A new framework for cosmological expansion in a reformulated Newtonian-Like gravity with variable G

Matter fields during the very early Universe are described by GUT models in curved spacetime. At high energies these fields are asymptotically free and conformally coupled to the external metric. The only possible quantum effect is the appearance of the conformal anomaly, which leads to the propagation of the new degree of freedom, the conformal factor. Simultaneously with the expansion of the Universe, the scale of energies decreases and the propagating conformal factor starts to interact with the Higgs field due to the violation of conformal invariance in the matter fields sector. In a previous paper we have shown that this interaction can lead to special physical effects like renormalization group flow, which ends at some fixed point. Furthermore, in the vicinity of this fixed point the first-order phase transition may occur. In the present paper we consider the same theory of the conformal factor coupled to the Higgs field and incorporate the temperature effects. We reduce the complicated higher-derivative operator to several of standard second-derivative form and calculate an exact effective potential with temperature on the anti-de Sitter (AdS) background. The physical analysis of the effective potential is performed within the framework of the high-temperature expansion.

High resolution and wide field of view (FOV) are always the goals of imaging, which are related to the space-bandwidth product (SBP) of the system. Currently, most methods focus on either resolution enhancement or FOV extension. Few works pay attention on both. There lacks a generalized framework for the joint space-frequency SBP expansion. We propose such a holographic imaging method, termed phase-space synthesized digital holography (PSH), which can improve and adjust resolution and FOV simultaneously, based on a phase-space analysis. Through a controllable SBP expansion in the phase space by multiangle divergent spherical wave illumination, a synthesized hologram is obtained to reconstruct a resolution-enhanced and FOV-extended image. As a general methodology of SBP expansion, the proposed method could open new insights for the imaging community.

The spherical Berlin-Katz model is considered in the framework of the epsilon expansion in one-dimensional and two-dimensional space. For the two-dimensional and threedimensional cases in this model, an exact solution was previously obtained in the presence of a field, and for the two-dimensional case the critical temperature is zero, that is, a “quantum” phase transition is observed. On the other hand, the epsilon expansion of critical exponents with an arbitrary number of order parameter components is known. This approach is consistent with the scaling paradigm. Some critical exponents are found for the spherical model in one-and twodimensional space in accordance with the generalized scaling paradigm and the ideas of quantum phase transitions. A new formula is proposed for the critical heat capacity exponent, which depends on the dynamic index z, at a critical temperature equal to zero. An expression is proposed for the order of phase transition with a change in temperature (developing the approach of R. Baxter), which also depends on the z index. An interpolation formula is presented for the effective dimension of space, which is valid for both a positive critical temperature and a critical temperature equal to zero. This formula is general. Transitions with a change in the field in a spherical model at absolute zero are also considered.

This chapter explores the intricate connections between number theory and theoretical physics, particularly through the lens of integer partitions and black-hole entropy, as articulated by Michele Nardelli in his recent papers. By constructing a bridge between Ramanujan's partition theory and the microstates of black holes, Nardelli demonstrates that the black-hole partition function can be expressed in terms of integer partitions proportional to horizon area, thereby recovering the Bekenstein–Hawking entropy and incorporating logarithmic corrections that account for quantum effects. He introduces the Ramanujan tau function as an algebraic character for emergent symmetries in near-extremal black holes, leading to a weighted partition function that unifies classical and quantum contributions to entropy. Nardelli's aesthetic approach to cosmological modeling, derived from modular arithmetic, offers a compelling framework for understanding cosmic expansion without extraneous parameters, aligning with historical perspectives on beauty in physics and yielding testable predict.

It is well known that time delays due to strong lensing offer the opportunity of a one-step measurement of the Hubble constant H 0 that is independent of the cosmic distance ladder. In this paper, we go further and propose a cosmological model-independent approach to simultaneously determine the Hubble constant and cosmic curvature with measurements of the time delay due to strong lensing, without any prior assumptions regarding the content of the universe. The data we use comprise the recent compilation of six well studied strongly lensed quasars, while the cosmic chronometer data are utilized to reconstruct distances via cosmographic parameters. In the framework of third-order Taylor expansion and (2, 1) order Padé approximation for cosmographic analysis, our results provide model-independent estimations of the Hubble constant and , which are well consistent with that derived from the local distance ladder by the SH0ES collaboration. The measured cosmic curvature and shows that zero spatial curvature is supported by the current observations of time delays due to strong lensing and cosmic chronometers. Imposing the prior of spatial flatness leads to more precise (at 1.6% level) determinations of the Hubble constant and , values located between the results from Planck and the SH0ES collaboration. If a prior of local (SH0ES) H 0 measurement is adopted, the constraint on curvature parameter can be further improved to and , supporting no significant deviation from a flat universe. Finally, we also discuss the effectiveness of the Padé approximation in reconstructing the cosmic expansion history for redshifts up to z ∼ 2.3, considering its better performance in the Bayes information criterion.

A query expansion framework in image retrieval domain based on local and global analysis