Search Results (41)

The derivations presented in this paper suggest an intimate relationship between geometry and the electroweak sector at the Planck scale. A Lorentz-invariant maximally symmetric stochastically perturbed spacetime transformed to spherical coordinates reveals an emergent Schwarzschild metric, entirely a statistical structure of stochastic spacetime. Similarly, the transition from a maximally symmetric universe with a complex $SU\left(2\right)$ scalar doublet $\varphi$, comprising four independent real scalar fields with a zero vacuum expectation value (VEV), to spherical coordinates at the Planck scale reveals the spontaneously broken electroweak (EW) sector. Working in the unitarity gauge, the resulting EW potential can be simultaneously mapped in space at the Planck scale and across the EW sector. In space, the resulting EW potential includes a deep well within the Schwarzschild sphere and a shallow well just outside corresponding to an accretion disk. The same potential mapped in the EW space provides an entire family of possible sombrero hat potentials with fourth-order coupling specific to a point in space. At the minimum points of the potential in space, inside the Schwarzschild sphere and at the accretion disk, the $\lambda$ corresponding to the Standard Model (SM) fourth-order coupling is instead derived as $\frac{\lambda }{5}$. The factor of $\frac{1}{5}$ is a simple consequence of the conservation of the EW VEV and the fact that the SM formulation of the EW potential does not account for situations where the perturbations in $\varphi$ dominate. A more general formulation of the EW potential restores the SM quartic coupling and preserves $\lambda$ in space. An emergent Higgs field inside the Schwarzschild black hole is found to directly relate to the stochastic spacetime fields normalized by the Schwarzschild radius. The corresponding Higgs vacuum has both a ground and excited state and the possibility of both positive and negative vacuum entropy. Finally, the scalar-field VEV degeneracy in EW space of the metastable Higgs vacuum appears instead differentiated in space with possible probability, tunneling, and entropy implications. Full article

The possibility of realizing Higgs inflation in a model with a small non-minimal coupling constant, which was demonstrated recently, provides grounds for further development of the model. Incorporating the electroweak SM into the Two-Measure theory (TMT) in a way that fully accounts for the TMT structure leads to a theory we call the Two-Measure Standard Model (TMSM). The TMSM is realized in the context of cosmology as a set of cosmologically modified copies of the Glashow–Weinberg–Salam (GWS) theory, such that each of the copies exists as a local quantum field theory defined on the classical cosmological background at the appropriate stage of its evolution. This basic idea is studied in detail for two stages of the cosmological background evolution: for slow-roll inflation and for the stage of approaching the vacuum. Mainly due to the presence of the ratio of two volume measures in all equations of motion, all TMSM coupling constants turn into a kind of “running” (classical) TMT-effective parameters. During the evolution of the cosmological background, changing these parameters yields new results: (1) the classical “running” TMT-effective Higgs self-coupling parameter increases from $\lambda \sim {10}^{-11}$ (which provides Higgs inflation consistent with the Planck CMB data at $\xi ={\displaystyle \frac{1}{6}}$) to $\lambda \sim 0.1$ at the stage close to the vacuum; (2) the mass term in the TMT-effective Higgs potential changes sign from positive to negative, which provides SSB in the standard way of GWS theory; (3) the classical “running” parameters of the gauge and Yukawa couplings change by several orders of magnitude; (4) the GWS theory is reproduced when the Yukawa constant in the original action is chosen to be universal for three generations of fermions. We show that, due to these classical-level results, taking into account quantum corrections in the one-loop approximation preserves the slow-roll inflation regime and does not violate the vacuum stability during inflation. Full article

