamilton equations for, where p = a ( - Ψ) N = (+ Φ) We consider k 0 so perturbations are functions of time only. We do not have any anisotropic pressure and from perturbated friedmann equations we have Φ = Ψ. 3H Ψ+ 3H Ψ = - δ... Ψ + 4HΨ+ ( 3H + H& ) Ψ = δp For the adiabatic perturbations we obtain.. Ψ+ (4 + 3c s.. ) H Ψ+[H+ 3H (+ c s )]Ψ = 0 This equation is almoust identical with the one from the standard FRW. Perturbations are frozen outside the ective sonic horizon. Michał Artymowski, University of Warsaw

11 The ective speed of sound In LQC the ective speed of sound becomes infinite for = cs = δ P δ = c s (+ P) / - - / No conserved information. left over from the H > 0 period The ective Big Bang scenario! c s is not a physical velocity!!! Michał Artymowski, University of Warsaw

12 The power spectrum Equations for the inflaton and it s perturbation are not changed by the loop correction... δφ+ 3Hδφ+ k δφ/a = 0 where δφ is the inflaton perturbation (- / V' ) V For the slow roll approximation, ε = V = V( V/ ) The power spectrum of the curvature perturbations is then in form of From the COBE normalisation we know, that if we want to avoid fine tuning we need to have > (0 6 GeV) 4 This gives us the limit for j. For big values of j The spectral index n s ( k) - = η -6ε < 4 Mpl/j j 0 is changed by the LQC to ns loop ( k) - = ns ( k) - ( -V / ) Michał Artymowski, University of Warsaw

13 Conclusions FRW Universe in the low energy limit for LQC No information about the scalar perturbations can oss the energy regime untouched We can limit the quantum of length by the COBE normalisation More models fit s the data for strong LQC holonomy efects Michał Artymowski, University of Warsaw

14 Nazwa rozdziału Loop Quantum Cosmology corrections in the inflationary models Michał Artymowski, University of Warsaw

15 Nazwa rozdziału Loop Quantum Cosmology corrections in the inflationary models Michał Artymowski, University of Warsaw

16 Nazwa rozdziału Loop Quantum Cosmology corrections in the inflationary models Michał Artymowski, University of Warsaw

Loop Quantum Cosmology holonomy corrections to inflationary models

Loop Quantum Cosmology holonomy corrections to inflationary models Michał Artymowski Loop Quantum Cosmology holonomy corrections to inflationary models University of Warsaw With colaboration with L. Szulc and Z. Lalak Oxford 4 09 008 Michał Artymowski, University of Warsaw

More information

arxiv: v1 [gr-qc] 1 Jul 2008

arxiv: v1 [gr-qc] 1 Jul 2008 Loop Quantum Cosmology corrections to inflationary models Micha l Artymowski Zygmunt Lalak and Lukasz Szulc Institute of Theoretical Physics, University of Warsaw ul. Hoża 69, 00-681 Warszawa, Poland arxiv:0807.0160v1

More information

Chapter 4. COSMOLOGICAL PERTURBATION THEORY

Chapter 4. COSMOLOGICAL PERTURBATION THEORY Chapter 4. COSMOLOGICAL PERTURBATION THEORY 4.1. NEWTONIAN PERTURBATION THEORY Newtonian gravity is an adequate description on small scales (< H 1 ) and for non-relativistic matter (CDM + baryons after

More information

Exact Inflationary Solution. Sergio del Campo

Exact Inflationary Solution. Sergio del Campo Exact Inflationary Solution Sergio del Campo Instituto de Física Pontificia Universidad Católica de Valparaíso Chile I CosmoSul Rio de Janeiro, 1 al 5 de Agosto, 2011 Inflation as a paradigm. Models Slow-roll

More information

Cosmological Signatures of Brane Inflation

Cosmological Signatures of Brane Inflation March 22, 2008 Milestones in the Evolution of the Universe http://map.gsfc.nasa.gov/m mm.html Information about the Inflationary period The amplitude of the large-scale temperature fluctuations: δ H =

More information

Cosmological perturbations in teleparallel LQC

Cosmological perturbations in teleparallel LQC Cosmological perturbations in teleparallel LQC Jaume Haro; Dept. Mat. Apl. I, UPC (ERE, Benasque, 09/2013) Isotropic LQC 1 Gravitational part of the classical Hamiltonian in Einstein Cosmology (flat FLRW

