arXiv subjects

Rinku Maji

Publications and source records attributed to Rinku Maji.

At least 19 recordsLinked to original sources

arXiv2026

Monopoles, Strings, Walls and Gravitational waves

The gauge symmetry breaking $SU(2) \to U(1) \to Z_2 \to 1$ successively produces monopoles, strings and domain walls bounded by strings (WBS), with the elementary monopole carrying a $U(1)$ magnetic flux twice as large as the elementary string. The elementary strings and subsequently WBS emit gravitational waves, and during their decay, the WBS yield a network of composite strings that carry the same $U(1)$ flux as the monopoles. Depending on the cosmological evolution, we provide the gravitational wave spectra generated by the elementary strings and WBS, in combination with the composite strings which are either effectively stable, quasistable, or metastable. These three scenarios are also realized in the symmetry breaking chain $SU(3) \to SO(3) \to Z_2 \to 1$. Both $SU(2)$ and $SU(3)$ have appeared in the literature as flavor gauge symmetries.

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arXiv2026

Cogenesis of baryon and lepton number asymmetries matching the EMPRESS Data

We show that a simple supersymmetric $U(1)_{B-L}$ extension of the standard model can explain simultaneously the large electron neutrino asymmetry hinted by the recent EMPRESS data as well as the observed tiny baryon asymmetry via the resonant leptogenesis mechanism. The condensation of $B-L$ Higgs dominating the universe at its decay is the sole source for these generation processes. Here, the infrequent decays of the $B-L$ Higgs to heavy right-handed neutrinos and successive prompt decays of these right-handed neutrinos around the electroweak phase transition produce the observed baryon asymmetry while the complete decay of the same $B-L$ Higgs at a later epoch leads to a large lepton number asymmetry. The right amounts of both asymmetries are found to be obtained for the symmetry breaking scale $v_ϕ\sim 10^{10}~{\rm GeV}$. Moreover, in a close connection to the positivity of both asymmetries, seemingly only the normal mass hierarchy of light neutrino species works. Finally, the gravitational wave background from the topologically stable strong type-I cosmic strings, generated from the breaking of $U(1)_{B-L}$ symmetry, can be within the reach of future experiments such as ultimate DECIGO.

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arXiv2026

Magnetic monopoles and high frequency gravitational waves from quasi-stable strings

The spontaneous breaking of $SO(10)$ via flipped $SU(5)$ to the Standard Model yields a novel scenario in which the superheavy topologically stable GUT monopole carrying a single unit ($2π/e$) of Dirac magnetic charge emerges from the merger of a confined but topologically distinct monopole-antimonopole pair that are pulled together by a string. The $SO(10)$ breaking via the subgroup $SU(4)_c\times SU(2)_L\times SU(2)_R$, following a similar reasoning, produces a topologically stable monopole that carries two units ($4π/e$) of Dirac charge. We explore the cosmological consequences of this scenario by assuming that the monopoles and strings experience a limited number of inflationary $e$-foldings, before re-entering the horizon and ultimately forming a network of quasi-stable strings bounded by monopole-antimonopole pairs. We identify regions of the parameter space that yield an observable number density of the GUT monopole from the collapse of the appropriate string segments. The gravitational waves emitted by these quasi-stable cosmic strings lie in the Hz to kHz range, which can be tested in a number of proposed and ongoing experiments.

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arXiv2025

The E6 route to multicomponent dark matter

We present a framework of dark- and visible-sector unification in the E6 embedding of the standard model. The demand for consistently getting the standard model leads to the existence of the dark-sector. We show that the hierarchy of vevs typifying unified models leads to multicomponent dark matter at the IR. The symmetry breaking itself categorises the matter content into dark- and visible-sector particles, the categorisation being uniform across different breaking chains. We discuss the stability of the dark matter particles and compare them to existing phenomenological models of dark matter. The central results follow from symmetry and hierarchy arguments. We present an indicative set of models of gauge coupling unification, to show that the framework can be embedded in realistic models of E6.

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arXiv2025

Superconducting Strings in $E_6$

We discuss the appearance of superconducting strings in $E_6$ grand unification, keeping track of the magnetic monopole flux that precedes the formation of the string flux tube. This flux matching ensures compatibility with the quantum tunneling of a monopole-antimonopole pair on a metastable string. We identify two realistic $E_6$ models with superconducting (metastable) strings that also carry zero modes of the right handed Majorana neutrinos and dark matter particles. Depending on the symmetry breaking scale associated with the strings, the latter could be a source of observable gravitational waves, intermediate scale dark matter, and the observed baryon asymmetry via leptogenesis. Topologically stable superconducting strings also appear if the $E_6$ symmetry breaking leaves unbroken the $Z_2$ subgroup of $Z_4$, the center of $SO(10)$. The zero modes of the SM fermions are the charge carriers in this case. Finally, the flux matching condition ensures that the Aharanov-Bohm phase change in going around the metastable strings is an integer multiple of $2 π$ for all fields. The fields in the spinorial representation of SO(10) acquire a phase change of $\exp(\pm iπ)$ if taken around the topologically stable $Z_2$ string.

