Is there a Cosmic Gravitational Background Radiation (CGBR)? The recent discovery by the LIGO made me wonder about this.

We know that there exists a CMBR, Cosmic Microwave Background Radiation, a blanket of electromagnetic energy covering the universe, made by the Big Bang.

But, the big bang was an explosive event. The huge "shockwave" made by it sent ripples in space time. (Primordial gravitational waves)

Wouldn't these ripples flood the universe creating sort of a Cosmic Gravitational Background Radiation (not exactly radiation)?

If such waves do flood the universe, couldn't a much more sensetive version of LIGO be able to detect this and use it as a contrast to create "gravitational telescopes"?
 A: Yes, there is a predicted cosmic gravitational wave background; an expanding universe is essentially transparent to gravitational waves once they are produced.
There are a number of scenarios in which GWs might be produced - these are listed in the eLISA white paper and include a transition from the inflationary epoch to the hot big bang, the electroweak phase transition at energy scales of $\sim 1$ TeV and by decaying cosmic strings (which I don't claim to understand). The frequency spectrum of these mechanisms is very broad but peaks around $10^{-4}$ Hz (wavelengths in excess of $10^{12}$ m) for the electroweak phase transition. The energy scale associated with inflation would be much higher and this produces waves at much lower frequencies, maybe $10^{-16}$ Hz, but there could be higher frequency signals (almost any frequency it seems), associated with the exit of the universe from the inflationary epoch. It also seems there are a broad range of possibilities for GWs from cosmic strings. A review of these mechanisms in the context of eLISA is given by Binetruy et al. (2012).
This means that whilst it is possible that some cosmic GW background might be detectable by ground-based interferometers in the range $10-10^4$ Hz, a better bet may be going to space (to avoid the overwhelming low frequency seismic noise on Earth) to look for mHz and below frequencies. Thus one needs an interferometer with very long arms in space.
Detecting the cosmic gravitational wave background is one of the things the space-based eLISA interferometer may be able to do with its proposed 1 million km arms. An alternative that works at even lower frequencies is the idea of pulsar timing arrays, that use the signals from a network of well-studied milli-second pulsars to look for timing distortions on the scales caused by really long wavelength GWs ($\geq 10^{15}$ m).
A: A review of the underlying theory as of Dec 2019:
Primordial backgrounds of relic gravitons
by Massimo Giovannini.

The diffuse backgrounds of relic gravitons with frequencies ranging
between the aHz band and the GHz region encode the ultimate
information on the primeval evolution of the plasma and on the
underlying theory of gravity well before the electroweak epoch. While
the temperature and polarization anisotropies of the microwave
background radiation probe the low-frequency tail of the graviton
spectra, during the next score year the pulsar timing arrays and the
wide-band interferometers (both terrestrial and hopefully space-borne)
will explore a much larger frequency window encompassing the nHz
domain and the audio band. The salient theoretical aspects of the
relic gravitons are reviewed in a cross-disciplinary perspective
touching upon various unsettled questions of particle physics,
cosmology and astrophysics.