The microscopic origin of the de Sitter entropy remains a central puzzle in quantum gravity that is related to the cosmological constant problem. Within the paradigm of $\mathcal{H}$olographic $\mathcal{N}$aturalness, we propose that this entropy is carried by a vast number of light, coherent degrees of freedom—called “hairons”—which emerge as the moduli of gravitational instantons on orbifolds. Starting from the Euclidean de Sitter instanton ($S^4$), we construct a new class of orbifold gravitational instantons, $S^4/{\mathbb{Z}}_N$, where N corresponds to the de Sitter entropy. We demonstrate that the dimension of the moduli space of these instantons scales linearly with N, and we identify these moduli with the hairon fields. A ${\mathbb{Z}}_N$ symmetry, derived from Wilson loops in the instanton background, ensures the distinguishability of these modes, leading to the correct entropy count. The hairons acquire a mass of the order of the Hubble scale and exhibit negligible mutual interactions, suggesting that the de Sitter vacuum is a coherent state, or Bose–Einstein condensate, of these fundamental excitations. Then, we present a novel framework which unifies neutrino mass generation with the cosmological constant through gravitational topology and holography. The small neutrino mass scale emerges naturally from first principles, without requiring new physics beyond the Standard Model and Gravity. The gravitational Chern–Simons structure and its anomaly with neutrinos force a topological Higgs mechanism, leading to neutrino condensation via $S^4/{\mathbb{Z}}_N$ gravitational instantons. The number of topological degrees of freedom $N\sim M_{\mathrm{P}}^2/\mathrm{\Lambda }\sim {10}^{120}$ provides both the holographic counting of the de Sitter entropy and a $1/N$information see-saw mechanism for neutrino masses. Our framework makes the following predictions: (i) a neutrino superfluid condensation forming Cooper pairs below meV energies, as a viable candidate for cold dark matter; (ii) a possible resolution of the strong CP problem through a QCD composite axion state; (iii) time-varying neutrino masses which track the evolution of dark energy; and (iv) several distinctive signatures in astroparticle physics, ultra-high-energy cosmic rays and high magnetic field experiments. Full article

The cosmological constant (CC, $\Lambda$) problem stands as one of the most profound puzzles in the theory of gravity, representing a remarkable discrepancy of about 120 orders of magnitude between the observed value of dark energy and its natural expectation from quantum field theory. This paper synthesizes two innovative paradigms—holographic naturalness (HN) and pre-geometric gravity (PGG)—to propose a unified and natural resolution to the problem. The HN framework posits that the stability of the CC is not a matter of radiative corrections but rather of quantum information and entropy. The large entropy $S_{\mathrm{dS}}\sim M_{\mathrm{P}}^2/\Lambda$ of the de Sitter (dS) vacuum (with $M_{\mathrm{P}}$ being the Planck mass) acts as an entropic barrier, exponentially suppressing any quantum transitions that would otherwise destabilize the vacuum. This explains why the universe remains in a state with high entropy and relatively low CC. We then embed this principle within a pre-geometric theory of gravity, where the spacetime geometry and the Einstein–Hilbert action are not fundamental, but emerge dynamically from the spontaneous symmetry breaking of a larger gauge group, SO($1,4$)→SO($1,3$), driven by a Higgs-like field ${\varphi }^A$. In this mechanism, both $M_{\mathrm{P}}$ and $\Lambda$ are generated from more fundamental parameters. Crucially, we establish a direct correspondence between the vacuum expectation value (VEV) v of the pre-geometric Higgs field and the de Sitter entropy: $S_{\mathrm{dS}}\sim v$ (or $v^3$). Thus, the field responsible for generating spacetime itself also encodes its information content. The smallness of $\Lambda$ is therefore a direct consequence of the largeness of the entropy $S_{\mathrm{dS}}$, which is itself a manifestation of a large Higgs VEV v. The CC is stable for the same reason a large-entropy state is stable: the decay of such state is exponentially suppressed. Our study shows that new semi-classical quantum gravity effects dynamically generate particles we call “hairons”, whose mass is tied to the CC. These particles interact with Standard Model matter and can form a cold condensate. The instability of the dS space, driven by the time evolution of a quantum condensate, points at a dynamical origin for dark energy. This paper provides a comprehensive framework where the emergence of geometry, the hierarchy of scales and the quantum-information structure of spacetime are inextricably linked, thereby providing a novel and compelling path toward solving the CC problem. Full article

