I don't believe there are pre-written algorithms for Cosine similarity or Pearson Porrelation in PySpark that you can re-use. If you end up writing your own implementation of the algorithm though, the project would definitely appreciate if you shared that code back with the project for future users to leverage!
One nice feature of PySpark is that you can easily use existing functions from NumPy and SciPy inside your Spark code. For a simple example, the following uses Spark's cartesian operation (which combines pairs of vectors into tuples), followed by NumPy's corrcoef to compute the pearson correlation coefficient between every pair of a set of vectors. The vectors are an RDD of numpy arrays.
>> from numpy import array, corrcoef
>> data = sc.parallelize([array([1,2,3]),array([2,4,6.1]),array([3,2,1.1])])