More information

PERTURBATIONS IN LOOP QUANTUM COSMOLOGY

PERTURBATIONS IN LOOP QUANTUM COSMOLOGY PERTURBATIONS IN LOOP QUANTUM COSMOLOGY William Nelson Pennsylvania State University Work with: Abhay Astekar and Ivan Agullo (see Ivan s ILQG talk, 29 th March ) AUTHOR, W. NELSON (PENN. STATE) PERTURBATIONS

More information

A STUDY OF INFLATIONARY PARADIGM

A STUDY OF INFLATIONARY PARADIGM A STUDY OF INFLATIONARY PARADIGM A Project Report By RATHUL NATH R The Institute of Mathematical Sciences, Chennai Under the joint-supervison of Prof. L. Sriramkumar and Prof. Ghanashyam Date June, 014

More information

Oddities of the Universe

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

More information

MATHEMATICAL TRIPOS Part III PAPER 53 COSMOLOGY

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

More information

Inflation. By The amazing sleeping man, Dan the Man and the Alices

Inflation. By The amazing sleeping man, Dan the Man and the Alices Inflation By The amazing sleeping man, Dan the Man and the Alices AIMS Introduction to basic inflationary cosmology. Solving the rate of expansion equation both analytically and numerically using different

More information

CHAPTER 4 INFLATIONARY MODEL BUILDING. 4.1 Canonical scalar field dynamics. Non-minimal coupling and f(r) theories

CHAPTER 4 INFLATIONARY MODEL BUILDING. 4.1 Canonical scalar field dynamics. Non-minimal coupling and f(r) theories CHAPTER 4 INFLATIONARY MODEL BUILDING Essentially, all models are wrong, but some are useful. George E. P. Box, 1987 As we learnt in the previous chapter, inflation is not a model, but rather a paradigm

More information

PAPER 71 COSMOLOGY. Attempt THREE questions There are seven questions in total The questions carry equal weight

PAPER 71 COSMOLOGY. Attempt THREE questions There are seven questions in total The questions carry equal weight MATHEMATICAL TRIPOS Part III Friday 31 May 00 9 to 1 PAPER 71 COSMOLOGY Attempt THREE questions There are seven questions in total The questions carry equal weight You may make free use of the information

More information

Cosmology from Brane Backreaction

Cosmology from Brane Backreaction Cosmology from Brane Backreaction Higher codimension branes and their bulk interactions w Leo van Nierop Outline Motivation Extra-dimensional cosmology Setup A 6D example Calculation Maximally symmetric

More information

School Observational Cosmology Angra Terceira Açores 3 rd June Juan García-Bellido Física Teórica UAM Madrid, Spain

School Observational Cosmology Angra Terceira Açores 3 rd June Juan García-Bellido Física Teórica UAM Madrid, Spain School Observational Cosmology Angra Terceira Açores 3 rd June 2014 Juan García-Bellido Física Teórica UAM Madrid, Spain Outline Lecture 1 Shortcomings of the Hot Big Bang The Inflationary Paradigm Homogeneous

More information

Computational Physics and Astrophysics

Computational Physics and Astrophysics Cosmological Inflation Kostas Kokkotas University of Tübingen, Germany and Pablo Laguna Georgia Institute of Technology, USA Spring 2012 Our Universe Cosmic Expansion Co-moving coordinates expand at exactly

More information

The Theory of Inflationary Perturbations

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

More information

Equation of state of dark energy. Phys. Rev. D 91, (2015)

Equation of state of dark energy. Phys. Rev. D 91, (2015) Equation of state of dark energy in f R gravity The University of Tokyo, RESCEU K. Takahashi, J. Yokoyama Phys. Rev. D 91, 084060 (2015) Motivation Many modified theories of gravity have been considered

More information

PAPER 310 COSMOLOGY. Attempt no more than THREE questions. There are FOUR questions in total. The questions carry equal weight.

