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Self-similarity, where observables at different length scales exhibit similar behavior, is ubiquitous in natural systems. Such systems are typically characterized by power-law correlations and universality, and are studied using the…
The point-particle approximation is foundational to modelling clustering of matter in the universe, but is fundamentally inconsistent within General Relativity due to associated spacetime singularities. This bottleneck has historically…
Dense relativistic matter has attracted a lot of attention over many decades now, with a focus on an understanding of the phase structure and thermodynamics of dense strong-interaction matter. The analysis of dense strong-interaction matter…
\noindent{\large\bf Abstract.} We develop a general formalism to study the renormalization group (RG) improved effective potential for renormalizable gauge theories ---including matter-$R^2$-gravity--- in curved spacetime. The result is…
Many cosmological observations call for the existence of dark matter. The most direct evidence for dark matter is inferred from the measured flatness of galactic rotation curves. The latter is based on Newtonian gravity. Alternative…
We formulate a renormalization group (RG) for the interaction parameters of the general two-body problem and show how a limit cycle emerges in the RG flow if the interaction approaches an inverse square law. This limit cycle generates a…
In this work, we investigate the possibility that the galaxy rotation curves can be explained in the framework of modified gravity models that introduce a Yukawa term in the gravitational potential. We include dark matter and assume that…
The detection of gravitational waves has intensified the need for efficient, high-precision modeling of the two-body problem in General Relativity. Current analytical methods, primarily the Post-Minkowskian and Post-Newtonian expansions,…
Dark sector mass relations, such as those which permit near-threshold or near-resonance annihilation in the early universe, could arise due to IR-attractive ratios in renormalization group equations. Achieving a particular ratio requires…
The renormalization-group improved effective potential ---to leading-log and in the linear curvature approximation--- is constructed for ``finite'' theories in curved spacetime. It is not trivial and displays a quite interesting,…
We apply the modified acceleration law obtained from Einstein gravity coupled explaining galaxy rotation curves without exotic dark matter. Our sample of galaxies includes low surface brightness (LSB) and high surface brightness (HSB)…
For a generic quantum field theory we study the role played by the renormalization-group (RG) running of the cosmological constant (CC) in determining the ultimate fate of the universe. We consider the running of the CC of generic origin…
Conformal gravity theory can explain observed flat rotation curves of galaxies without invoking hypothetical dark matter. Within this theory, we obtain a generic formula for the sizes of galaxies exploiting the stability criterion of…
Quantum gravity effects are traditionally tied to short distances and high energies. In this essay we argue that, perhaps surprisingly, quantum gravity may have important consequences for the phenomenology of the infrared. We center our…
It is well known that the renormalization group equations depend on the scale where they are applied. This phenomenon is especially relevant for the massive fields in curved space, because the decoupling effects may be responsible for…
We discuss the effect of wave function renormalization (WFR) in asymptotically safe gravity. We show that there are two WFR-invariant quantities, and the renormalization (RG) equations may be written entirely in terms of these quantities.…
It is a well known fact that, in the absence of Dark Matter, the observation of the rotation curves of galaxies cannot be explained in terms of Newtonian gravity. Rotation curves become flat in the outer regions, in contrast to what is…
Recently a new -quantum motivated- theory of gravity has been proposed that modifies the standard Newtonian potential at large distances when spherical symmetry is considered. Accordingly, Newtonian gravity is altered by adding an extra…
The dark matter accretion theory (around a central body) of the author on the basis of his 5-dimensional Projective Unified Field Theory (PUFT) is applied to the orbital motion of stars around the center of the Galaxy. The departure of the…
Wilson's Numerical Renormalization Group (NRG) is so far the only nonperturbative technique that can reliably access low-energy properties of quantum impurity systems. We present a recent extension of the method, the DM-NRG, which yields…