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arXiv2025

Superheavy Metastable Strings in SO(10)

The spontaneous breaking of $SO(10)$ grand unified symmetry to $SU(3)_c \times SU(2)_L \times U(1)_Y \times U(1)_χ$ yields the GUT monopole as well as a comparably heavy $U(1)_χ$ monopole which also carries $U(1)_Y$ flux. A metastable string scenario in this case requires that the $U(1)_χ$ symmetry is necessarily broken close to the GUT scale, thus resulting in a dimensionless string tension $G μ\sim 10^{-6}$. We show that the $χ$ monopole does not carry any unconfined flux following the electroweak symmetry breaking. Coupled with $G μ\sim 10^{-6}$, this metastable string network appears to provide a good fit to the recent Pulsar Timing Array data on the stochastic gravitational background. Gauge coupling unification, especially in the presence of low scale supersymmetry, determines the GUT scale and, in combination with constraints from proton decay experiments, one is able to constrain some of the key parameters in this setup. The breaking of $SO(10)$ via $SU(5) \times U(1)_χ$ also yields superheavy metastable strings with no unconfined flux associated with the monopoles. Finally, we consider $SO(10)$ breaking via $SU(4)_c \times SU(2)_L \times U(1)_R$, $SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$ and flipped $SU(5)$ that yield metastable strings where the associated monopoles carry unconfined flux after the electroweak breaking.

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arXiv2025

C-parity, magnetic monopoles and higher frequency gravitational waves

We consider the spontaneous breaking of $SO(10)$ grand unified symmetry to the left-right symmetric model $SU(3)_c \times SU(3)_L \times SU(2)_R \times U(1)_{B-L}$ with C-parity also unbroken [$C$ converts $Q\to -Q$, where $Q$ is the electric charge operator in $SO(10)$.] This breaking produces the topologically stable GUT monopole as well as a GUT scale C-string. The subsequent breaking at an intermediate scale of C-parity produces domain walls bounded by C-strings, found by Kibble, Lazarides and Shafi. A limited number of inflationary $e$-foldings experienced during these breakings can yield an observable number density of primordial GUT monopoles. The C-strings also experience this inflationary phase, and the subsequent string-wall network decays through the emission of gravitational waves. We estimate the gravitational wave spectrum from these composite structures over a range of values of the domain wall tension $σ$. Depending on $σ$ the spectrum displays a peak in the higher frequency range between $10^2$ to $10^5$ Hz.

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arXiv2024

Induced gravitational waves, metastable cosmic strings and primordial black holes in GUTs

We explore the cosmological and astrophysical implications of a realistic hybrid inflation model based on flipped $SU(5)$. The model contains superheavy metastable cosmic strings arising from a waterfall field that encounters a limited number of $e$-foldings during the inflationary phase. In addition to the gravitational waves emitted by the metastable strings, there also appear scalar induced gravitational waves linked to the waterfall phase transition. These two independent sources of gravitational waves can yield a combined spectrum that is compatible with the recent PTA measurements, and with additional features that can be probed in future experiments. We also show the appearance of primordial black holes with mass on the order of $10^{29}$ g from the waterfall phase transition, and with an abundance that can be tested in the gravitational lensing experiments.

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arXiv2024

Kinetic Mixing, Proton Decay and Gravitational Waves in SO(10)

We present an $SO(10)$ model in which a dimension five operator induces kinetic mixing at the GUT scale between the abelian subgroups $U(1)_{B-L}$ and $U(1)_R$. We discuss in this framework gauge coupling unification and proton decay, as well as the appearance of superheavy quasistable strings with $Gμ\sim 10^{-8} - 10^{-5}$, where $μ$ denotes the dimensionless string tension parameter. We use Bayesian analysis to show that for $Gμ$ values $\sim 4 \times 10^{-7} - 10^{-5}$, the gravitational wave spectrum emitted from the quasistable strings is in good agreement with the recent pulsar timing array data. Corresponding to $G μ$ values $\sim 10^{-8} - 2 \times 10^{-7}$, proton decay is expected to occur at a rate accessible in the Hyper-Kamiokande experiment. Finally, we present the gravitational wave spectrum emitted by effectively stable strings with $Gμ\approx 10^{-8}$ that have experienced a certain amount of inflation. This can be tested with future detectors in the $μ$Hz frequency range.

