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