  We consider the possibility of probing left-right symmetric model (LRSM) via
cosmic microwave background (CMB). We adopt the minimal LRSM with Higgs
doublets, also known as the doublet left-right model (DLRM), where all fermions
including the neutrinos acquire masses only via their couplings to the Higgs
bidoublet. Due to the Dirac nature of light neutrinos, there exist additional
relativistic degrees of freedom which can thermalise in the early universe by
virtue of their gauge interactions corresponding to the right sector. We
constrain the model from Planck 2018 bound on the effective relativistic
degrees of freedom and also estimate the prospects for planned CMB Stage IV
experiments to constrain the model further. We find that $W_R$ boson mass below
4.06 TeV can be ruled out from Planck 2018 bound at $2\sigma$ CL in the exact
left-right symmetric limit which is equally competitive as the LHC bounds from
dijet resonance searches. On the other hand Planck 2018 bound at $1\sigma$ CL
can rule out a much larger parameter space out of reach of present direct
search experiments, even in the presence of additional relativistic degrees of
freedom around the TeV corner. We also study the consequence of these
constraints on dark matter in DLRM by considering a right handed real fermion
quintuplet to be the dominant dark matter component in the universe.