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arXiv2024

Topological structures, dark matter and gravitational waves in $E_6$

We discuss the appearance of topological structures from the spontaneous breaking of $E_6$ to the Standard Model via its maximal subgroup $SO(10) \times U(1)_ψ$. They include dumbbells, metastable strings, as well as domain walls bounded by necklaces. We provide a novel scenario for producing metastable strings based on the symmetry breaking $U(1)_ψ\longrightarrow Z_8 \longrightarrow Z_4$. The metastable string arises from the merger of $Z_8$ strings that bound a domain wall. An unbroken gauge $Z_2$ symmetry from $SO(10)$ breaking yields viable stable dark matter candidates as well as topologically stable strings. We discuss the gravitational wave emission from two varieties of cosmic strings, namely the superheavy metastable ones and the intermediate scale topologically stable cosmic strings.

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arXiv2024

Quantum tunneling in the early universe: Stable magnetic monopoles from metastable cosmic strings

We present a novel mechanism for producing topologically stable monopoles (TSMs) from the quantum mechanical decay of metastable cosmic strings in the early universe. In an $SO(10)$ model this mechanism yields TSMs that carry two units ($4π/e$) of Dirac magnetic charge as well as some color magnetic charge which is screened. For a dimensionless string tension parameter $Gμ\approx 10^{-9} - 10^{-5}$, the monopoles are superheavy with masses of order $10^{15} - 10^{17}$ GeV. Monopoles with masses of order $10^8 - 10^{14}$ GeV arise from metastable strings for $Gμ$ values from $\sim 10^{-22}$ to $10^{-10}$. We identify the parameter space for producing these monopoles at an observable level with detectors such as IceCube and KM3NeT. For lower $Gμ$ values the ultra-relativistic monopoles should be detectable at Pierre Auger and ANITA. The stochastic gravitational wave emission arises from metastable strings with $Gμ\sim 10^{-9}-10^{-5}$ and should be accessible at HLVK and future detectors including the Einstein Telescope and Cosmic Explorer. An $E_6$ extension based on this framework would yield TSMs from the quantum mechanical decay of metastable strings that carry three units ($6π/e$) of Dirac magnetic charge.

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arXiv2024

Inflation, superheavy metastable strings and gravitational waves in non-supersymmetric flipped SU(5)

Motivated by the NANOGrav 15 year data and other recent investigations of stochastic gravitational background radiation based on pulsar timing arrays, we show how superheavy strings survive inflation but the slightly heavier monopoles do not in a non-supersymmetric hybrid inflation model based on flipped $SU(5)$. With the dimensionless string tension parameter $G μ\sim 10^{-6}$, the gravitational wave spectrum emitted by the strings, which are metastable due to breaking caused by monopole-antimonopole quantum mechanical tunneling, is compatible with the latest NANOGrav measurement as well as the advanced LIGO-VIRGO third run data. The string network undergoes about 30 $e$-foldings of inflation which suppresses the spectrum in the LIGO-VIRGO frequency range. With the symmetry breaking chain $SU(5) \times U(1)_X \to SU(3)_c \times SU(2)_L\times U(1)_Z \times U(1)_X \to SU(3)_c \times SU(2)_L \times U(1)_ Y$, the estimated proton lifetime is of order $10^{36}-10^{37}$ yrs.

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arXiv2023

Supersymmetric $U(1)_{B-L}$ flat direction and NANOGrav 15 year data

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.

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arXiv2023

Superheavy quasi-stable strings and walls bounded by strings in the light of NANOGrav 15 year data

Composite topological structures such as superheavy "quasi-stable strings" (QSS) and "walls bounded by strings" (WBS) arise in realistic extensions of the Standard Model of high energy physics. We show that the gravitational radiation emitted in the early universe by these two unstable structures with a dimensionless string tension $Gμ\approx 10^{-6}$ is consistent with the NANOGrav evidence of low frequency gravitational background as well as the recent LIGO-VIRGO constraints, provided the superheavy strings and monopoles experience a certain amount of inflation. For the case of walls bounded by strings, the domain walls arise from the spontaneous breaking of a remnant discrete gauge symmetry around the electroweak scale. The quasi-stable strings, on the other hand, arise from a two step breaking of a local gauge symmetry. The monopoles appear from the first breaking and get connected to strings that arise from the second breaking. Both composite structures decay by emitting gravitational waves over a wide frequency range. The Bayes factors for QSS and WBS relative to the inspiraling supermassive black hole binaries are estimated to be about 60 and 30 respectively, which are comparable with that of metastable strings and cosmic superstrings.

