# Presentation: 942148

## Portsmouth

## Models of inflation and primordial perturbations

- David Wands
- Institute of Cosmology and Gravitation
- University of Portsmouth

- Cosmo – 02					Chicago, September 2002

## Cosmological inflation:

-  requires negative pressure
-     e.g.	self-interacting scalar field
-  speculative and uncertain physics

- Starobinsky (1980)
- Guth (1981)

## Models of inflation:

-  observed through primordial perturbation spectra
- gravitational waves *(we hope)*
- matter/radiation perturbations

## Perturbations in FRW universe:

*Characteristic timescales for comoving wavemode k*
*   **oscillation period/wavelength**	**a / k*
*  **Hubble damping time-scale**	**	**H** -1*
*small-scales k > aH**	**under-damped oscillator*
*large-scales k < aH**	**over-damped oscillator*

- wave equation

## Vacuum fluctuations

*small-scale/underdamped zero-point fluctuations*
*large-scale/overdamped perturbations in growing mode*
*	**linear evolution  ****  Gaussian random field*

*fluctuations of any light fields (m<3H/2) `frozen-in’ on large scales*

- Hawking ’82, Starobinsky ’82, Guth & Pi ‘82

- *** assumes Bunch-Davies vacuum on small scales ***
- probe of trans-Planckian effects for ***k/a > M******Pl******	***Brandenberger & Martin (2000)
- effect likely to be small for ***H << M******Pl******	******      ***Starobinsky; Niemeyer; Easther et al (2002)

## Inflation -> matter perturbations

*during  inflation*
* **scalar field fluctuation, ****	**	**	**	*
*scalar curvature *
* **on uniform-field *
* **hypersurfaces**	**	*
*	**	*

## Single-field models:

- 1. **large field** ( *** **** M**Pl *)
- e.g. chaotic inflation
- not-so-high energy / very slow roll
- 2. **small field**
- e.g. new or natural inflation
- 3. **hybrid inflation**
- e.g., susy or sugra models

- see, e.g., Lyth & Riotto

## can be distinguished by observations

- slow time-dependence during inflation
-  -> weak scale-dependence of spectra
- tensor/scalar ratio suppressed at low energies/slow-roll

## Microwave background +2dF + BBN + Sn1A + HST

							  Lewis & Bridle (2002)

- <date/time>

- Microwave background +2dF + BBN + Sn1A + HST
- 							  Lewis & Bridle (2002)

- Observational constraints

## digging deeper:

-  initial state		new inflation
-  ending inflation	hybrid inflation
-  enhancing inflation	assisted inflation
- 		warm inflation
- 		brane-world inflation
-  may yield additional information
-  **non-gaussianity**
-  **isocurvature (non-adiabatic) modes**

## Inflation -> primordial perturbations (II)

*scalar field fluctuations**	**	**density perturbations*
*two fields (****,****)**	**	**	**	**matter and radiation (m,****)*
*curvature of uniform-field slices**	**	**curvature of uniform-density slices*

## initial power spectra:

*uncorrelated at horizon-crossing*

## primordial power spectra:

*correlated! **	**Langlois (1999)*

## consistency conditions:

*single-field inflation:*
*  **Liddle and Lyth (1992)*

*gravitational waves:*

*two-field inflation:*
* **Wands, Bartolo, Matarrese & Riotto (2002)*

*multi-field inflation:*
*  **Sasaki & Stewart (1996)*

## microwave background predictions

- <date/time>

- adiabatic

- isocurvature

- correlation

*C**l** = A**2** ***

*+ B**2***

*+ 2 A B *cos **

- Bucher, Moodley & Turok ’00	nS = 1
- Trotta, Riazuelo & Durrer ’01
- Amendola, Gordon, Wands & Sasaki ’01
- 	best-fit to Boomerang, Maxima & DASI
- 	B/A = 0.3,  cos = +1,  nS = 0.8
- 	b = 0.02,  cdm = 0.1,   = 0.7

- }

## curvaton scenario:

**large-scale density perturbation generated entirely by      non-adiabatic modes      after inflation**

- Lyth & Wands, Moroi & Takahashi, Enqvist & Sloth (2002)

- negligible gravitational waves
- 100%correlated residual isocurvature modes
- detectable non-Gaussianity if ,decay<<1

## primordial non-gaussianity

- simple definition in terms of conformal Newtonian potential *******=3R/5***
- 		where*** f******NL****** = 0 ***for linear evolution

- Komatsu & Spergel (2001)
- also Wang & Kamiokowski (2000)

- significant constraints on ***f******NL*** from all-sky microwave background surveys
- COBE	***f******NL****** < 2000***
- MAP	***f******NL****** < 20***
- Planck 	***f******NL****** < 5***

- theoretical predictions
- non-linear inflaton dynamics	constrained	 ***f******NL****** < 1******	******  ***Gangui et al ‘94
- dominant effect from second-order metric perturbations? Acquaviva et al (2002)
- but non-linear isocurvature modes could allow	***f******NL****** >> 1******	******   ***Bartolo et al (2002)
- e.g., curvaton 	***f******NL****** ************ 1 / ******************,decay***		  Lyth, Ungarelli & Wands (2002)

## Conclusions:

***Observations**** *of ***tilt  ***of density perturbations* (**n****1**) *and ***gravitational waves**** (****>0**) *can distinguish between slow-roll models
***Isocurvature**** *perturbations and/or* ****non-Gaussianity**** *may provide valuable info
***Non-adiabatic ***perturbations (off-trajectory) in multi-field models are an additional source of curvature perturbations on large scales
***Consistency relations*** remain an important test in multi-field models -  can falsify slow-roll inflation