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Register a new userPhoton and Graviton Mass Limits
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Added by
Michael Martin Nieto
Publication date
2010
fields
Physics
and research's language is
English
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Efforts to place limits on deviations from canonical formulations of electromagnetism and gravity have probed length scales increasing dramatically over time.Historically, these studies have passed through three stages: (1) Testing the power in the inverse-square laws of Newton and Coulomb, (2) Seeking a nonzero value for the rest mass of photon or graviton, (3) Considering more degrees of freedom, allowing mass while preserving explicit gauge or general-coordinate invariance. Since our previous review the lower limit on the photon Compton wavelength has improved by four orders of magnitude, to about one astronomical unit, and rapid current progress in astronomy makes further advance likely. For gravity there have been vigorous debates about even the concept of graviton rest mass. Meanwhile there are striking observations of astronomical motions that do not fit Einstein gravity with visible sources. Cold dark matter (slow, invisible classical particles) fits well at large scales. Modified Newtonian dynamics provides the best phenomenology at galactic scales. Satisfying this phenomenology is a requirement if dark matter, perhaps as invisible classical fields, could be correct here too. Dark energy {it might} be explained by a graviton-mass-like effect, with associated Compton wavelength comparable to the radius of the visible universe. We summarize significant mass limits in a table.
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In Einsteins general relativity, gravity is mediated by a massless spin-2 metric field, and its extension to include a mass for the graviton has profound implication for gravitation and cosmology. In 2002, Finn and Sutton used the gravitational-wave (GW) back-reaction in binary pulsars, and provided the first bound on the mass of graviton. Here we provide an improved analysis using 9 well-timed binary pulsars with a phenomenological treatment. First, individual mass bounds from each pulsar are obtained in the frequentist approach with the help of an ordering principle. The best upper limit on the graviton mass, $m_{g}<3.5times10^{-20} , {rm eV}/c^{2}$ (90% C.L.), comes from the Hulse-Taylor pulsar PSR B1913+16. Then, we combine individual pulsars using the Bayesian theorem, and get $m_{g}<5.2times10^{-21} , {rm eV}/c^{2}$ (90% C.L.) with a uniform prior for $ln m_g$. This limit improves the Finn-Sutton limit by a factor of more than 10. Though it is not as tight as those from GWs and the Solar System, it provides an independent and complementary bound from a dynamic regime.
The superradiant instability of black hole space-times has been used to place limits on ultra-light bosonic particles. We show that these limits are model dependent. While the initial growth of the mode is gravitational and thus model independent, the ability to place a limit on new particles requires the mode to grow unhindered to a large number density. Non-linear interactions between the particle and other light degrees of freedom that are mediated through higher dimension operators can damp this growth, eliminating the limit. However, these non-linearities may also destroy a cosmic abundance of these light particles, an attractive avenue for their discovery in several experiments. We study the specific example of the QCD axion and show that it is easy to construct models where these non-linearities eliminate limits from superradiance while preserving their cosmic abundance.
Recent literature has shown that photon-photon forward scattering mediated by Euler-Heisenberg interactions may generate some amount of the circular polarization ($V$ modes) in the cosmic microwave background (CMB) photons. However, there is an apparent contradiction among the different references about the predicted level of the amplitude of this circular polarization. In this work, we will resolve this discrepancy by showing that with a quantum Boltzmann equation formalism we obtain the same amount of circular polarization as using a geometrical approach that is based on the index of refraction of the cosmological medium. We will show that the expected amplitude of $V$ modes is expected to be $approx$ 8 orders of magnitude smaller than the amplitude of $E$-polarization modes that we actually observe in the CMB, thus confirming that it is going to be challenging to observe such a signature. Throughout the paper, we also develop a general method to study the generation of $V$ modes from photon-photon and photon-spin-1-massive-particle forward scatterings without relying on a specific interaction, which thus represent possible new signatures of physics beyond the Standard Model.
We study the space of all kinematically allowed four photon and four graviton S-matrices, polynomial in scattering momenta. We demonstrate that this space is the permutation invariant sector of a module over the ring of polynomials of the Mandelstam invariants $s$, $t$ and $u$. We construct these modules for every value of the spacetime dimension $D$, and so explicitly count and parameterize the most general four photon and four graviton S-matrix at any given derivative order. We also explicitly list the local Lagrangians that give rise to these S-matrices. We then conjecture that the Regge growth of S-matrices in all physically acceptable classical theories is bounded by $s^2$ at fixed $t$. A four parameter subset of the polynomial photon S-matrices constructed above satisfies this Regge criterion. For gravitons, on the other hand, no polynomial addition to the Einstein S-matrix obeys this bound for $D leq 6$. For $D geq 7$ there is a single six derivative polynomial Lagrangian consistent with our conjectured Regge growth bound. Our conjecture thus implies that the Einstein four graviton S-matrix does not admit any physically acceptable polynomial modifications for $Dleq 6$. A preliminary analysis also suggests that every finite sum of pole exchange contributions to four graviton scattering also such violates our conjectured Regge growth bound, at least when $Dleq 6$, even when the exchanged particles have low spin.
Rapidly rotating black holes are known to develop instabilities in the presence of a sufficiently light boson, a process which becomes efficient when the bosons Compton wavelength is roughly the size of the black hole. This phenomenon, known as black hole superradiance, generates an exponentially growing boson cloud at the expense of the rotational energy of the black hole. For astrophysical black holes with $M sim mathcal{O}(10) , M_odot$, the superradiant condition is achieved for bosons with $m_b sim mathcal{O}(10^{-11} ) , {rm eV}$; intriguingly, photons traversing the intergalactic medium (IGM) acquire an effective mass (due to their interactions with the ambient plasma) which naturally resides in this range. The implications of photon superradiance, i.e. the evolution of the superradiant photon cloud and ambient plasma in the presence of scattering and particle production processes, have yet to be thoroughly investigated. Here, we enumerate and discuss a number of different processes capable of quenching the growth of the photon cloud, including particle interactions with the ambient electrons and back-reactions on the effective mass (arising e.g. from thermal effects, pair-production, ionization of of the local background, and modifications to the dispersion relation from strong electric fields). This work naturally serves as a guide in understanding how interactions may allow light exotic bosons to evade superradiant constraints.
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