Abstract: We analyse the f(R) gravity in the so-called Jordan frame, as implemented to the isotropic Universe dynamics. The goal of the present study is to show that according to recent data analyses of the supernovae Ia Pantheon sample, it is possible to account for an effective redshift dependence of the Hubble constant. This is achieved via the dynamics of a non-minimally coupled scalar field, as it emerges in the f(R) gravity. We face the question both from an analytical and purely numerical point of view, following the same technical paradigm. We arrive to establish that the expected decay of the Hubble constant with the redshift z is ensured by a form of the scalar field potential, which remains essentially constant for z less than or similar to 0.3, independently if this request is made a priori, as in the analytical approach, or obtained a posteriori, when the numerical procedure is addressed. Thus, we demonstrate that an f(R) dark energy model is able to account for an apparent variation of the Hubble constant due to the rescaling of the Einstein constant by the f(R) scalar mode.

Abstract: The framed standard model (FSM), constructed to explain the empirical mass and mixing patterns (including CP phases) of quarks and leptons, in which it has done quite well, gives otherwise the same result as the standard model (SM) in almost all areas in particle physics where the SM has been successfully applied, except for a few specified deviations such as the W mass and the g-2 of muons, that is, just where experiment is showing departures from what SM predicts. It predicts further the existence of a hidden sector of particles some of which may function as dark matter. In this paper, we first note that the above results involve, surprisingly, the FSM undergoing a vacuum transition (VTR1) at a scale of around 17MeV, where the vacuum expectation values of the colour framons (framed vectors promoted into fields) which are all nonzero above that scale acquire some vanishing components below it. This implies that the metric pertaining to these vanishing components would vanish also. Important consequences should then ensue, but these occur mostly in the unknown hidden sector where empirical confirmation is hard at present to come by, but they give small reflections in the standard sector, some of which may have already been seen. However, one notes that if, going off at a tangent, one imagines colour to be embedded, Kaluza-Klein (KK) fashion, into a higher-dimensional space-time, then this VTR1 would cause 2 of the compactified dimensions to collapse. This might mean then that when the universe cooled to the corresponding temperature of 1011 K when it was about 10-3 s old, this VTR1 collapse would cause the three spatial dimensions of the universe to expand to compensate. The resultant expansion is estimated, using FSM parameters previously determined from particle physics, to be capable, when extrapolated backwards in time, of bringing the present universe back inside the then horizon, solving thus formally the horizon problem. Besides, VTR1 being a global phenomenon in the FSM, it would switch on and off automatically and simultaneously over all space, thus requiring seemingly no additional strategy for a graceful exit. However, this scenario has not been checked for consistency with other properties of the universe and is to be taken thus not as a candidate solution of the horizon problem but only as an observation from particle physics which might be of interest to cosmologists and experts in the early universe. For particle physicists also, it might serve as an indicator for how relevant this VTR1 can be, even if the KK assumption is not made.

Abstract: We propose a minimal gauged U(1)(B-L) extension of the minimal supersymmetric Standard Model (MSSM) which resolves the cosmological moduli problem via thermal inflation, and realizes late-time Affleck-Dine leptogensis so as to generate the right amount of baryon asymmetry at the end of thermal inflation. The present relic density of dark matter can be explained by sneutrinos, MSSM neutralinos, axinos, or axions. Cosmic strings from U(1)(B-L) breaking are very thick, and so the expected stochastic gravitational wave background from cosmic string loops has a spectrum different from the one in the conventional Abelian-Higgs model, as would be distinguishable at least at LISA and DECIGO. The characteristic spectrum is due to a flat potential, and may be regarded as a hint of supersymmetry. Combined with the resolution of moduli problem, the expected signal of gravitational waves constrains the U(1)(B-L) breaking scale to be O(10(12-13)) GeV. Interestingly, our model provides a natural possibility for explaining the observed ultra-high-energy cosmic rays thanks to the fact that the core width of strings in our scenario is very large, allowing a large enhancement of particle emissions from the cusps of string loops. Condensation of LHu flat-direction inside of string cores arises inevitably and can also be the main source of the ultra-high-energy cosmic rays accompanied by ultra-high-energy lightest supersymmetric particles.

Abstract: We show that, when connected with monopoles, the flat D-flat direction breaking the local U(1)B-L symmetry as an extension of the minimal supersymmetric standard model can be responsible for the signal of a stochastic gravitational wave background recently reported by NANOGrav collaborations, while naturally satisfying constraints at high frequency band. Thanks to the flatness of the direction, a phase of thermal inflation arises naturally. The reheating temperature is quite low, and suppresses signals at frequencies higher than the characteristic frequency set by the reheating temperature. Notably, forthcoming spaced based experiments such as LISA can probe the cutoff frequency, providing an indirect clue of the scale of soft SUSY-breaking mass parameter.