In the immediate aftermath of the Big Bang, the universe existed in an extremely hot, dense state in which particle interactions occurred not in vacuum but within a thermal medium. Under such conditions, the standard framework of quantum field theory (QFT) requires a finite-temperature extension, wherein propagators—and hence the fundamental structure of the theory—are modified to reflect thermal background effects. These thermal modifications are central to understanding the nature of electroweak symmetry breaking (EWSB) as a high-temperature phase transition, potentially leading to qualitatively different vacuum structures for the Higgs field as the universe cooled. Finite-temperature corrections naturally regulate ultraviolet divergences in propagators, hinting at a possible route toward ultraviolet completion. However, these same thermal effects exacerbate infrared pathologies and can lead to imaginary contributions to the effective potential, particularly when analyzing metastable or multi-vacuum configurations. Additional theoretical challenges, such as gauge dependence and renormalization scale ambiguity, further obscure the precise characterization of the electroweak phase transition—even in minimal extensions of the Standard Model (SM). This review presents the theoretical foundations of finite-temperature QFT with an emphasis on how different field species respond to thermal effects, identifying the bosonic sector as the primary source of key theoretical subtleties. We focus particularly on the scalar extension of the SM, which offers a compelling framework for realizing first-order electroweak phase transitions, electroweak baryogenesis, and accommodating dark matter candidates depending on the underlying ${\mathbb{Z}}_2$ symmetry structure. Full article

Thermal inflation was proposed as a mechanism to dilute the density of cosmological moduli. Thermal inflation is driven by a complex scalar field possessing a large vacuum expectation value and a very flat potential, called a “flaton”. Such a model admits cosmic string solutions, and a network of such strings will inevitably form in the symmetry breaking phase transition at the end of the period of thermal inflation. We discuss the differences of these strings compared to the strings which form in the Abelian Higgs model. Specifically, we find that the upper bound on the symmetry breaking scale is parametrically lower than in the case of Abelian Higgs strings, and that the lower cutoff on the string loop distribution is determined by cusp annihilation rather than by gravitational radiation (for the value of the transition temperature proposed in the original work on thermal inflation). Full article

A model of a physical vacuum defined by a Gross–Pitaevskij equation and characterized by dissipative features close to the Planck scale is proposed, which provides an emergent explanation of scales, hierarchies and Higgs mass generation of the Standard Model. A fundamental nonlocal and nonlinear texture of the vacuum is introduced in terms of planckeons, sub-Planckian objects defined by a generalized Compton wavelength, which lead to find Planckian signatures of the Standard Model. Full article

I consider the electro-weak (EW) masses and interactions generated by photons using vacuum expectation values of Stueckelberg and Higgs fields. I provide a prescription to relate their parametric values to a cosmological range derived from the fundamental Heisenberg uncertainty principle and the Einstein–de Sitter cosmological constant and horizon. This yields qualitative connections between microscopic ranges acquired by $W^{\pm }$ or $Z^0$ gauge Bosons and the cosmological scale and minimal mass acquired by g-photons. I apply this procedure to an established Stueckelberg–Higgs mechanism, while I consider a similar procedure for a pair of Higgs fields that may spontaneously break all U(1) × SU(2) gauge invariances. My estimates of photon masses and their additional parity-breaking interactions with leptons and neutrinos may be detectable in suitable accelerator experiments. Their effects may also be observable astronomically through massive g-photon condensates that may contribute to dark matter and dark energy. Full article

Higher derivative terms in the gravitational action are natural from the perspective of quantum gravity, but are perceived as leading to a lack of well-posedness. The Gauss–Bonnet term has second-order equations of motion, but does not impact gravitational dynamics in 4D, so one might expect that it is not physically relevant. We discuss how signatures can show up in tunnelling processes and whether these will likely be physically accessible in Higgs vacuum decay. Full article

The commonly quoted bistable Higgs potential is not a proper description of the Higgs field because, among other technical reasons, one of its stable states acquires a negative expectation value in vacuum. We rely on formal catastrophe theory to derive the form of the Higgs potential that admits only one positive mean value in vacuum. No symmetry is broken during the ensuing phase transition that assigns mass to the Higgs field; only gauge redundancy is “broken” by the appearance of phase in the massive state, but this redundancy is not a true symmetry of the massless field. Furthermore, a secondary, certainly amusing conclusion, is that, in its high-energy state, the field oscillates about its potential minimum between positive and negative masses, but it is doubtful that such evanescent states can survive below the critical temperature of $159.5$ GeV, where the known particles were actually created. Full article

