# Presentation: 082773

## Cosmic Harmony

-  Comprehensive Picture of Structure Formation
-  Anisotropy Spectrum
-  Our Universe: Parameters

- Scott Dodelson
- Tropical Workshop on Particle Physics & Cosmology
- June 12, 2003

- Coherent picture of formation of structure in the universe

- Quantum      Mechanical Fluctuations during Inflation

- Perturbation Growth: Pressure vs. Gravity

- t~100,000 years

- Matter perturbations grow into non-linear structures observed today

- Photons *freestream: *Inhomogeneities turn into anisotropies

## Inflation produces perturbations

- Quantum mechanical fluctuations        (**k,t**)**k’,t****k-k’****k,t**
- Inflation stretches wavelength beyond horizon: **k,t**becomes constant
- Infinite number of independent perturbations w/ independent amplitudes, but ...

## All modes remain constant until they re-enter horizon.

- Inflation synchronizes all modes

## Evolution upon re-entry

- Pressure of radiation acts against clumping
- If a region gets overdense, pressure acts to reduce the density
- Similar to height of guitar string (pressure replaced by tension)

## Acoustic Peaks

- Displacement of a string

- Temperature perturbation

## Musical Acoustics

- Middle C
- Middle C on a piano

- Technical problems: How does string vibration affect air? How do air vibrationsaffect ear? ... How do perturbations in temperature at LSS show up asanisotropies today?

- Fourier transformof temperature atLast Scattering Surface

- Anisotropy spectrum today

## Why peaks and troughs?

- Vibrating String: Characteristic frequencies because ends are tied down
- Temperature in the Universe: Small scale modes enter the horizon earlier than large scale modes

## Interference could destroy peak structure

- There are many, many modes with similar values of k. All have different initial amplitude. But all are in phase.

- First Peak

## An infinite number of violins are synchronized 

- Similarly, all modes corresponding to first trough are in phase: they all have zero amplitude at recombination

## Without synchronization:

- First “Peak”

- First “Trough”

## When we see this, we conclude that modes were set in phase during inflation!

- Bennett et al. 2003

## Three Step argument for <TE>

- Polarization proportional to quadrupole
- Quadrupole proportional to dipole
- Dipole out of phase with monopole

## Isotropic radiation field produces no polarization after Compton scattering

*Modern Cosmology*
- Adapted from Hu & White 1997

- Radiation with a dipole produces no polarization

- A quadrupole is needed

## Quadrupole proportional to dipole

- Dipole is out of phase with monopole

- Roughly,

- The product of monopole and dipole is initially positive (but small, since dipole vanishes as k goes to zero); and then switches signs several times.

## DASI initially detected TE signal

- Kovac et al. 2002

## WMAP has indisputable evidence that monopole and dipole are out of phase

- This is most remarkable for scales around l~100, which
- were not in causal contact at recombination.

- Kogut et al.
- 2003

## Parameter I: Curvature

-  Same wavelength subtends smaller angle in an open universe
-  Peaks appear on smaller scales in open universe

## Parameters I: Curvature

- As early as 1998, observations favored flat universe

- DASI, Boomerang, Maxima (2001)

## Parameters II

- Reionization lowers the signal on small scales
- A tilted primordial spectrum (n<1) increasingly reduces signal on small scales
- Tensors reduce the scalar normalization, and thus the small scale signal

## Parameters III

- Baryons accentuate odd/even peak disparity
- Less matter implies changing potentials, greater driving force, higher peak amplitudes
- Cosmological constant changes the distance to LSS

## E.g.: Baryon density

- Here, F is forcing term due to gravity.

- As baryon density goes up, frequency goes down. Greater odd/even peak disparity.

## Bottom line

-  h often used instead of

-  CMB data says matter density is only 30% of critical: Need Dark Energy

## Conclusions

- Strong evidence for inflation from CMB anisotropy/polarization spectra
- Baryon and matter densities tightly constrained,  consistent with other determinations. Dark energy needed
- Connection between particle physics & cosmology (inflation, dark matter, dark energy) more solid than ever. We need new tools ...

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