The spontaneous breaking of SO(10) grand unified symmetry to SU(3) × SU(2) × U(1) × U(1) yields the GUT monopole as well as a comparably heavy U(1) monopole which also carries U(1) flux. A metastable string scenario in this case requires that the U(1) symmetry is necessarily broken close to the GUT scale, thus resulting in a dimensionless string tension $\textit{Gμ}$ ~ 10 . We show that the $\textit{χ}$ monopole does not carry any unconfined flux following the electroweak symmetry breaking. Coupled with $\textit{Gμ}$ ~ 10 , 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) × U(1) also yields superheavy metastable strings with no unconfined flux associated with the monopoles. Finally, we consider SO(10) breaking via SU(4) × SU(2) × U(1) , SU(3) × SU(2) × SU(2) × U(1) and flipped SU(5) that yield metastable strings where the associated monopoles carry unconfined flux after the electroweak breaking.

South Korea

Rinku Maji

United States

Qaisar Shafi

Superheavy metastable strings in SO(10)

We consider the spontaneous breaking of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></math> grand unified symmetry to the left-right symmetric model <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><msub><mo stretchy="false">)</mo><mi>c</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><msub><mo stretchy="false">)</mo><mi>L</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>R</mi></msub><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math> with C-parity also unbroken [<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi></math> converts <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mo stretchy="false">→</mo><mo>−</mo><mi>Q</mi></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi></math> is the electric charge operator in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo></math>.] This breaking produces the topologically stable grand unified theory (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 et al. A limited number of inflationary <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi></math>-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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math>. Depending on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>σ</mi></math> the spectrum displays a peak in the higher frequency range between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mn>2</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mn>10</mn><mn>5</mn></msup><mtext> </mtext><mtext> </mtext><mi>Hz</mi></mrow></math>.

C-parity, magnetic monopoles, and higher frequency gravitational waves

We develop a scenario based on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math>-hybrid inflation within the framework of a left-right symmetric model defined by the gauge symmetry group <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>G</mi><mn>3221</mn></msub><mo>=</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><msub><mo stretchy="false">)</mo><mi>c</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>L</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>R</mi></msub><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math>. This model features a two-stage symmetry breaking to the Standard Model, with inflation occurring between the two stages, resulting in the dilution of primordial monopoles produced during the symmetry breaking of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>R</mi></msub></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>R</mi></msub></math>. The second symmetry breaking gives rise to a network of metastable cosmic strings, which produces gravitational waves that can be observed by current and future experiments. A crucial aspect of this model is the inclusion of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi></math>-symmetry breaking terms in the superpotential, which helps explain the origin of the first symmetry breaking scale and ensures experimentally viable inflation with a minimal (canonical) Kähler potential. We show that the model successfully implements consistent inflation, leptogenesis, metastable cosmic strings, and gravitino dark matter, all in agreement with the observational data and constraints on reheating temperature from leptogenesis and gravitino overproduction bounds. We explore the potential embedding of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>G</mi><mn>3221</mn></msub></math> within the gauge symmetry <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>G</mi><mn>422</mn></msub><mo>=</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>4</mn><msub><mo stretchy="false">)</mo><mi>c</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>L</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mi>R</mi></msub></math> and provide a brief discussion on the proton decay predictions, which can be tested by the upcoming experiments.

Pakistan

Muhammad Nadeem Ahmad

Maria Mehmood

Saudi Arabia

Mansoor Ur Rehman

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>μ</mi></math>-hybrid inflation and metastable cosmic strings in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><msub><mrow><mo stretchy="false">)</mo></mrow><mi>c</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi>L</mi></mrow></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi>R</mi></mrow></msub><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></mrow></math>

We present a class of supersymmetric (SUSY) GUT models that can explain the apparent discrepancy between the SM predictions and experimental values of muon <math><mrow><mi>g</mi><mo>−</mo><mn>2</mn></mrow></math> while providing testable signals for lepton flavor violation in charged lepton decays. Moreover, these models predict LSP neutralino abundance that is compatible with the Planck dark matter bounds. We find that scenarios in the framework of <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>4</mn><msub><mo>)</mo><mi>c</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mi>L</mi></msub><mo>×</mo><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mi>R</mi></msub></math> unification, with additional symmetries to explain fermion masses and neutrino oscillations, provide interesting benchmarks for the search of SUSY by correlating a possible manifestation of it in dark matter, rare lepton decays, and LHC signals.

Spain

Mario E. Gómez

Greece

Smaragda Lola

Türkiye

Cem Salih Ün

Muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> and lepton flavor violation in supersymmetric GUTs

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 ~ 10−8 – 10−5, where μ denotes the dimensionless string tension parameter. We use Bayesian analysis to show that for Gμ values ~ 4 × 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 Gμ values ~ 10−8 − 2 × 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 ≈ 10−8 that have experienced a certain amount of inflation. This can be tested with future detectors in the μHz frequency range.

Kinetic mixing, proton decay and gravitational waves in SO(10)

We discuss the appearance of topological structures from the spontaneous breaking of E 6 to the Standard Model via its maximal subgroup SO(10) × 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  ⟶ ℤ 8 ⟶ 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.

