Relic High Frequency Gravitational waves from the Big Bang and How to Detect Them
Andrew Beckwith · Glen A. Robertson
Abstract and summary · read the original at the source
In one page
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.
Why it matters hereThe 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.
What it claims
01Jack 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
Published and peer-reviewed02Weinberg’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
Published and peer-reviewed03The 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
Designed, not yet built04Li’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’
What to watch05There 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
What to watch06Vigorous 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
What to watch
Read it · abstract
Abstract
This paper shows how entropy generation from numerical density calculations of relic gravitons can be measured via the Li-Baker high-frequency gravity wave (HFGW) detector, and suggests the implications this has for the physics of early-universe phase transitions. This paper indicates the role of Ng’s revised statistics in gravitational wave physics detection and the application of Baumann et al. (2007) formalism of reduction of rank-two tensorial contributions to density wave physics, using the HFGW approximation directly at the beginning as well as Li’s treatment of energy density explicitly. This formalism is a way to refine and add more capacity to the Li-Baker HFGW detector in reconstructing early-universe conditions at the onset of the big bang. Furthermore, we bring up how the HFGW detector can have its data sets compared and swapped with ice cube relic neutrino physics data taken at the south pole. This will enable us to begin to get criteria to falsify different inflation models as alluded to at the end of this manuscript.
The way in
https://doi.org/10.1063/1.3115567Published as AIP Conference Proceedings 1103, 571-581 (2009), from the SPESIF meeting, under the publisher’s copyright. The preprint is free to read at arxiv.org/abs/0809.1454 under the arXiv non-exclusive distribution licence, which is not a Creative Commons licence, so this sheet carries the authors’ own abstract and sends the reader to the source. The Crossref record for the proceedings paper lists Andrew Beckwith and Glen A. Robertson; the arXiv preprint carries A. W. Beckwith alone.
How 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
Where it sits in the curriculum
The metric, warp drives and wormholesScalar waves and the field behind the fieldsThe unified picture