Historical research guide · 0818 · 2009
Relic High Frequency Gravitational waves from the Big Bang and How to Detect Them
Andrew Beckwith · Glen A. Robertson
In one minute
Andrew Beckwith asks what the first instants of the universe left behind, and whether a detector could hear it. His subject is the graviton, the quantum of a gravitational wave, produced in a burst as the young universe passed through a temperature near ten to the thirty-second kelvin, at frequencies reaching about ten billion hertz — far above the band LIGO listens in. Borrowing Jack Ng’s counting argument, in which entropy is simply the number of particles present, Beckwith turns an entropy jump in the early universe into a graviton production rate, and feeds that rate into the detector design Fangyu Li and Robert Baker had published: a strong static magnetic field that a passing gravitational wave stirs into a small flux of photons, read out on a fractal membrane. His estimate is that roughly one in a hundred high-frequency waves arriving at such a detector would be relic, the rest made by later astrophysics. He proposes cross-checking those counts against relic neutrinos at the IceCube observatory, and using the pair to rule inflation models in or out.
Connection
The Li-Baker instrument at the centre of this paper works by the inverse Gertsenshtein effect — a gravitational wave crossing a static magnetic field turns into photons — which is chapter 10’s electromagnetic-to-gravitational coupling running in the direction that can be measured. That makes it the natural companion to the Li group’s own signal-and-noise analysis at /library/stm-c15757c634 and to the twenty-five-author survey of megahertz-to-gigahertz detection at /library/stm-96e41ddb23. Chapter 4 gains a concrete number for the metric’s highest-frequency ripples, and chapter 13 gains the link Beckwith is really after: one measurement that reaches back to the conditions at the start.
From the source
Jack Ng’s revised counting, in which the factorial term is dropped from the partition function so that entropy becomes proportional to the number of particles present rather than negative, establishes a one-to-one relationship between change in entropy and change in particle number, and Beckwith applies it to the numerical density of relic gravitons.Section ’Reviewing Jack Ng’s arguments’, equations 1 to 3
Weinberg’s 1972 expression gives the number of gravitons per unit volume in a frequency interval, and with a threshold temperature near ten to the thirty-second kelvin — where quantum gravity dominates classical gravity — the upper frequency for relic graviton production is about ten to the tenth hertz, as Grishchuk gives it.Introduction, numbered assumptions 1 to 3; section ’Weinberg’s 1972 numerical estimate’, equation 4; equations 24 and 25
The Li-Baker detector measures the interaction of high-frequency gravitational waves with a static magnetic field: the wave generates a first-order perturbative photon flux by the inverse Gertsenshtein effect together with a synchro-resonance effect against a background Gaussian beam, and because the signal flux and the background flux differ in direction, distribution, phase, polarization and decay, the two can be separated in special regions of the detector.Sections ’Ties to the Li-Baker HFGW detector’ and ’Contribution of the Li-Baker detector’, equations 26 and 30
Li’s numerical simulation gives an incident relic graviton flux of about 2.89 times ten to the fourteenth per second at the detector site against 3.77 times ten to the sixteenth per second for high-frequency gravitational waves generally, a ratio near 8.76 times ten to the minus two — so about one arriving wave in a hundred is relic in origin, and separating that one calls for a next-generation detector using quantum entanglement, following Yeo’s calculation that a passing gravitational wave changes the spin entropy and spin negativity of a system of massive spin-one-half particles.Equation 27 and the section ’Quantum Entanglement’
There are roughly one hundred thousand relic neutrinos for every relic graviton, so a high-frequency gravitational-wave detector reading about 2.89 times ten to the fourteenth relic gravitons per second and the IceCube South Pole neutrino observatory reading about ten to the twentieth relic neutrinos can have their data sets compared and swapped, which Beckwith argues makes the correlation a workable rather than an insurmountable problem.Section ’Thoughts and commentary upon swapping HFGW data with relic neutrinos’, equations 28 to 31
Vigorous chaotic inflation with a simple quadratic potential keeps the gravitational-wave energy density non-zero, with a scalar spectral tilt near 0.95 plus or minus 0.016 and a tensor tilt well below 0.1; if that density were zero there would be no relic gravitational waves to find at all, which is what makes a high-frequency detection or non-detection a falsification criterion for competing inflation models.Section ’Why use simple chaotic inflation’, equations 32 to 39; Table 1 graviton burst
The way in
https://doi.org/10.1063/1.3115567How to cite it
Andrew Beckwith, Glen A. Robertson (2009) Relic High Frequency Gravitational waves from the Big Bang and How to Detect Them doi:10.1063/1.3115567