Pre-Phase A Report - Lisa - Nasa

36 Chapter 1 Scientific Objectives
had no characteristic length scale. Observations of the microwave background by COBE
constrain the time at which inflation occurred, and this in turn constrains the energy
density today at LISA frequencies (and, incidentally, at ground-based frequencies as well)
to ΩGW ≤ 8×10−14 [58].
The most-discussed cosmic gravitational wave background has probably been that produced
by cosmic strings. These are defects that could have been left over from a GUT-scale
phase transition at a much earlier epoch than the electroweak transition. Therefore, by
the LISA production time, the strings would not have had any characteristic length-scale,
and the spectrum today would again be essentially scale-free at LISA frequencies, rising at
lower frequencies [59]. This spectrum is constrained by present observations of frequency
fluctuations in millisecond pulsars. This limit suggests that, at LISA and ground-based
frequencies, ΩGW ≤ 10−8 . This is still an interesting level for LISA, although ground-based
detectors are likely to reach this level first.
One example of a process that would produce a spectrum with features in the LISA band
is the collision of vacuum bubbles in the early Universe. This could occur at the end of a
phase transition that occurred randomly throughout space. The expanding bubbles of the
“new” vacuum state collide, and the resulting density discontinuities give off gravitational
waves. If the electroweak phase transition produced such bubbles, the spectrum might
peak at 0.1 mHz with a density ΩGW ∼ 3×10−7 [60]. This would easily be detected
by LISA, and it would again be an extremely important and fundamental result. Such
radiation from the electroweak transition would not be observable from the ground.
It should be emphasized that the cosmic background of gravitational waves is the leastunderstood
prospective source for LISA. The observational constraints are few, and the
predictions of possible spectra depend on relatively simple theoretical models of the early
Universe and on toy models of high-energy physics. LISA’s frequency band is orders of
magnitude different from that which is accessible to ground-based detectors or to pulsar
timing experiments, and it is very possible that LISA will find unexpected surprises here.
These would give us unparalleled insight into the mechanics of the early Universe.
An interesting feature of LISA’s observations of a background is that it can test its isotropy.
As LISA rotates, its sensitivity to different directions changes. The low-frequency CWDB
background is likely to be concentrated near the galactic plane, so by comparing two
3-month stretches of data LISA should have no difficulty seeing this background and identifying
this effect. But even the cosmological background should have a dipole anisotropy
caused by the motion of the solar system, just as the cosmic microwave background has.
If LISA makes a 3-month observation of this background, then its frequency resolution will
be about 10−7 Hz, and there will be about 105 resolvable frequencies near 10 mHz. Given
random fluctuations, the strength of the background at this frequency can be estimated
to a precision of something like √ N, or 0.3 %. Successive periods of 3 months can then
be compared to look for changes. While this is not quite precise enough to detect the
expected anisotropy of about 0.1% in a single year, if the mission lasts 10 yr then LISA
will be getting close to the required level. If the gravitational wave background turned
out not to have the same dipole anisotropy as the cosmic microwave background, then
cosmological models would have to be drastically revised.
3-3-1999 9:33 Corrected version 2.08