Amit Tiwari

Topological structures, dark matter and gravitational waves in E6

Renormalization group analysis with the present measurements of the top quark mass <math><msub><mi>m</mi><mi>t</mi></msub><mo>=</mo><mn>172.69</mn><mo>±</mo><mn>0.30</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> [1] indicates that the Standard Model (SM) Higgs potential becomes unstable at energy scales <math><mo>∼</mo><msup><mn>10</mn><mn>10</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. This may be interpreted as hinting at new particles at high energy. The minimal extension of the SM that can avoid this instability while leaving the SM Higgs as the sole scalar particle of the theory is obtained by adding suitable fermions to the SM. These fermions are good dark matter candidates and the model is known as the minimal dark matter model. We revisit the inflationary scenario based on the minimal dark matter model, taking into account updated parameter constraints and recent understanding of reheating dynamics. We explore the model with different values of the right-handed neutrino mass and find that the cosmological prediction is insensitive to such details. We obtained a spectral index of the cosmic microwave background <math><msub><mi>n</mi><mi>s</mi></msub><mo>=</mo><mn>0.9672</mn></math> and a tensor-to-scalar ratio <math><mi>r</mi><mo>=</mo><mn>0.0031</mn></math> as a robust prediction of this scenario.

Shinsuke Kawai

Nobuchika Okada

Standard model Higgs inflation supplemented by minimal dark matter

We discuss <math><msub><mrow><mi>E</mi></mrow><mrow><mn>6</mn></mrow></msub></math> based extensions of the Standard Model (SM) containing two varieties of superheavy metastable cosmic strings (CSs) that respectively have neutral and electrically charged current carriers. We employ an extended version of the velocity-dependent one-scale (VOS) model, recently discussed by some authors, to estimate the gravitational wave (GW) spectrum emitted by metastable strings with a dimensionless string tension <math><mi>G</mi><mi>μ</mi><mo>≈</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></math> that carry a right-handed neutrino (RHN) current. We find that with a low to moderate amount of current, the spectrum is compatible with the LIGO O3 run and also consistent at the 1σ level with the recent PTA signals.

Adeela Afzal

Gravitational wave emission from metastable current-carrying strings in

Composite topological structures such as superheavy “quasistable 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 <math><mrow><mi>G</mi><mi>μ</mi><mo>≈</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></math> 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 quasistable 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.

George Lazarides

Superheavy quasistable strings and walls bounded by strings in the light of NANOGrav 15 year data

We investigate the inflationary cosmology involving an <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> GUT (grand unified theory) singlet scalar with nonminimal coupling to the Ricci scalar. In this scenario the scale of grand unification is set by the inflaton vacuum expectation value when the inflaton rolls down its potential towards its minimum <math><mi>v</mi></math>, thereby relating inflationary dynamics to GUT symmetry breaking with a prediction of <math><mi>r</mi><mo>≃</mo><mn>0.025</mn></math> for the tensor-to-scalar ratio to be tested by the next generation of CMB experiments. We show in this inflationary framework involving an inflection point how a suitable choice of parameters in <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> leads to a bump in the scalar power spectrum with the production of primordial blackholes (PBH) of masses <math><msup><mn>10</mn><mn>17</mn></msup><mi>–</mi><msup><mn>10</mn><mn>18</mn></msup><mtext> </mtext><mtext> </mtext><mi>g</mi></math> (<math><msup><mn>10</mn><mrow><mo>−</mo><mn>16</mn></mrow></msup><mi>–</mi><msup><mn>10</mn><mrow><mo>−</mo><mn>15</mn></mrow></msup><msub><mi>M</mi><mo>⊙</mo></msub></math>). We derive the constraints on the self-quartic and mixed-quartic couplings of the inflaton in <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> that are consistent with the inflationary analysis. Moreover, we also show that this scenario leads to large amplitude induced second-order tensor perturbations propagating as gravitational waves (GWs) with an amplitude <math><msub><mi>Ω</mi><mi>GW</mi></msub><msup><mi>h</mi><mn>2</mn></msup><mo>∼</mo><mn>5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>10</mn></mrow></msup><mi>–</mi><msup><mn>10</mn><mrow><mo>−</mo><mn>8</mn></mrow></msup></math> and peak frequency <math><mrow><msub><mrow><mi>f</mi></mrow><mrow><mi>peak</mi></mrow></msub><mo>∼</mo><mo>(</mo><mn>0.1</mn><mi>–</mi><mn>300</mn><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>Hz</mi></mrow></math>, which can be detected in the next-generation GW observatories like LISA, BBO, ET, etc. Thus, we unify the <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> framework with PBH via inflection-point inflation showing how the upcoming measurements of PBH and GW will enable us to probe the scale of <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>5</mn><mo>)</mo></math> symmetry breaking, and thereby complementing the laboratory-based experiments. We also discuss scenarios involving the Pati-Salam and trinification gauge groups and its impact on quartic and mixed-quartic couplings that may lead to PBH and detectable GW signals.