Bounds on graviton mass using weak lensing and SZ effect in galaxy
  clusters
  In General Relativity (GR), the graviton is massless. However, a common
feature in several theoretical alternatives of GR is a non-zero mass for the
graviton. These theories can be described as massive gravity theories. Despite
many theoretical complexities in these theories, on phenomenological grounds,
the implications of massive gravity have been widely used to put bounds on
graviton mass. One of the generic implications of giving a mass to the graviton
is that the gravitational potential will follow a Yukawa-like fall off. We use
this feature of massive gravity theories to probe the mass of graviton by using
the largest gravitationally bound objects, namely galaxy clusters. In this
work, we use the mass estimates of galaxy clusters measured at various
cosmologically defined radial distances measured via weak lensing (WL) and
Sunyaev-Zel'dovich (SZ) effect. We also use the model independent values of
Hubble parameter $H(z)$ smoothed by a non-parametric method, Gaussian process.
Within $1\sigma$ confidence region, we obtain the mass of graviton $m_g < 5.9
\times 10^{-30}$ eV with the corresponding Compton length scale $\lambda_g >
6.82$ Mpc from weak lensing and $m_g < 8.31 \times 10^{-30}$ eV with $\lambda_g
> 5.012$ Mpc from SZ effect. This analysis improves the upper bound on graviton
mass obtained earlier from galaxy clusters.