Natural systems of units $\left\{U_i\right\}$ need to be overhauled to include the dimensionless coupling constants $\left\{{\mathsf{\alpha }}_{U_i}\right\}$ of the natural forces. Otherwise, they cannot quantify all the forces of nature in a unified manner. Thus, each force must furnish a system of units with at least one dimensional and one dimensionless constant. We revisit three natural systems of units (atomic, cosmological, and Planck). The Planck system is easier to rectify, and we do so in this work. The atomic system discounts $\{G,{\mathsf{\alpha }}_G\}$, thus it cannot account for gravitation. The cosmological system discounts $\{\cancel{h},{\mathsf{\alpha }}_{\cancel{h}}\}$, thus it cannot account for quantum physics. Here, the symbols have their usual meanings; in particular, ${\mathsf{\alpha }}_G$ is the gravitational coupling constant and ${\mathsf{\alpha }}_{\cancel{h}}$ is Dirac’s fine-structure constant. The speed of light c and the impedance of free space $Z_0$ are resistive properties imposed by the vacuum itself; thus, they must be present in all systems of units. The upgraded Planck system with fundamental units $\mathrm{UPS}:=\{c,Z_0,G,{\mathsf{\alpha }}_G,\cancel{h},{\mathsf{\alpha }}_{\cancel{h}},\dots \}$ describes all physical scales in the universe—it is nature’s system of units. As such, it reveals a number of properties, most of which have been encountered previously in seemingly disjoint parts of physics and some of which have been designated as mere coincidences. Based on the UPS results, which relate (sub)atomic scales to the Planck scale and the fine-structure constant to the Higgs field, we can state with confidence that no observed or measured physical properties are coincidental in this universe. Furthermore, we derive from first principles Koide’s $K=2/3$ enigmatic constant and additional analogous quark and vector boson constants. These are formal mathematical proofs that justify a posteriori the use of geometric means in deriving the quark/boson mass ladder. This ladder allows us to also calculate the Higgs couplings to the vector bosons and the Weinberg angle in terms of K only, and many of the “free” parameters of the Standard Model of particle physics were previously expected to be determined only from experiments. Full article

A new approach to the Dirac equation and the associated hadronic symmetries is proposed. In this approach, we linearize the second Casimir operator of the Lorentz Group, which is defined by the energy–momentum four-vector and the fermion spin, thereby using the spinor-helicity representation instead of the three-vector representation of the particle momentum and spin vector. We then expand the so-obtained standard Dirac equation by employing an inner abstract “hadronic” isospin, initially describing a $SU\left(2\right)$ fermion doublet. Application of the spin-helicity representation of that isospin leads to the occurrence of a quadruplet of inner states, revealing the $SU\left(4\right)$ symmetry via the isospin helicity operator. This further leads to two independent fermion state spaces, specifically, singlet and triplet states, which we interpret as $U\left(1\right)$ symmetry of the leptons and $SU\left(3\right)$ symmetry of the three quarks, respectively. These results indicate the genuinely very different physical nature of the strong $SU\left(4\right)$ symmetry in comparison to the chiral $SU\left(2\right)$ symmetry. While our approach does not require the a priori concept of grand unification, such a notion arises naturally from the formulation with the isospin helicity. We then apply the powerful procedures developed for the electroweak interactions in the SM, in order to break the $SU\left(4\right)$ symmetry by means of the Higgs mechanism involving a scalar Higgs field as an $SU\left(4\right)$ quadruplet. Its finite vacuum creates the masses of the three vector bosons involved, which can change the three quarks into a lepton and vice versa. Finally, we consider a toy model for calculation of the strong coupling constant of a Yukawa potential. Full article

We conjecture that the Higgs potential can be significantly modified when it is in close proximity to the horizon of an astrophysical black hole, leading to the destabilization of the electroweak vacuum. In this situation, the black hole should be encompassed by a shell consisting of a “bowling substance” of the nucleating new-phase bubbles. In a binary black-hole merger, just before the coalescence, the nucleated bubbles can be prevented from falling under their seeding horizons, as they are simultaneously attracted by the gravitational potential of the companion. For a short time, the unstable vacuum will be “sandwiched” between two horizons of the binary black hole, and therefore the bubbles may collide and form micro-black holes, which are rapidly evaporated by thermal emission of Hawking radiation of all Standard Model species. This evaporation, being triggered by a gravitational wave signal from the binary black-hole merger, can manifest itself in observations of gamma rays and very-high-energy neutrinos, which makes it a perfect physics case for multi-messenger astronomical observations. Full article