PAPER 310 COSMOLOGY. Attempt no more than THREE questions. There are FOUR questions in total. The questions carry equal weight. MATHEMATICAL TRIPOS Part III Wednesday, 1 June, 2016 9:00 am to 12:00 pm PAPER 310 COSMOLOGY Attempt no more than THREE questions. There are FOUR questions in total. The questions carry equal weight. STATIONERY

More information

Quantum Fluctuations During Inflation

Quantum Fluctuations During Inflation In any field, find the strangest thing and then explore it. (John Archibald Wheeler) Quantum Fluctuations During Inflation ( ) v k = e ikτ 1 i kτ Contents 1 Getting Started Cosmological Perturbation Theory.1

More information

Observational signatures of holographic models of inflation

Observational signatures of holographic models of inflation Observational signatures of holographic models of inflation Paul McFadden Universiteit van Amsterdam First String Meeting 5/11/10 This talk I. Cosmological observables & non-gaussianity II. Holographic

More information

Classical Dynamics of Inflation

Classical Dynamics of Inflation Preprint typeset in JHEP style - HYPER VERSION Classical Dynamics of Inflation Daniel Baumann School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540 http://www.sns.ias.edu/ dbaumann/

More information

Propagation of Gravitational Waves in a FRW Universe. What a Cosmological Gravitational Wave may look like

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

More information

Bianchi I Space-times and Loop Quantum Cosmology

Bianchi I Space-times and Loop Quantum Cosmology Bianchi I Space-times and Loop Quantum Cosmology Edward Wilson-Ewing Institute for Gravitation and the Cosmos The Pennsylvania State University Work with Abhay Ashtekar October 23, 2008 E. Wilson-Ewing

More information

Bouncing Cosmologies with Dark Matter and Dark Energy

Bouncing Cosmologies with Dark Matter and Dark Energy Article Bouncing Cosmologies with Dark Matter and Dark Energy Yi-Fu Cai 1, *, Antonino Marcianò 2, Dong-Gang Wang 1,3,4 and Edward Wilson-Ewing 5 1 CAS Key Laboratory for Research in Galaxies and Cosmology,

More information

Introduction to Inflation

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

More information

Observational signatures in LQC?

Observational signatures in LQC? Observational signatures in LQC? Ivan Agullo Penn State International Loop Quantum Gravity Seminar, March 29 2011 Talk based on: I.A., A. Ashtekar, W. Nelson: IN PROGRESS! CONTENT OF THE TALK 1. Inflation

More information

Astro 321 Set 4: Inflationary Perturbations. Wayne Hu

Astro 321 Set 4: Inflationary Perturbations. Wayne Hu Astro 321 Set 4: Inflationary Perturbations Wayne Hu Outline Review of canonical single-field slow roll inflation Scalar field Comoving curvature Gravitational waves EFT of inflation Application to P (X,

More information

Quantum Gravity and the Every Early Universe

Quantum Gravity and the Every Early Universe p. Quantum Gravity and the Every Early Universe Abhay Ashtekar Institute for Gravitation and the Cosmos, Penn State Will summarize the work of many researchers; especially: Agullo, Barrau, Bojowald, Cailleatau,

More information

Signatures of Trans-Planckian Dissipation in Inflationary Spectra

Signatures of Trans-Planckian Dissipation in Inflationary Spectra Signatures of Trans-Planckian Dissipation in Inflationary Spectra 3. Kosmologietag Bielefeld Julian Adamek ITPA University Würzburg 8. May 2008 Julian Adamek 1 / 18 Trans-Planckian Dissipation in Inflationary

More information

COSMIC INFLATION AND THE REHEATING OF THE UNIVERSE

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

More information

From Inflation to TeV physics: Higgs Reheating in RG Improved Cosmology

From Inflation to TeV physics: Higgs Reheating in RG Improved Cosmology From Inflation to TeV physics: Higgs Reheating in RG Improved Cosmology Yi-Fu Cai June 18, 2013 in Hefei CYF, Chang, Chen, Easson & Qiu, 1304.6938 Two Standard Models Cosmology CMB: Cobe (1989), WMAP (2001),

More information

Graceful exit from inflation for minimally coupled Bianchi A scalar field models

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

More information

Cosmic Bubble Collisions

Cosmic Bubble Collisions Outline Background Expanding Universe: Einstein s Eqn with FRW metric Inflationary Cosmology: model with scalar field QFTà Bubble nucleationà Bubble collisions Bubble Collisions in Single Field Theory

More information

Dark inflation. Micha l Artymowski. Jagiellonian University. January 29, Osaka University. arxiv:

Dark inflation. Micha l Artymowski. Jagiellonian University. January 29, Osaka University. arxiv: Dark inflation Micha l Artymowski Jagiellonian University January 29, 2018 Osaka University arxiv:1711.08473 (with Olga Czerwińska, M. Lewicki and Z. Lalak) Cosmic microwave background Cosmic microwave

