Inflation and the SLAC Theory Group I was a one-year visitor from a postdoc position at Cornell. My research problem (working with Henry Tye

Size: px

Start display at page:

Download "Inflation and the SLAC Theory Group I was a one-year visitor from a postdoc position at Cornell. My research problem (working with Henry Tye"

Allison Bishop
6 years ago
Views:

2 Inflation and the SLAC Theory Group I was a one-year visitor from a postdoc position at Cornell. My research problem (working with Henry Tye back at Cornell): Why were so few magnetic monopoles produced by the big bang? SLAC group (with visitors): Sidney Coleman (visiting from Harvard) Lenny Susskind (recently arrived) Paul Langacker (visiting from Penn, working on GUTs review) So-Young Pi Erick Weinberg (visited spring term, from Columbia) Marvin Weinstein Helen Quinn Stan Brodsky ::: 1

3 Inflation and the SLAC Theory Group I was a one-year visitor from a postdoc position at Cornell. My research problem (working with Henry Tye back at Cornell): Why were so few magnetic monopoles produced by the big bang? SLAC group (with visitors): Sidney Coleman (visiting from Harvard) Lenny Susskind (recently arrived) Paul Langacker (visiting from Penn, working on GUTs review) So-Young Pi Erick Weinberg (visited spring term, from Columbia) Marvin Weinstein Helen Quinn Stan Brodsky ::: 1

4 Inflation as Applied Particle Theory with General Relativity For a scalar field ffi(x), the pressure p = 1 μffi@ μ ffi V (ffi) : If the potential energy dominates, then p ß V (ffi). Positive energy density V (ffi) =) negative pressure. GR: Negative pressure =) gravitational repulsion. New Inflation Linde, 1982 Albrecht & Steinhardt Chaotic Inflation Linde,

5 Inflation as Applied Particle Theory with General Relativity For a scalar field ffi(x), the pressure p = 1 μffi@ μ ffi V (ffi) : If the potential energy dominates, then p ß V (ffi). Positive energy density V (ffi) =) negative pressure. GR: Negative pressure =) gravitational repulsion. New Inflation Linde, 1982 Albrecht & Steinhardt Chaotic Inflation Linde,

Positive energy density V (ffi) =) negative pressure.

6 Inflation as Applied Particle Theory with General Relativity For a scalar field ffi(x), the pressure p = 1 μffi@ μ ffi V (ffi) : If the potential energy dominates, then p ß V (ffi). Positive energy density V (ffi) =) negative pressure. GR: Negative pressure =) gravitational repulsion. New Inflation Linde, 1982 Albrecht & Steinhardt Chaotic Inflation Linde,

7 Successes of Inflation 1) Horizon / Uniformity Problem: The universe appears to be uniform (to a few parts in 10 5 ) on length scales fl the horizon distance of classical cosmology. With inflation, uniformity can be established before inflation, on tiny length scales. Inflation stretches these tiny length scales to cosmological proportions. 2) Flatness / Mass Density Problem: Pre-1998: Ω Planck 2015: Mass density Critical mass density ß 0:3 : Ω = 0:999 ± 0:004 (95%confidence). 3

8 Successes of Inflation 1) Horizon / Uniformity Problem: The universe appears to be uniform (to a few parts in 10 5 ) on length scales fl the horizon distance of classical cosmology. With inflation, uniformity can be established before inflation, on tiny length scales. Inflation stretches these tiny length scales to cosmological proportions. 2) Flatness / Mass Density Problem: Pre-1998: Ω Planck 2015: Mass density Critical mass density ß 0:3 : Ω = 0:999 ± 0:004 (95%confidence). 3

3) Cosmological Density Fluctuations A Mind-Boggling Success Story The Time-Delay Description: Expansion of universe is described by scale factor a(t), which grows with time.

9 3) Cosmological Density Fluctuations A Mind-Boggling Success Story The Time-Delay Description: Expansion of universe is described by scale factor a(t), which grows with time. Field equation for the inflaton scalar field: Given one solution ffi 0 (t), the general solution is ffi(~x; t) =ffi 0 t ffit(~x) = ffi 0 (t) _ ffi0 ffit(~x) ffi 0 (t)+ffiffi(~x; t) : Perturbations in rolling scalar field are characterized by a time delay ffit(~x) = ffiffi(~x; t) _ffi 0 (t) 4

10 3) Cosmological Density Fluctuations A Mind-Boggling Success Story The Time-Delay Description: Expansion of universe is described by scale factor a(t), which grows with time. Field equation for the inflaton scalar field: Given one solution ffi 0 (t), the general solution is ffi(~x; t) =ffi 0 t ffit(~x) = ffi 0 (t) _ ffi0 ffit(~x) ffi 0 (t)+ffiffi(~x; t) : Perturbations in rolling scalar field are characterized by a time delay ffit(~x) = ffiffi(~x; t) _ffi 0 (t) 4

