The Heisenberg limit at cosmological scales

Abstract

For an observation time equal to the universe age, the Heisenberg principle fixes the value of the smallest measurable mass at mH = 1.35 × 10 −69 kg and prevents to probe the masslessness for any particle using a balance. The corresponding reduced Compton length to mH is λH, and represents the length limit beyond which masslessness cannot be proved using a metre ruler. In turns, λH is equated to the luminosity distance dH which corresponds to a red shift zH. When using the Concordance-Model parameters, we get dH = 8.4 Gpc and zH = 1.3. Remarkably, dH falls quite short to the radius of the observable universe. According to this result, tensions in cosmological parameters could be nothing else but due to comparing data inside and beyond zH. Finally, in terms of quantum quantities, the expansion constant H0 reveals to be one order of magnitude above the smallest measurable energy, divided by the Planck constant.

Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies

“…In this subsection, we list some specific solutions of interest to the community that cannot be classified in the previous sections, whether because they are broad enough to enclose very different scenarios, or they simply have an impact along the whole cosmic history. We refer the reader to the more complete review [48] or the original papers for a more detailed discussion of proposed solutions of the Hubble tension in: inflationary models [1058][1059][1060][1061], self-interacting dark matter [1062], Über-gravity [1063], Nonlocal gravity [1064], Modified Gravity [927,1065], unified fluid [1066], quintessential models [1067], screened fifth forces [1068], Generalized Chaplygin gas models [1069][1070][1071][1072], Viscous Generalized Chaplygin gas [1073], addition of extra SNIa systematic uncertainties with a varying DE [1074], metastable DE [1075][1076][1077], Super-ΛCDM [1078,1079], DM-photon coupling [1080], Local Inhomogeneity [1081], Interaction in the anisotropic Universe [1082], Heisenberg uncertainty [1083,1084], Enhanced Early gravity model [97,1085], CMB monopole temperature [601], Decaying Ultralight Scalar [1086], Decaying coupled fermions [1087], Early mass varying neutrino DE [1088], Neutrino-majoron interactions [1089][1090]…”

Test of the Ampère-Maxwell law on the photon mass and Lorentz-Poincaré symmetry violation with MMS multi-spacecraft data

“…We consider all explorations below 10 −51 kg being worth of a scrupulous analysis. The lowest value for any mass is dictated by Heisenberg's principle m ≥ /∆tc 2 , and gives 1.3 × 10 −69 kg, where ∆t is the supposed age of the Universe [36,37].…”

Investigating dark energy by electromagnetic frequency shifts

“…( 16) to SN Ia data, the factor (1 + z) refers to the heliocentric red shift, that is the apparent red shift affected by the relative motion of the Sun, and not to the red shift observed in a cosmological rest frame [96], Instead, the latter appears in the integrals of Eqs. (17,18). Both these quantities are provided by the Pantheon catalogue.…”

“…The difficulty of finding out new fundamental particles has led to extend General Relativity (GR) at infrared scales as possible solution of the puzzle [16]. In particular, the issue of the Hubble tension could be a manifestation of the GR inadequacy to represent the whole cosmic history involving also the possibility to consider a sort of Heisenberg principle working at cosmological scales [17,18]. The preceding is accompanied by the difficulty of applying GR at the microscopic scale, the suspicion of deviations from GR in the strong field regime, and the 120 orders of magnitude surplus that vacuum energy possesses with respect to the dark energy fluid [19].…”