More information

Week 6: Inflation and the Cosmic Microwave Background

Week 6: Inflation and the Cosmic Microwave Background Week 6: Inflation and the Cosmic Microwave Background January 9, 2012 1 Motivation The standard hot big-bang model with an (flat) FRW spacetime accounts correctly for the observed expansion, the CMB, BBN,

More information

1. De Sitter Space. (b) Show that the line element for a positively curved FRW model (k = +1) with only vacuum energy (P = ) is

1. De Sitter Space. (b) Show that the line element for a positively curved FRW model (k = +1) with only vacuum energy (P = ) is 1. De Sitter Space (a) Show in the context of expanding FRW models that if the combination +3P is always positive, then there was a Big Bang singularity in the past. [A sketch of a(t) vs.t may be helpful.]

More information

Archaeology of Our Universe YIFU CAI ( 蔡一夫 )

Archaeology of Our Universe YIFU CAI ( 蔡一夫 ) Archaeology of Our Universe YIFU CAI ( 蔡一夫 ) 2013-11-05 Thermal History Primordial era 13.8 billion years by WMAP/NASA Large Scale Structure (LSS) by 2MASS Cosmic Microwave Background (CMB) by ESA/Planck

More information

Week 10: Theoretical predictions for the CMB temperature power spectrum

Week 10: Theoretical predictions for the CMB temperature power spectrum Week 10: Theoretical predictions for the CMB temperature power spectrum April 5, 2012 1 Introduction Last week we defined various observable quantities to describe the statistics of CMB temperature fluctuations,

More information

Cosmological Issues. Consider the stress tensor of a fluid in the local orthonormal frame where the metric is η ab

Cosmological Issues. Consider the stress tensor of a fluid in the local orthonormal frame where the metric is η ab Cosmological Issues Radiation dominated Universe Consider the stress tensor of a fluid in the local orthonormal frame where the metric is η ab ρ 0 0 0 T ab = 0 p 0 0 0 0 p 0 () 0 0 0 p We do not often

More information

Gravitation: Cosmology

Gravitation: Cosmology An Introduction to General Relativity Center for Relativistic Astrophysics School of Physics Georgia Institute of Technology Notes based on textbook: Spacetime and Geometry by S.M. Carroll Spring 2013

More information

INFLATION. - EARLY EXPONENTIAL PHASE OF GROWTH OF SCALE FACTOR (after T ~ TGUT ~ GeV)

INFLATION. - EARLY EXPONENTIAL PHASE OF GROWTH OF SCALE FACTOR (after T ~ TGUT ~ GeV) INFLATION - EARLY EXPONENTIAL PHASE OF GROWTH OF SCALE FACTOR (after T ~ TGUT ~ 10 15 GeV) -Phenomenologically similar to Universe with a dominant cosmological constant, however inflation needs to end

More information

Misao Sasaki YITP, Kyoto University. 29 June, 2009 ICG, Portsmouth

Misao Sasaki YITP, Kyoto University. 29 June, 2009 ICG, Portsmouth Misao Sasaki YITP, Kyoto University 9 June, 009 ICG, Portsmouth contents 1. Inflation and curvature perturbations δn formalism. Origin of non-gaussianity subhorizon or superhorizon scales 3. Non-Gaussianity

More information

Instabilities during Einstein-Aether Inflation

Instabilities during Einstein-Aether Inflation Instabilities during Einstein-Aether Inflation Adam R Solomon DAMTP, University of Cambridge, UK Based on work to appear soon: AS & John D Barrow arxiv:1309.xxxx September 3 rd, 2013 Why consider Lorentz

More information

Theoretical implications of detecting gravitational waves

Theoretical implications of detecting gravitational waves Theoretical implications of detecting gravitational waves Ghazal Geshnizjani Department of Applied Mathematics University of Waterloo ggeshniz@uwaterloo.ca In collaboration with: William H. Kinney arxiv:1410.4968

More information

Inflationary Trajectories

Inflationary Trajectories Inflationary Trajectories Pascal M. Vaudrevange 19.09.2007 Scanning Inflaton Goals: Reconstruction of Primordial Power Spectra Reconstruction of Inflaton Potential Inflation driven by a scalar field -

More information

Astro 507 Lecture 28 April 2, 2014

Astro 507 Lecture 28 April 2, 2014 Astro 507 Lecture 28 April 2, 2014 Announcements: PS 5 due now Preflight 6 posted today last PF! 1 Last time: slow-roll inflation scalar field dynamics in an expanding universe slow roll conditions constrain

