Testing the slow roll inflation paradigmTesting the slow roll inflation paradigmwith the Big Bang Observerwith the Big Bang Observer

Carlo UngarelliSchool of Physics and Astronomy

Astrophysics and Space Research Group

In collaboration with A.Vecchio, P. Corasaniti (Columbia, NY), R. A. Mercer

The paradigm of (slow-roll) inflationThe paradigm of (slow-roll) inflationSolves the shortcomings of the standard cosmological model Solves the shortcomings of the standard cosmological model (flatness and horizon problem) by postulating the existence of (flatness and horizon problem) by postulating the existence of an early phase of accelerated expansion driven by the energy an early phase of accelerated expansion driven by the energy density of a scalar field slowly rolling towards its minimumdensity of a scalar field slowly rolling towards its minimum

Predictions: 1)The Universe is spatially flat 2)Quantum Predictions: 1)The Universe is spatially flat 2)Quantum zero-point fluctuations of space-time metric are stretched over zero-point fluctuations of space-time metric are stretched over astrophysical scales producing a astrophysical scales producing a nearly scale invariant nearly scale invariant spectrum of density perturbations spectrum of density perturbations and a spectrum of and a spectrum of gravitational waves as a gravitational waves as a cosmic gravitational wave stochastic cosmic gravitational wave stochastic background (CGWB)background (CGWB)

The first prediction and part of the second have been The first prediction and part of the second have been confirmed by the measurement of the Cosmic Microwave confirmed by the measurement of the Cosmic Microwave Background (CMB).Background (CMB). The existence of CGWB is yet untestedThe existence of CGWB is yet untested

CGWB produced during slow-roll inflationCGWB produced during slow-roll inflation

fd

dρ

ln

1 gw

c

GW

Hz10

107)(

16

11

0

2

0

GW

2

0

fH

f

HfhCOBE bound

(Koranda, Turner 94)

Hz]10,10[,10 34max

GW

2

0

15 fh

Almost flat spectrum (see e.g. Turner ’97)

Detection of stochastic backgrounds

Earth-based interferometers

Design sensitivity of current Interferometers

Second generation detectors [Advanced LIGO]

3rd generation European Gravitational Observatory

610~MIN

GW

2

0

h810~MIN

GW

2

0

h1010~MIN

GW

2

0

h

String-inspired inflationary models (e.g. pre-big-bang) could be tested by second generation detectors (Allen, Brustein 97; U, Vecchio 99) Warnings: the models do not provide reliable description of transition to Post-big-bang era; the observability of GW spectrum depends on the detail of the transition

~f 3

Detection of stochastic background: LISA

Astrophysical backgroundsIncoherent superpositionof GW emitted by short-period, solarmass binary systems (WD,NS..)Galactic and extra-galactic contribution (Bender et al, 90,97; Postnov et al, Schneider et al 00)

3/11

obs

1

3/53/113

1

obs

1

003.0

5.0Hz1080~

)(,1

T

yr

yr

M

fN

Tffdf

dNN

coal

bb

Towards testing slow-roll inflation: BBOTo avoid the astrophysical background the frequency band To avoid the astrophysical background the frequency band

should be around 0.1 Hzshould be around 0.1 Hz(U and Vecchio 01, Bender and Hogan 01, Seto et al 01)

name LaserPower (W)

LaserWav.(mm)

Opt.Eff.

ArmLength(km)

MirrorDiameter

(m)

Acc noise vsLISA

BBOlite

100 1.06 0.3 20000 3 0.1

BBO 300 0.5 0.3 50000 3.5 0.01

BBOgrand

500 0.5 0.5 20000 4.0 0.001

GWs in single field slow-roll inflation

8

~16

~2

2

R

2

T

2

pl

2

T

1

2

2

R

rn

r

km

H

kHH

T

n

n

T

S

Curvature (R) and Tensor (T)

perturbations spectra

81

2

N1

8

Hz101.3,ln

101.5

)exp(

GW

17

0

0

15

0

GW0GW

rn

rn

ff

f

nAr

S

(See Turner ’97)

The GW spectrum depends on two primordial parameters (r,nS) andone cosmological parameter A (~0.7 see e.g. Spergel et al ’03)

BBO-lite BBO

BBO-grandWMAP 1,2,3- confidence levels (Kinney et al 04)

(U, Vecchio,Corasaniti, Mercer Astro-ph/…to appear)

BBO vs future CMB experiments (I)

BBO vs PLANCK BBO-GRAND vs CMBPol

BBO vs future CMB experiments (II)

Residual foregroundsfrom NS-radio pulsars

2

2 pulsar 20

0 gw

5

5 100.1Hz

1.4 10

fh

r

CMB B-modeForegrounds from gravitational lensing impose a lower limit

(Knox and Song ’02)

4106 r

BBO design sensitivity depends strongly on the antenna diameter and laser wavelength

1

4

L

3

482 Hzm5.3W300

nm500104~

~

DPhn

Some Remarks

Advanced earth-based GW detectors cannot test the standard slow-roll inflation paradigm. They could detect signal from inflation if Universe underwent a ``pre-big-bang phase’’ (or accelerated contraction). More robust predictions are needed.

A dedicated post-LISA mission can detect a stochastic background of GW produced during an epoch of slow-roll inflation with a design sensitivity beyond the sensitivity of PLANCK surveyor one. The sensitivity of post-PLANCK missions to stochastic backgrounds of GW strongly depends on the ability of removing the foregrounds due to lensing