Constraining CSL strength parameter $\lambda$ from standard cosmology and spectral distortions of CMBR

Models of spontaneous wave function collapse modify the linear Schr\"{o}dinger equation of standard Quantum Mechanics by adding stochastic non-linear terms to it. The aim of such models is to describe the quantum (linear) nature of microsystems along with the classical nature (violation of superposition principle) of macroscopic ones. The addition of such non-linear terms in the Schr\"{o}dinger equation leads to non-conservation of energy of the system under consideration. Thus, a striking feature of collapse models is to heat non-relativistic particles with a constant rate. If such a process is physical, then it has the ability to perturb the well-understood thermal history of the universe. In this article we will try to investigate the impacts of such heating terms on standard evolution of non-relativistic matter and on the formation of CMBR. We will use the CSL model, the most widely used collapse model. We will also put constraints on the CSL collapse rate $\lambda$ by considering that the standard evolution of non-relativistic matter is not hampered and the observed precise blackbody spectrum of CMBR would not get distorted (in the form of $\mu-$type and $y-$type distortions) so as to violate the observed bounds.