More information

Inflation and the Primordial Perturbation Spectrum

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

More information

Cosmology and particle physics

Cosmology and particle physics Cosmology and particle physics Lecture notes Timm Wrase Lecture 9 Inflation - part I Having discussed the thermal history of our universe and in particular its evolution at times larger than 10 14 seconds

More information

MATHEMATICAL TRIPOS PAPER 67 COSMOLOGY

MATHEMATICAL TRIPOS PAPER 67 COSMOLOGY MATHEMATICA TRIPOS Part III Wednesday 6 June 2001 9 to 11 PAPER 67 COSMOOGY Attempt THREE questions. The questions are of equal weight. Candidates may make free use of the information given on the accompanying

More information

Cosmology and the origin of structure

Cosmology and the origin of structure 1 Cosmology and the origin of structure ocy I: The universe observed ocy II: Perturbations ocy III: Inflation Primordial perturbations CB: a snapshot of the universe 38, AB correlations on scales 38, light

More information

Non-singular quantum cosmology and scale invariant perturbations

Non-singular quantum cosmology and scale invariant perturbations th AMT Toulouse November 6, 2007 Patrick Peter Non-singular quantum cosmology and scale invariant perturbations Institut d Astrophysique de Paris GRεCO AMT - Toulouse - 6th November 2007 based upon Tensor

More information

Dark inflation. Micha l Artymowski. Jagiellonian University. December 12, 2017 COSPA arxiv:

Dark inflation. Micha l Artymowski. Jagiellonian University. December 12, 2017 COSPA arxiv: Dark inflation Micha l Artymowski Jagiellonian University December 12, 2017 COSPA 2017 arxiv:1711.08473 (with Olga Czerwińska, M. Lewicki and Z. Lalak) Cosmic microwave background Cosmic microwave background

More information

The early and late time acceleration of the Universe

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

More information

Misao Sasaki. KIAS-YITP joint workshop 22 September, 2017

Misao Sasaki. KIAS-YITP joint workshop 22 September, 2017 Misao Sasaki KIAS-YITP joint workshop September, 017 Introduction Inflation: the origin of Big Bang Brout, Englert & Gunzig 77, Starobinsky 79, Guth 81, Sato 81, Linde 8, Inflation is a quasi-exponential

More information

Priming the BICEP. Wayne Hu Chicago, March BB

Priming the BICEP. Wayne Hu Chicago, March BB Priming the BICEP 0.05 0.04 0.03 0.02 0.01 0 0.01 BB 0 50 100 150 200 250 300 Wayne Hu Chicago, March 2014 A BICEP Primer How do gravitational waves affect the CMB temperature and polarization spectrum?

More information

Inflationary cosmology from higher-derivative gravity

Inflationary cosmology from higher-derivative gravity Inflationary cosmology from higher-derivative gravity Sergey D. Odintsov ICREA and IEEC/ICE, Barcelona April 2015 REFERENCES R. Myrzakulov, S. Odintsov and L. Sebastiani, Inflationary universe from higher-derivative

More information

Inflationary density perturbations

Inflationary density perturbations Cosener s House 7 th June 003 Inflationary density perturbations David Wands Institute of Cosmology and Gravitation University of Portsmouth outline! some motivation! Primordial Density Perturbation (and

More information

Warm intermediate inflationary universe models with a generalized dissipative coefficient / 34

Warm intermediate inflationary universe models with a generalized dissipative coefficient / 34 Warm intermediate inflationary universe models with a generalized dissipative coefficient Departamento de Física Universidad de Chile In collaboration with: Ramón Herrera and Marco Olivares CosmoSur III

More information

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 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

More information

Open Inflation in the String Landscape

Open Inflation in the String Landscape Chuo University 6 December, 011 Open Inflation in the String Landscape Misao Sasaki (YITP, Kyoto University) D. Yamauchi, A. Linde, A. Naruko, T. Tanaka & MS, PRD 84, 043513 (011) [arxiv:1105.674 [hep-th]]

More information

Multifield Dark Energy (Part of the Master Thesis)

Multifield Dark Energy (Part of the Master Thesis) Multifield Dark Energy (Part of the Master Thesis) Valeri Vardanyan Institut für Theoretische Physik Universität Heidelberg Bielefeld 2015 Valeri Vardanyan (ITP, Uni. Heidelberg) Multifield Dark Energy

More information

The Quantum to Classical Transition in Inflationary Cosmology

The Quantum to Classical Transition in Inflationary Cosmology The Quantum to Classical Transition in Inflationary Cosmology C. D. McCoy Department of Philosophy University of California San Diego Foundations of Physics Munich, 31 July 2013 Questions to Address 1.

