# About the *Measure* of the Bare Cosmological Constant

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## Abstract

I try to revive, and possibly reconcile, a debate started a few years ago, about the relative roles of a bare cosmological constant and of a vacuum energy, by taking the attitude to try to get the most from the physics now available as established. I notice that the bare cosmological constant of the Einstein equations, which is there ever since GR emerged, is actually constrained (if not measured) *indirectly* combining the effective cosmological constant observed *now*, as given by ΛCDM Precision Cosmology, with the cumulative vacuum contribution of the particles of the Standard Model, SM. This comes out when the vacuum energy is regularized, as given by many Authors, still within well established Quantum Field Theory, QFT, but without violating Lorentz invariance. The fine tuning, implied by the compensation to a small positive value of the two large contributions, could be seen as offered by Nature, which provides one more fundamental constant, the bare Lambda. The possibility is then discussed of constraining (measuring) *directly* such a bare cosmological constant by the features of primordial gravitational wave signals coming from epoch’s precedent to the creation of particles. I comment on possibilities that would be lethal, that is if the vacuum does not gravitate. This last issue is often raised, and I discuss the current situation about. Finally a hint is briefly discussed for a possible “bare Lambda inflation” process.

## Keywords

Cosmological constant Relativistic aspects of cosmology Vacuum energy Primordial gravitational waves Inflation## Notes

### Acknowledgements

I am grateful to my wife Annamaria for bearing with me during the preparation of this paper and to Naresh Dadhich for correspondence on the matter. I thank Alessandro Bettini and Gianni Carugno for lively discussions. I am thankful to Philippe Jetzer for a discussion and for helpful suggestions. I am much indebted to Stefano Liberati for a critical reading of the manuscript, with comments I took in due consideration for the present version.

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