Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: CMB Constraints on the Stochastic Gravitational-Wave Background at Mpc
  scales   We present robust constraints on the stochastic gravitational waves (GWs) at
Mpc scales from the cosmic microwave background (CMB) data. CMB constraints on
GWs are usually characterized as the tensor-to-scalar ratio, assuming
specifically a power-law form of the primordial spectrum, and are obtained from
the angular spectra of CMB. Here, we relax the assumption of the power-law
form, and consider to what extent one can constrain a monochromatic GW at
shorter wavelengths. Previously, such a constraint has been derived at the
wavelengths larger than the resolution scale of the CMB measurements, typically
above $100$Mpc (below $10^{-16}$Hz in frequency). However, GWs whose wavelength
is much shorter than $100$Mpc can imprint a small but non-negligible signal on
CMB anisotropies at observed angular scales, $\ell<1000$. Here, using the CMB
temperature, polarization, and lensing data set, we obtain the best constraints
to date at $10^{-16}-10^{-14}$Hz of the GWs produced before the time of
decoupling, which are tighter than those derived from the astrometric
measurements and upper bounds on extra radiations. In the future, the
constraints on GWs at Mpc scales will be further improved by several orders of
magnitude with the precision $B$-mode measurement on large scales, $\ell<100$.

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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th