More information

Reheating of the Universe and Gravitational Wave Production

Reheating of the Universe and Gravitational Wave Production Imperial College London MSc Quantum Fields and Fundamental Forces Reheating of the Universe and Gravitational Wave Production Author: Luisa Lucie-Smith Supervisor: Prof. Arttu Rajantie Submitted in partial

More information

Key: cosmological perturbations. With the LHC, we hope to be able to go up to temperatures T 100 GeV, age t second

Key: cosmological perturbations. With the LHC, we hope to be able to go up to temperatures T 100 GeV, age t second Lecture 3 With Big Bang nucleosynthesis theory and observations we are confident of the theory of the early Universe at temperatures up to T 1 MeV, age t 1 second With the LHC, we hope to be able to go

More information

What have we learnt about the early universe?

What have we learnt about the early universe? What have we learnt about the early universe? V(φ) φ Hiranya Peiris STFC Advanced Fellow University of Cambridge Roadmap Lecture 1: The physics of the cosmic microwave background. Lecture 2: What have

More information

The Standard model Higgs boson as the inflaton

The Standard model Higgs boson as the inflaton The Standard model Higgs boson as the inflaton F. Bezrukov M. Shaposhnikov EPFL, Lausanne, Suisse Institute for Nuclear Research, Moscow, Russia PONT d Avignon 08 23 May 2008 Phys. Lett. B 659, 703 (2008)

More information

Scalar fields and vacuum fluctuations II

Scalar fields and vacuum fluctuations II Scalar fields and vacuum fluctuations II Julian Merten ITA July 12, 2007 Julian Merten (ITA) Scalar fields and vacuum fluctuations II July 12, 2007 1 / 22 Outline 1 What we did so far 2 Primordial curvature

More information

Inflation and the origin of structure in the Universe

Inflation and the origin of structure in the Universe Phi in the Sky, Porto 0 th July 004 Inflation and the origin of structure in the Universe David Wands Institute of Cosmology and Gravitation University of Portsmouth outline! motivation! the Primordial

More information

Gravitational Waves and the Scale of Inflation

Gravitational Waves and the Scale of Inflation Gravitational Waves and the Scale of Inflation Mehrdad Mirbabayi with L. Senatore, E. Silverstein, M. Zaldarriaga Institute for Advanced Study COSMO2014, Chicago Aug 29, 2014 Mehrdad Mirbabayi (IAS) GW

More information

arxiv: v1 [gr-qc] 9 Mar 2019

arxiv: v1 [gr-qc] 9 Mar 2019 Deformed Starobinsky model in gravity s rainbow Phongpichit Channuie1, 2, 3, 1 College of Graduate Studies, Walailak University, Thasala, Nakhon Si Thammarat, 80160, Thailand 2 School of Science, Walailak

More information

The multi-field facets of inflation. David Langlois (APC, Paris)

The multi-field facets of inflation. David Langlois (APC, Paris) The multi-field facets of inflation David Langlois (APC, Paris) Introduction After 25 years of existence, inflation has been so far very successful to account for observational data. The nature of the

More information

Astro 448 Lecture Notes Set 1 Wayne Hu

Astro 448 Lecture Notes Set 1 Wayne Hu Astro 448 Lecture Notes Set 1 Wayne Hu Recombination Equilibrium number density distribution of a non-relativistic species n i = g i ( mi T 2π ) 3/2 e m i/t Apply to the e + p H system: Saha Equation n

More information

Multi-disformal invariance of nonlinear primordial perturbations

Multi-disformal invariance of nonlinear primordial perturbations Multi-disformal invariance of nonlinear primordial perturbations Yuki Watanabe Natl. Inst. Tech., Gunma Coll.) with Atsushi Naruko and Misao Sasaki accepted in EPL [arxiv:1504.00672] 2nd RESCEU-APCosPA

More information

Higgs field in cosmology

Higgs field in cosmology Higgs field in cosmology Christian Friedrich Steinwachs Albert-Ludwigs-Universität Freiburg 678th Wilhelm and Else Heraeus Seminar: Hundred Years of Gauge Theory, Bad Honnef, 02.08.2018 Cosmic history

More information

Summary of equations for CMB power spectrum calculations

Summary of equations for CMB power spectrum calculations Summary of equations for CMB power spectrum calculations Hans Kristian Eriksen 9. april 2010 1 Definitions and background cosmology Four time variables: t = physical time, η = t 0 ca 1 (t)dt = conformal

More information

ρ r + 4Hρ r = Γ φ 2.