11 3) Cosmological Density Fluctuations A Mind-Boggling Success Story The Time-Delay Description: Expansion of universe is described by scale factor a(t), which grows with time. Field equation for the inflaton scalar field: Given one solution ffi 0 (t), the general solution is ffi(~x; t) =ffi 0 t ffit(~x) = ffi 0 (t) _ ffi0 ffit(~x) ffi 0 (t)+ffiffi(~x; t) : Perturbations in rolling scalar field are characterized by a time delay ffit(~x) = ffiffi(~x; t) _ffi 0 (t) 4

12 3) Cosmological Density Fluctuations A Mind-Boggling Success Story The Time-Delay Description: Expansion of universe is described by scale factor a(t), which grows with time. Field equation for the inflaton scalar field: Given one solution ffi 0 (t), the general solution is ffi(~x; t) =ffi 0 t ffit(~x) = ffi 0 (t) _ ffi0 ffit(~x) : ffi 0 (t)+ffiffi(~x; t) : Perturbations in rolling scalar field are characterized by a time delay ffit(~x) = ffiffi(~x; t) _ffi 0 (t) 4

13 3) Cosmological Density Fluctuations A Mind-Boggling Success Story The Time-Delay Description: Expansion of universe is described by scale factor a(t), which grows with time. Field equation for the inflaton scalar field: Given one solution ffi 0 (t), the general solution is ffi(~x; t) =ffi 0 t ffit(~x) = ffi 0 (t) _ ffi0 ffit(~x) ffi 0 (t)+ffiffi(~x; t) : Perturbations in rolling scalar field are characterized by a time delay ffit(~x) = ffiffi(~x; t) _ffi 0 (t) 4

14 Initial State: Bunch-Davies/Gibbons-Hawking Vacuum Fourier expand the scalar field, as an operator, in terms of Fourier mode operators ~ ffi( ~ k; t): ffi(~x; t) = 1 (2ß) 3 Z d 3 ke i~ k ~x ~ffi( ~ k; t) : For each Fourier mode ~ k, the physical wavelength is phys (t) =a(t) 2ß j ~ kj : At asymptotically early times, is very small, the frequency is very high, and the expansion of the universe is comparatively very slow it looks more and more like Minkowski space at earlier and earlier times. The vacuum" is the state in which each mode is in its Minkowski ground state (i.e., harmonic oscillator ground state) as t! 1: 5

The End of Inflation Key properties: 1) Nearly scale invariant spectrum: V (ffi) and V 0 (ffi) change very little while the visible modes are generated.

15 The End of Inflation Key properties: 1) Nearly scale invariant spectrum: V (ffi) and V 0 (ffi) change very little while the visible modes are generated. 2) Nearly Gaussian: it's a nearly free quantum field theory. 3) Adiabatic (all components photons, baryons, dark matter are compressed by the same factor): the fluctuations are generated before the components are differentiated. 6

16 Ripples in the Cosmic Microwave Background 7

17 Spectrum of CMB Ripples 8

18 Planck 2015 TE Power Spectrum 9

19 Planck 2015 EE Power Spectrum 10

20 Gaussianity of the CMB Nongaussianites are measured by f NL, where Planck 2015 set the bounds f local NL =0:8 ± 5:0 ; f equil NL = 4 ± 43 ; f ortho NL = 26 ± 21 (68% CL statistical). Local, equil, and ortho refer to three different shapes" for the 3-point function (bispectrum). f NL is defined by Φ=Φ g + f NL Φ 2 g ; where Φ is the Bardeen potential. Note that the nongaussian term will be comparable to the gaussian term when f NL ο 10 5, so the limits imply that the CMB is VERY gaussian. 11

21 B-Modes (Gravitational Waves) Modes to describe the polarization of the CMB fall in two classes, E-modes and B-modes. The B-modes cannot be generated in linear approximation by density perturbations. BUT: can be generated by (nonlinear) scattering from dust. Intensity measured by the tensor-scalar ratio r, the ratio of the power in B-modes to the power in (scalar) density perturbations. Currently, r<0:7 at 95% confidence. The search is on! CMB Stage 4 proposes to reach a sensitiviy of Aprimordial B-mode observation would pin down the energy scale of inflation. 12

22 Summary Inflation is a consequence of the dynamics of a scalar field. It's a very natural consequence of any extension of known physics to higher energies. Successes of inflation include: Explanation of the homogeneity of the universe. Explanation of why the total mass density is so close to the critical value. Gives very successful predictions for the spectrum of density perturbations observed in the CMB. Also predicts polarization patterns, and Gaussianity. The sensitivity for primordial B-modes is improving dramatically. If they can be found, they will give a powerful new tool for studying the early universe. 13

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