The violation of charge-parity symmetry and the baryon asymmetry of the universe are two of the most significant unresolved problems in physics. This article presents further research on the CP violation problem in the Standard Model with 32 candidate sets of the 10 “natural” parameters that exhibit the same Cabibbo–Kobayashi–Maskawa performance. These parameters are considered “natural” because they consist solely of the Yukawa couplings and the vacuum expectation value of the unique Higgs doublet in the Standard Model. Then, the problems of CP violation and the baryon asymmetry of the universe are investigated by using the Jarlskog measure of CP violation, ${\Delta }_{CP}=J(m_t^2-m_c^2)(m_t^2-m_u^2)(m_c^2-m_u^2)(m_b^2-m_s^2)(m_b^2-m_d^2)(m_s^2-m_d^2)/T^{12}$, given that CP symmetry is violated following the breakdown of $S_N$ symmetries. Subsequently, numerical tests are performed in a simplified scenario where eight of the ten parameters are assumed to be fixed by two assumptions, and the remaining two parameters are allowed to vary from the $S_2$-symmetric point $(\mathbf{x},\mathbf{y})=(-1,1)$ to their current values in all 32 parameter sets. To estimate the enhancement of CP violation in such processes, a ratio $R_{\Delta }\equiv {\Delta }_{CP}/{\Delta }_{CP}^{\left(0\right)}$ is proposed between the running ${\Delta }_{CP}$ and its current value, denoted by ${\Delta }_{CP}^{\left(0\right)}$, which is approximately ${10}^{-20}$. In all 32 cases, the three-dimensional plots of $R_{\Delta }$ exhibit many regions that stick out of the $R_{\Delta }={10}^{10}$ plane, especially in regions very close to $(\mathbf{x},\mathbf{y})=(-1,1)$. These results demonstrate that the $S_N$-breaking Standard Model is already sufficient to violate CP symmetry explicitly and generate a significant amount of baryon asymmetry of the universe. Furthermore, it solves existing problems without creating new ones, at least in the scenario presented in this article. Full article

This paper surveys recent progress in our search for an appropriate internal space algebra for the standard model (SM) of particle physics. After a brief review of the existing approaches, we start with the Clifford algebras involving operators of left multiplication by octonions. A central role is played by a distinguished complex structure that implements the splitting of the octonions $\mathbb{O}=\mathbb{C}\oplus {\mathbb{C}}^3$, which reflect the lepton-quark symmetry. Such a complex structure on the 32-dimensional space $\mathcal{S}$ of $C{\ell }_{10}$ Majorana spinors is generated by the $C{\ell }_6(\subset C{\ell }_{10})$ volume form, ${\omega }_6={\gamma }_1\cdots {\gamma }_6$, and is left invariant by the Pati–Salam subgroup of $Spin\left(10\right)$, $G_{\mathrm{PS}}=Spin\left(4\right)\times Spin\left(6\right)/{\mathbb{Z}}_2$. While the $Spin\left(10\right)$ invariant volume form ${\omega }_{10}={\gamma }_1\dots {\gamma }_{10}$ of $C{\ell }_{10}$ is known to split $\mathcal{S}$ on a complex basis into left and right chiral (semi)spinors, $\mathcal{P}=\frac{1}{2}(1-i{\omega }_6)$ is interpreted as the projector on the 16-dimensional particle subspace (which annihilates the antiparticles).The standard model gauge group appears as the subgroup of $G_{\mathrm{PS}}$ that preserves the sterile neutrino (which is identified with the Fock vacuum). The ${\mathbb{Z}}_2$-graded internal space algebra $\mathcal{A}$ is then included in the projected tensor product $\mathcal{A}\subset \mathcal{P}C{\ell }_{10}\mathcal{P}=C{\ell }_4\otimes C{\ell }_6^0$. The Higgs field appears as the scalar term of a superconnection, an element of the odd part $C{\ell }_4^1$ of the first factor. The fact that the projection of $C{\ell }_{10}$ only involves the even part $C{\ell }_6^0$ of the second factor guarantees that the color symmetry remains unbroken. As an application, we express the ratio $\frac{m_H}{m_W}$ of the Higgs to the W boson masses in terms of the cosine of the theoretical Weinberg angle. Full article