ρ r + 4Hρ r = Γ φ 2. Physics Letters B 526 (2002 1 8 wwwelseviercom/locate/npe Density perturbations in warm inflation and COBE normalization HP de Oliveira ab a NASA Fermilab Astrophysics Center Fermi National Accelerator

More information

arxiv: v1 [gr-qc] 15 Feb 2018

arxiv: v1 [gr-qc] 15 Feb 2018 On the initial conditions of scalar and tensor fluctuations in fr gravity arxiv:8.556v gr-qc] 5 eb 8 S. Cheraghchi,. Shojai, Department of Physics, University of Tehran, Tehran, Iran. oundations of Physics

More information

Geometrical Measures of Non-Gaussianity Generated by Single Field Models of Inflation. by Muhammad Junaid. Doctor of Philosophy

Geometrical Measures of Non-Gaussianity Generated by Single Field Models of Inflation. by Muhammad Junaid. Doctor of Philosophy Geometrical Measures of Non-Gaussianity Generated by Single Field Models of Inflation by Muhammad Junaid A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy

More information

Lecture 12. Inflation. What causes inflation. Horizon problem Flatness problem Monopole problem. Physical Cosmology 2011/2012

Lecture 12. Inflation. What causes inflation. Horizon problem Flatness problem Monopole problem. Physical Cosmology 2011/2012 Lecture 1 Inflation Horizon problem Flatness problem Monopole problem What causes inflation Physical Cosmology 11/1 Inflation What is inflation good for? Inflation solves 1. horizon problem. flatness problem

More information

Evolution of Scalar Fields in the Early Universe

Evolution of Scalar Fields in the Early Universe Evolution of Scalar Fields in the Early Universe Louis Yang Department of Physics and Astronomy University of California, Los Angeles PACIFIC 2015 September 17th, 2015 Advisor: Alexander Kusenko Collaborator:

More information

arxiv:hep-th/ v1 12 Mar 2002

arxiv:hep-th/ v1 12 Mar 2002 UPR-978-T On the Signature of Short Distance Scale in the Cosmic Microwave Background ariv:hep-th/0203113v1 12 Mar 2002 Gary Shiu 1 and Ira Wasserman 2 1 Department of Physics and Astronomy, University

More information

Inflationary Cosmology and Alternatives

Inflationary Cosmology and Alternatives Inflationary Cosmology and Alternatives V.A. Rubakov Institute for Nuclear Research of the Russian Academy of Sciences, Moscow and Department of paricle Physics abd Cosmology Physics Faculty Moscow State

More information

Cosmic Inflation Tutorial

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

More information

Physics 463, Spring 07. Formation and Evolution of Structure: Growth of Inhomogenieties & the Linear Power Spectrum

Physics 463, Spring 07. Formation and Evolution of Structure: Growth of Inhomogenieties & the Linear Power Spectrum Physics 463, Spring 07 Lecture 3 Formation and Evolution of Structure: Growth of Inhomogenieties & the Linear Power Spectrum last time: how fluctuations are generated and how the smooth Universe grows

More information

Constraints on Inflationary Correlators From Conformal Invariance. Sandip Trivedi Tata Institute of Fundamental Research, Mumbai.

Constraints on Inflationary Correlators From Conformal Invariance. Sandip Trivedi Tata Institute of Fundamental Research, Mumbai. Constraints on Inflationary Correlators From Conformal Invariance Sandip Trivedi Tata Institute of Fundamental Research, Mumbai. Based on: 1) I. Mata, S. Raju and SPT, JHEP 1307 (2013) 015 2) A. Ghosh,

More information

Loop Quantum Gravity & the Very Early Universe

Loop Quantum Gravity & the Very Early Universe Loop Quantum Gravity & the Very Early Universe Abhay Ashtekar Institute for Gravitation and the Cosmos, Penn State Will summarize the work of many researchers; especially: Agullo, Barrau, Bojowald, Cailleatau,