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arXiv2023

Gravitational waves from walls bounded by strings in $SO(10)$ model of pseudo-Goldstone dark matter

We explore the gravitational wave spectrum generated by string-wall structures in an $SO(10)$ ($Spin(10)$) based scenario of pseudo-Goldstone boson dark matter (pGDM) particle. This dark matter candidate is a linear combination of the Standard Model (SM) singlets present in the 126 and 16 dimensional Higgs fields. The Higgs $126$-plet vacuum expectation value (VEV) $\left<126_H\right>$ leaves unbroken the $\mathbb{Z}_2$ subgroup of $\mathbb{Z}_4$, the center of $SO(10)$. Among other things, this yields topologically stable cosmic strings with a string tension $μ\sim \left<126_H\right>^2$. The subsequent (spontaneous) breaking of $\mathbb{Z}_2$ at a significantly lower scale by the $16$-plet VEV $\left<16_H\right>$ leads to the appearance of domain walls bounded by the strings produced earlier. We display the gravitational wave spectrum for $G μ$ values varying between $10^{-15}$ and $10^{-9}$ ($\left<126_H\right>\sim 10^{11}$ - $10^{14}$ GeV), and $\left<16_H\right>\sim 0.1$ - $10^2$ TeV range ($G$ denotes Newton's constant.) These predictions can be tested, as we show, by a variety of (proposed) experiments including LISA, ET, CE and others.

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arXiv2023

Monopoles, Strings and Gravitational Waves in Non-minimal Inflation

We discuss how in $SO(10)$ grand unification an observable number density of topologically stable intermediate mass ( $\sim 10^{14}$ GeV) monopoles survive inflation driven by a Coleman-Weinberg potential and non-minimal coupling of the inflaton field to gravity. The scalar spectral index $n_s$ is in excellent agreement with the current observations, and the tensor to scalar ratio $r\gtrsim 0.003$. The model also predicts the presence of intermediate scale topologically stable cosmic strings, and their gravitational wave spectrum reflects the amount of cosmic inflation experienced by the associated symmetry breaking. The discovery of these primordial monopoles and the stochastic gravitational wave background from the strings would provide important new insights regarding the symmetry breaking patterns in the early universe.

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arXiv2022

A Predictive $SO(10)$ Model

We discuss some testable predictions of a non-supersymmetric $SO(10)$ model supplemented by a Peccei-Quinn symmetry. We utilize a symmetry breaking pattern of $SO(10)$ that yields unification of the Standard Model gauge couplings, with the unification scale also linked to inflation driven by an $SO(10)$ singlet scalar field with a Coleman-Weinberg potential. Proton decay mediated by the superheavy gauge bosons may be observable at the proposed Hyper-Kamiokande experiment. Due to an unbroken $Z_2$ gauge symmetry from $SO(10)$, the model predicts the presence of a stable intermediate mass fermion which, together with the axion, provides the desired relic abundance of dark matter. The model also predicts the presence of intermediate scale topologically stable monopoles and strings that survive inflation. The monopoles may be present in the Universe at an observable level. We estimate the stochastic gravitational wave background emitted by the strings and show that it should be testable in a number of planned and proposed space and land based experiments. Finally, we show how the observed baryon asymmetry in the Universe is realized via non-thermal leptogenesis.

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arXiv2022

Heavier $W$ boson, dark matter and gravitational waves from strings in an $SO(10)$ axion model

Inspired by the recent determination of the $W$-boson mass by the CDF collaboration, we revisit an $SO(10)$ axion model in which a scalar $SU(2)_L$ triplet field with zero hypercharge is known to acquire a non-zero VEV through its mixing with the Standard Model Higgs doublet. The triplet VEV provides a sizable contribution to the $W$ mass, which helps in significantly lowering the $7σ$ discrepancy between the Standard Model prediction and the higher CDF value for $m_W$. We show that the relatively light triplet mass ($\sim (1-50)$ TeV) is compatible with gauge coupling unification and observable proton decay. An unbroken $Z_2$ gauge symmetry, coupled with the presence of two fermionic $10$-plets required to resolve the axion domain wall problem, means that both axions and a stable intermediate mass ($\sim 10^9-10^{10}$ GeV) fermion are plausible dark matter candidates. We also display the gravitational wave spectrum from the intermediate scale topologically stable cosmic strings predicted by the model.

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