Go to previous page Go up Go to next page

7.2 Cosmology

Cosmology also provides a way to test Lorentz violation. The most obvious connection is via inflation. If the number of e-foldings of inflation is high enough, then the density fluctuations responsible for the observed cosmic microwave background (CMB) spectrum have a size shorter than the Planck scale before inflation. It might therefore be possible for trans-Planckian physics/quantum gravity to influence the currently observed CMB spectrum. If Lorentz violation is present at or near the Planck scale (as is implicit in models that use a modified dispersion relation at high energies [213]), then the microwave background may still carry an imprint.33 A number of authors have addressed the possible signatures of trans-Planckian physics in the CMB (for a sampling see [9421221426210116466236] and references therein). While the possibility of such constraints is obviously appealing, the CMB imprint (if any) of trans-Planckian physics, much less Lorentz violation, is model dependent and currently the subject of much debate.34 In short, although such cosmological explorations are interesting and may provide an eventual method for ultra-high energy tests of Lorentz invariance, for the purposes of this review we forego any more discussion on this approach. A simple low energy method to limit the coefficients in the aether model (47View Equation) that is less fraught with ambiguities has been explored by Carroll and Lim [76]. They consider a simplified version of the model (47View Equation) without the c4 term and choose the potential a V (uau ) to be of the form a 2 c(u ua - a ), where c is a Lagrange multiplier. Without loss of generality, we can rescale the coefficients ci in Equation (47View Equation) to set a2 = 1. In the Newtonian limit Carroll and Lim find that Newton’s constant as measured on earth is rescaled to be
obs --2G-- G N = 2 - c . (110) 1
In comparison, the effective cosmological Newton’s constant is calculated to be
2G Gobcossmo = ------------------. (111) 2 - (c1 + 3c2 + c3)

The difference between the cosmological and Newtonian regimes implies that we have to adjust our measured Newton’s constant before we insert it into cosmological evolution equations. Such an adjustment modifies the rate of expansion. A change in the expansion rate modifies big bang nucleosynthesis and changes the ratio of the primordial abundance of 4He to H. By comparing this effect with observed nucleosynthesis limits, Carroll and Lim are able to constrain the size of c1, c2, and c3. In addition to the nucleosynthesis constraint, the authors impose restrictions on the choice of coefficients such that in the preferred frame characterized by ua the perturbations dua have a positive definite Hamiltonian, are non-tachyonic, and propagate subluminally. With these assumptions Carroll and Lim find the following constraint:

0 < (14 c + 21c + 7c + 7c ) < 2, (112) 1 2 3 4
where the c4 dependence has been included for completeness.
  Go to previous page Go up Go to next page