More information

Lectures on Inflation

Lectures on Inflation Lectures on Inflation Leonardo Senatore Stanford Institute for Theoretical Physics Department of Physics, Stanford University, Stanford, CA 94306 Kavli Institute for Particle Astrophysics and Cosmology,

More information

Loop Quantum Cosmology: Interplay between Theory and Observations

Loop Quantum Cosmology: Interplay between Theory and Observations Loop Quantum Cosmology: Interplay between Theory and Observations Abhay Ashtekar Institute for Gravitation and the Cosmos, Penn State Will summarize the work of many researchers; especially: Agullo, Barrau,

More information

Examining the Viability of Phantom Dark Energy

Examining the Viability of Phantom Dark Energy Examining the Viability of Phantom Dark Energy Kevin J. Ludwick LaGrange College 12/20/15 (11:00-11:30) Kevin J. Ludwick (LaGrange College) Examining the Viability of Phantom Dark Energy 12/20/15 (11:00-11:30)

More information

Cosmic Large-scale Structure Formations

Cosmic Large-scale Structure Formations Cosmic Large-scale Structure Formations Bin HU bhu@bnu.edu.cn Astro@BNU Office: 京师 大厦 9907 18 weeks outline Background (1 w) universe geometry and matter components (1 hr) Standard candle (SNIa) (0.5 hr)

More information

arxiv: v1 [gr-qc] 20 Nov 2018

arxiv: v1 [gr-qc] 20 Nov 2018 The effective dynamics of loop quantum R cosmology Long Chen College of Physics and Electrical Engineering, Xinyang Normal University, Xinyang, 464000, Henan, China Dated: November 1, 018) arxiv:1811.085v1

More information

Primordial Gravity s Breath

Primordial Gravity s Breath EJTP 9, No. 26 (2012) 1 10 Electronic Journal of Theoretical Physics Primordial Gravity s Breath Christian Corda 1 International Institute for Theoretical Physics and Advanced Mathematics Einstein-Galilei,

More information

Closed Universes, de Sitter Space and Inflation

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

More information

arxiv:hep-ph/ v2 22 Jul 1994

arxiv:hep-ph/ v2 22 Jul 1994 BROWN-HET-957 Revised version July 1994 arxiv:hep-ph/9407247v2 22 Jul 1994 UNIVERSE REHEATING AFTER INFLATION Y. Shtanov, 1,2) J. Traschen 3) and R. Brandenberger 2) 1) Bogolyubov Institute for Theoretical

More information

The Cosmological Signature of Covariant Bandlimitation

The Cosmological Signature of Covariant Bandlimitation The Cosmological Signature of Covariant Bandlimitation Aidan Chatwin-Davies 1, Achim Kempf 2, Robert T. W. Martin 3 1 California Institute of Technology 2 University of Waterloo 3 University of Cape Town

More information

CHAPTER 3 THE INFLATIONARY PARADIGM. 3.1 The hot Big Bang paradise Homogeneity and isotropy

CHAPTER 3 THE INFLATIONARY PARADIGM. 3.1 The hot Big Bang paradise Homogeneity and isotropy CHAPTER 3 THE INFLATIONARY PARADIGM Ubi materia, ibi geometria. Johannes Kepler 3.1 The hot Big Bang paradise In General Relativity, the Universe as a whole becomes a dynamical entity that can be modeled

More information

Evading non-gaussianity consistency in single field inflation

Evading non-gaussianity consistency in single field inflation Lorentz Center 7 Aug, 013 Evading non-gaussianity consistency in single field inflation Misao Sasaki Yukawa Institute for Theoretical Physic (YITP) Kyoto University M.H. Namjoo, H. Firouzjahi& MS, EPL101

More information

Scale symmetry a link from quantum gravity to cosmology

Scale symmetry a link from quantum gravity to cosmology Scale symmetry a link from quantum gravity to cosmology scale symmetry fluctuations induce running couplings violation of scale symmetry well known in QCD or standard model Fixed Points Quantum scale symmetry

More information

Modern Cosmology Final Examination Solutions 60 Pts

Modern Cosmology Final Examination Solutions 60 Pts Modern Cosmology Final Examination Solutions 6 Pts Name:... Matr. Nr.:... February,. Observable Universe [4 Pts] 6 Pt: Complete the plot of Redshift vs Luminosity distance in the range < z < and plot (i)

More information