Gravitational Wave Backgrounds from Mesoscopic Dynamics of

the Extra DimensionsAnd possibly observable with LIGO,

VIRGO, LISA, etc.

PRL in press, astro-ph/0005044LIGO-G000255-00-D

Cosmology: micro-, meso-, macroscopic observables

Possible observable relics of early mesoscopic activity: mean baryon number, dark matter (?), stochastic gravitational wave background

Cosmology with and without extra dimensions

The “Hubble Length” (Friedmann equation):

“Redshifted Hubble Frequency”(frequency of observed waves):

LISA(0.1 to 100 mHz): 1TeV to 1000 TeV, 1 mm to 10ALIGO (up to kHz): up to 10^7 TeV, down to 10^-14 mm

“Maximal amplitude” of primordial gravitational wave background given by the density of relativistic particles

SBBN constrains gravitational wave energy density to less than 0.1 of this

LIGO and LISA can reach well below this maximal amplitude

Primordial Gravitational Wave Sources

• Inflationary quantum fluctuations (CBR)

• First-order phase transitions (EW? SUSY?)

• Transitions associated with baryogenesis

• Defects (strings, textures, Goldstone modes)

• Formation of 3-brane in higher dimensional space

• Stabilization of size of extra dimensions

Formation of a “brane+bulk” setup naturally creates an intense classical gravitational wave background

Gravity may propagate in the “bulk” of extra dimensions

Standard Model fields propagate in 3+1 dimensions

They may be confined to a “3-brane” in a larger space

Contexts for “brane+bulk”models

• Quantum gravity needs 10 space dimensions• Where are the extra dimensions?• Wrapped close to Planck scale (Kaluza-Klein)?• Direct particle constraints: TeV scale• Direct gravity constraints: mm scale• Hierarchy problem: huge range of scales• Cosmological constant: 0.1mm scale• Infinite extra dimensions with mm curvature?• “Holography”, AdS5 projection• Stabilization of the extra dimensions

Below the size or curvature radius b of n extra dimensions, gravity is no longer an inverse square law but R^-(3+n-1)(Gauss’ law)

Relation of standard (apparent) Planck scale to the true unification scale and the volume of n extra dimensions

A large volume V leads to a large apparent Planck mass

Why is gravity so weak compared to the other forces?

For large n, can solve the “hierarchy problem”

Examples of phenomenological constraints

• New particles/ missing energy at accelerators• “Kaluza-Klein tower” states• New energy losses from supernovae, red giants• Overproduction of stable relics (dark matter)• Direct measurement of inverse square law at short

distances (less than 0.3mm, EotWash group)• Most limits close to mm/TeV frontier scales

Gravitational wave background radiation from brane formation and dimensional stabilization

• Probes gravity and unification on much smaller scales than direct particle or gravity experiments

• Probes cosmology at much earlier times and smaller scales than other relics

Broken Poincare symmetry during condensation of a brane: random displacements in the higher dimensions lead to intrinsic curvature

time 1

These are dynamically converted into tensor modes close to maximal amplitude up to Hubble frequency, suppressed at low frequencies

Nambu-Goldstone displacement modes

space

time 2 time 3

size b

Radion vev may be represented by an order parameter with a first-order phase transition

time

Barrier penetration by nucleation of macroscopic bubbles on a scale up to about 0.01/H leads to relativistic energy flows

Stabilization of the extra dimension size/curvature

“Radion turbulence”

Dimension size b(x) may be thought of as a new field in 3-space, the “radion”

Examples of backgrounds in the LISA band

If n of the largest extra dimensions have the same size/curvature radius b_0,

The unification scale and dimension size are unknown but are related:

Parameters of a model with many equal dimensions

What range of these parameters produces detectable backgrounds?

Frequency bands for gravitational wave backgrounds

Extra dimensions probed by LISA, LIGO, VIRGO

Size of largest extra dimensions, Hubble length

Unification scale, temperature