Table of Links

Abstract and 1 Introduction

2 Calculating the Stochastic Wave Vector Dark Matter Signal

2.1 The Dark Photon Field

2.2 The Detector Signal

3 Statistical Analysis and 3.1 Signal Likelihood

3.2 Projected Exclusions

4 Application to Accelerometer Studies

4.1 Recasting Generalised Limits onto B − L Dark Matter

5 Future Directions

6 Conclusions, Acknowledgments, and References

A Equipartition between Longitudinal and Transverse Modes

B Derivation of Marginal Likelihood with Stochastic Field Amplitude

C Covariance Matrix

D The Case of the Gradient of a Scalar

C Covariance Matrix

To treat the total likelihood as the product of the individual likelihoods in each frequency bin, we must check that the covariance matrix is diagonal.

We will consider a signal-only analysis, discarding the noise, since the noise merely adds to the power and is uncorrelated between different frequency bins. We may write the values of the three peaks as

We wish to compute the quantity

We can do this using the expression for the raw moments,

where, for us, σ = 1/ √ 2. Aside from this, we need to know that

We then get that

Crucially, we get that the covariance between peaks is 0, allowing us to treat them as statistically independent and hence permitting us to express the total likelihood as the product of the individual likelihoods.